Split (1)

train · 1.93M rows

text stringlengths 0 190k
quant-ph9911091.txt \|@word represent:1 extrapolated:1 limited:1 magnetic:6 reversibility:1 existing:1 circuitry:4 computation:5 disintegration:1 semiconductor:3 charge:1 device:1 present:2 giga:2 dramatically:1 sound:1 string:1 sitting:1 very:4 frequencies:3 continues:1 inhibit:1 wave:1 electron:13 manipulated:1 every:1 mixing:2 emphasized:1 electronics:1 encounter:1 entire:1 level:2 did:1 hawaii:1 large:3 small:1 eigenvalues:1 upper:1 smaller:3 ten:2 trend:1 past:1 fold:1 rate:3 design:2 estimated:1 machines:4 linear:1 unavailable:1 clock:18 section:1 interactions:2 above:7 flowing:2 new:6 increasing:3 ever:1 full:1 evanescent:2 whose:1 component:1 equals:8 answers:1 desired:1 explore:1 mev:2 operating:4 twentieth:1 separation:1 represented:1 november:1 strong:1 equations:1 simulating:1 thirty:1 study:1 burdensome:1 throughput:2 domains:2 devices:1 changes:1 involves:1 uniquely:1 useful:3 addresses:1 requiring:1 semiconductors:2 logical:3 highly:1 volt:3 decrease:1 implausible:1 apply:1 total:1 tools:1 unit:1 use:3 manufacturing:1 takes:1 would:5 distinct:1 nine:1 predictions:1 next:1 few:1 therefore:3 memory:1 taken:1 markets:1 capital:1 today:6 more:4 sort:1 clever:1 conclusions:1 localization:1 limitation:1 aware:1 controlling:2 particular:1 known:6 hole:1 producing:1 must:9 states:10 quantized:3 work:3 values:1 era:1 concepts:1 making:2 example:10 control:1 figure:1 process:6 relativistic:18 inaccessible:1 purposes:1 high:5 minimum:5 performed:1 want:1 sense:2 hydrogen:1 evidently:1 information:8 rays:3 requirements:2 provide:2 travel:1 means:1 range:3 dismissed:1 machine:7 far:1 exponentially:1 simplicity:1 may:5 after:3 applications:1 produce:1 tier:1 end:1 choice:1 data:2 parallel:1 accelerates:1 light:3 lines:1 ghz:1 mark:1 cannot:3 so:3 ultimate:6 fundamental:5 discussion:2 operate:1 order:6 typical:1 operations:1 six:2 produces:1 developed:1 thresholds:1 mainly:1 soon:1 years:5 radar:1 paper:1 through:5 keyboard:1 mentioned:1 existence:1 kinetic:1 its:2 hundredth:1 fit:1 how:2 energies:1 interesting:1 boson:1 better:2 estimating:1 production:2 systems:2 might:4 eventually:1 non:1 greater:1 combination:1 practice:1 femto:1 energizing:1 effects:8 they:3 nov:1 now:3 discuss:1 represents:3 university:1 identified:1 desirable:1 possibilities:1 micro:1 magnitude:4 each:7 repeating:1 quarter:1 characterized:1 individually:1 square:4 series:1 energy:30 principles:1 frequency:22 measurement:2 quantum:22 our:1 operation:1 ev:1 eq:2 event:1 out:4 ultimately:1 reducing:1 opened:1 furthermore:1 since:1 research:2 increase:8 collisions:2 reader:1 surprise:1 get:1 earlier:1 theory:5 barrier:6 associate:1 million:2 given:3 possibility:2 quite:2 fourteen:1 formation:1 put:1 estimate:2 pairs:2 interaction:1 could:2 computers:7 times:4 turn:1 place:1 due:1 circuit:14 quadratically:1 facilitate:1 think:1 speeds:2 major:1 number:7 infinite:1 specifically:1 another:3 carry:1 electronic:4 owning:1 engineer:1 differ:1 long:1 similarly:1 introduction:1 twenty:1 tata:1 least:2 cycle:5 bits:4 final:1 store:2 low:1 collapse:1 relationship:2 environmental:1 part:3 honolulu:1 wasted:1 probably:1 operates:1 representing:1 than:9 distance:1 hundred:2 anticipate:1 second:10 limiting:1 annihilation:1 matter:2 future:5 were:1 gives:1 distinguished:1 result:1 seth:1 modern:1 mind:1 any:4 forced:2 strength:3 aside:1 mechanism:2 note:4 equipment:5 internal:3 build:1 performance:2 closer:1 begin:2 added:1 electric:1 shall:2 who:2 reach:1 most:1 involving:1 eight:1 amongst:1 significant:2 remarks:1 measured:2 appear:1 exa:1 up:2 average:1 morse:1 flow:1 unreasonable:1 electrons:9 principle:3 mechanical:1 physics:6 fact:2 applied:1 incorporate:1 spaced:1 show:1 supported:1 relation:9 lloyd:2 threshold:1 decade:1 pause:1 based:2 just:4 parameters:1 proportion:1 enough:2 should:1 technologically:1 only:6 astronomical:1 do:1 over:2 his:2 goes:1 localizing:1 meanwhile:1 designing:1 ones:1 fastest:5 progress:4 during:2 chips:1 processes:3 fields:1 arxiv:1 yield:1 circuits:11 common:1 release:1 implication:1 require:1 atomic:1 respond:1 set:2 bounds:1 relative:1 computer:18 miniaturization:1 accelerators:1 entailing:1 pakvasa:1 said:1 ways:1 accomplished:1 illusory:1 eigenstates:2 importance:1 state:2 various:1 limit:5 approach:1 across:1 wide:1 available:5 multiplied:1 recently:1 august:1 positron:1 qubits:1 however:4 job:1 rapid:1 distinguish:4 watts:1 come:1 suggested:1 both:3 essentially:1 toward:1 last:1 limits:2 many:1 uncertainty:11 demanded:1 etc:1 became:1 logic:4 qubit:5 comes:1 reasons:1 seems:1 recycling:1 corresponds:2 simply:2 moreover:1 considering:1 described:1 three:1 been:4 quickly:1 willing:1 interest:1 ph:2 choose:1 wants:1 arises:1 corresponding:1 restrictions:1 thousand:1 gap:1 dramatic:1 angles:1 demand:1 spin:9 those:1 case:1 multi:1 look:1 exponential:1 indefinitely:1 decades:4 single:7 will:22 pace:2 while:1 suppose:6 applies:2 engineers:6 compton:1 orientation:1 century:3 almost:1 thus:4 them:3 encountered:2 positrons:1 technology:6 grant:1 perform:1 suggest:1 make:1 radiation:4 cross:1 same:5 orders:2 complex:1 quant:2 units:1 finite:1 higher:5 development:7 used:8 upon:3 effect:2 hand:2 calculators:1 v2:1 levels:4 uses:1 entanglement:1 changing:1 passing:2 recent:3 shortly:1 well:4 roughly:1 solids:2 materials:3 machinery:1 components:1 entry:1 model:1 newest:1 proposed:2 less:2 generally:2 extrapolation:1 influx:1 shape:1 stored:2 voltage:3 kilo:1 speed:13 yet:3 previous:1 unique:1 application:1 informal:1 character:1 day:2 simple:2 causing:1 input:1 take:3 real:1 aspects:1 around:1 code:1 read:1 unlimited:1 possible:2 period:2 early:2 increases:4 simmons:1 know:1 desk:3 using:6 bit:9 designers:1 necessary:1 like:5 particle:4 sizes:1 follows:1 manual:1 specific:1 communications:1 continue:2 mhz:1 become:7 crudest:1 twelve:1 exceed:1 because:1 often:1 deal:3 plausible:1 some:5 back:1 trends:1 tera:1 enormous:1 users:1 electromagnetic:1 per:3 does:1 assuming:1 particles:1 limitations:6 core:1 power:18 dictates:2 continuing:1 exciting:1 properties:5 stage:3 cranked:1 about:8 consumption:1 entailed:2 completing:1 discussed:3 practical:1 carries:1 commit:1 replacement:1 gamma:3 manoa:1 communication:3 into:2 within:1 year:1 negative:1 nothing:1 references:1 determine:2 einstein:1 elementary:4 proportional:2 imposed:1 your:2 fast:2 classical:3 there:9 question:1 hertz:22 start:1 quadratic:1 physicists:5 way:2 forward:1 was:3 naturally:1 manufacture:1 speculate:1 complete:1 form:1 but:3 sophisticated:1 volume:1 heat:1 hi:1 atom:1 sustained:1 line:1 made:3 annihilate:1 places:1 whether:3 maximum:3 us:8 below:2 complications:1 uh:1 problem:2 piece:1 similar:1 mechanics:4 associated:2 computing:7 abstract:1 describe:1 surpassing:1 general:2 multiparticle:1 engineering:5 wavelength:1 lifetime:1 proceeds:1 physical:1 functions:2 improving:1 no:5 individual:2 when:2 elemental:1 field:8 other:1 digital:1 department:2 nice:1 elements:5 superposition:3 problems:1 important:4 additionally:1 included:1 astronomy:1 billion:1 implies:4 faster:5 assume:1 typically:1 required:4 together:3 equivalently:1 impossibility:1 inhibited:1 dot:1 time:11 push:1 requires:1 cpu:1 once:1

quant-ph9911092.txt \|@word represent:1 externally:1 consider:3 rev:13 results:2 leads:1 scalar:3 computation:2 follow:1 expressions:1 rigidity:1 preserves:1 concerned:2 deterministic:1 tr:1 environment:1 finally:3 those:2 γm:1 stable:1 alternating:1 applied:1 fax:1 rational:1 orthogonal:2 very:3 rise:1 lyapunov:3 electron:1 condition:3 common:1 entire:1 swapping:3 immediately:1 hamiltonian:3 integrated:1 large:1 discrete:1 vector:2 small:8 shows:6 optics:1 mahler:3 force:3 periodicity:1 deutsch:1 direct:2 mantica:1 second:2 dordrecht:2 concludes:1 dynamics:13 odd:4 remarkably:1 machines:1 dρρ:5 even:6 established:1 appear:1 rate:1 sum:1 bergman:1 networks:6 reminiscent:1 version:1 above:1 new:2 3a:2 increasing:2 ˆn:1 3d:2 satisfy:1 edited:2 chaotic:25 wavefunctions:2 respectively:6 spacing:1 here:8 understanding:1 behaviour:4 represented:1 along:1 observing:1 ensembles:1 solid:1 great:1 study:2 vectors:2 spheres:1 periodic:13 products:1 usually:1 studies:1 composed:1 via:1 useful:3 figure:9 propagations:1 total:7 superpositions:1 would:4 waintal:2 remains:3 contains:1 negative:1 properties:1 few:2 ψn:12 taken:1 generators:1 nential:1 type:2 until:1 more:1 sort:1 th:1 operators:3 under:3 odinger:1 phone:1 correspondingly:1 loss:2 cases:3 must:2 mα1:1 springer:2 erratum:1 ed:1 nonn:1 equation:7 oscillator:2 remain:2 itself:2 concepts:1 following:5 example:2 numbers:1 control:9 indicated:1 give:1 echon:1 table:2 states:7 indicates:2 riedel:1 fibonacci:13 occur:1 information:1 respective:3 soc:4 verify:1 acts:1 feature:1 orthogonality:1 machine:2 far:1 pair:1 pure:6 gate:1 parameter:6 sin:14 map:2 product:7 description:2 may:2 turing:31 orbits:8 applications:1 tries:1 plane:3 distances:1 physik:3 unentangled:1 realized:1 dynamical:2 lines:1 yielding:1 su:1 ubner:1 complexity:1 so:5 specifying:1 correlation:1 acknowledges:1 order:1 typical:1 operations:1 holds:1 noteworthy:1 indeed:2 perturbed:3 years:1 course:1 through:1 its:4 features:1 derive:1 rapidly:1 thank:1 ln:1 interesting:2 temporal:1 exhibits:1 fruitful:1 fib:4 systems:3 quant:3 might:3 eur:2 theo:1 eventually:1 non:6 they:1 nov:1 now:3 day:1 nor:1 represents:1 lies:1 undertaking:1 level:2 theory:2 trap:2 each:1 instability:3 universit:1 characterized:2 referred:1 domain:1 another:1 simplicity:1 mesoscopic:2 manifests:1 measure:2 quantum:53 our:4 operation:2 transitions:1 special:1 shown:3 network:10 driving:4 space:6 restricted:1 since:2 squared:3 chaos:22 denotes:1 attracted:1 acting:1 performs:1 suffices:1 occurs:1 predicted:1 linear:1 localization:1 gardiner:1 free:2 standard:1 completely:1 york:2 asi:1 generate:1 additional:1 benioff:1 english:1 transition:1 iterative:1 m22:3 quantummechanical:1 length:1 period:4 exponentially:1 consequence:1 βm:1 onto:1 first:1 origin:1 major:1 there:5 demonstrating:1 striking:1 aperiodic:1 powerful:1 number:5 thereof:1 system:2 restrict:2 utilized:1 directly:2 open:1 tively:1 kouwenhoven:1 given:1 perturbation:6 rempe:1 revival:2 similarly:1 introduction:1 nondissipative:1 theoretische:1 relations:2 their:1 too:1 calculations:1 realization:1 scheme:1 braun:1 α2m:2 larger:2 than:1 distance:6 kind:1 princeton:2 namely:2 lim:4 classes:1 expo:1 contrasted:2 exhibit:1 explicit:1 spectrum:1 needs:1 constrained:2 any:11 genuine:1 smallest:1 mapping:1 studying:1 latter:1 able:1 note:2 entirety:1 potential:1 destroy:1 haake:1 qtms:1 spectral:2 multiple:1 scripta:1 though:2 enter:1 most:1 regular:4 germany:1 revivals:1 utilize:2 acknowledgements:1 extremely:1 class:1 forever:1 especially:2 considered:2 calculated:1 later:1 physica:2 feynman:1 points:1 electrons:1 principle:3 urr:1 mechanical:5 typically:1 fact:1 signatures:1 show:2 random:1 implying:2 relation:1 analogue:2 trivial:1 find:2 kadanoff:1 based:6 just:1 parameters:3 enough:1 should:4 only:2 explicitly:2 tape:14 reducibility:1 originally:1 circle:1 hamiltonians:1 local:8 means:4 zurek:1 de:1 nanostructures:1 cannot:1 during:1 interpreted:1 evolution:8 αm:37 arxiv:1 summary:1 qc:3 architecture:3 analytical:1 london:4 fixed:2 pichard:2 set:1 sensitivity:10 evolving:1 maximum:1 see:6 computer:4 result:3 discussions:1 close:1 qtm:11 satisfying:1 exponent:3 2πp:3 nature:1 liouville:1 eigenstates:1 naturwissenschaften:1 qubits:2 state:27 future:1 various:1 between:8 progress:1 neither:1 αj:3 conditions:3 email:1 c2m:26 terms:1 2m:26 initially:2 attention:1 weak:1 however:5 ascribed:1 ultimate:1 implementing:1 jk:1 distinguish:1 2αm:2 received:1 cos:80 realizable:1 zoller:1 according:2 display:1 stuttgart:3 berry:1 uni:1 qubit:1 expression:3 finds:1 experimental:2 otherwise:1 comment:1 cn:3 character:1 harmonic:1 2nd:1 dimensional:2 sequences:3 respect:1 considering:1 described:1 transformations:2 addition:1 trajectory:2 create:1 due:3 been:8 int:1 much:1 interest:1 basic:1 expected:1 ph:3 pi:1 fig:1 dots:1 contribute:1 controlled:7 both:6 wheeler:1 subspace:3 essentially:1 fortschr:1 cor:1 lives:1 external:3 angles:1 general:1 spin:5 present:2 case:3 exponential:10 tang:1 expanded:1 conserved:1 will:5 while:1 jagannathan:1 applies:1 wild:1 irrespective:1 property:2 correspondence:1 unitary:7 almost:2 metric:3 cerdeira:1 thus:3 conditioned:1 characterize:2 obstacle:1 primitives:2 technology:1 different:4 confirms:2 propagation:2 generic:1 recursion:1 realizing:1 cumulative:2 same:4 poincar:1 potentially:1 resulting:2 finite:2 otte:1 grows:2 difficult:1 independent:1 gnutzmann:1 singapore:1 numerical:2 effect:1 hand:2 driven:5 ion:2 kim:2 potentials:1 entanglement:9 angle:4 uˆ:6 recent:1 task:1 schr:1 kicked:1 weinmann:1 well:2 analysis:1 bohr:1 thought:1 patterns:2 without:1 solve:1 easily:3 dimension:2 usual:1 gates:2 proposed:2 less:1 being:1 obtain:4 schack:4 identify:1 using:5 λk:6 λj:2 λi:2 yet:1 blow:1 cut:1 kluwer:2 density:1 alternate:2 seems:1 source:1 nato:1 lett:11 versa:1 input:6 transformation:1 scientific:1 identical:1 boxed:1 unter:1 read:1 showing:1 measurement:1 spanned:1 cf:4 world:2 mod:18 semiclassical:2 like:7 follows:2 fingerprints:1 chaotically:3 harmonically:1 specific:1 δm:3 steps:1 alternatively:2 evolutions:1 output:2 reduced:3 spins:4 right:1 kohmoto:1 classical:8 sequence:7 some:4 growth:1 specified:1 oscillations:1 ourselves:2 transport:2 separately:1 scale:3 lead:1 broad:1 per:7 umel:1 does:2 decomposition:1 tends:1 whereas:2 unstable:2 proc:4 demonstrated:1 nmr:1 obey:2 bl:1 bm:6 processing:1 m11:5 likewise:1 e345:1 step:11 found:3 hilbert:2 o:4 practical:1 convenient:1 repulsion:1 mixed:1 connected:1 constraints:1 slightly:1 bloch:7 primitive:2 computational:1 real:1 into:1 within:1 rotations:1 phase:2 because:1 references:2 operator:2 methods:1 institut:1 deal:1 vˆ:3 classically:1 support:1 initial:16 long:1 brun:1 way:1 series:1 function:2 head:26 form:1 but:3 ford:1 reminds:1 pfaffenwaldring:1 delta:1 line:4 bures:2 longer:1 absent:1 responding:1 rotation:2 instructive:1 circuits:1 up:4 us:3 ur:1 discretized:1 mth:2 limit:1 similar:1 called:2 inputs:1 mechanics:1 cirac:1 constant:1 computing:1 defined:2 certain:1 abstract:1 describe:1 am:6 evidence:1 peres:1 single:1 proves:1 rule:1 corresponding:1 ing:1 check:1 regime:5 avoided:1 dotted:1 no:5 individual:1 detail:1 other:2 test:1 sohn:1 theor:1 conclusion:1 deviation:2 equations:1 intend:1 superposition:4 calculating:1 models:2 become:1 problems:2 shepelyansky:1 evolves:1 benakli:1 studied:1 n2:2 building:1 correlated:1 implies:2 coupling:1 vice:1 physics:3 baker:1 interval:1 pseudo:3 orbit:4 together:1 inset:2 observe:1 reprinted:1 time:4 decoherence:2 starting:1

quant-ph9911093.txt \|@word represent:1 partial:7 consider:2 results:6 generalize:1 follow:2 expressions:2 research:1 2r3:1 2r1:1 relationships:6 whose:1 certainly:1 inverse:1 calculate:4 integral:1 alamos:2 tq:3 program:1 those:2 yˆ2:1 alberta:1 analogous:3 include:1 division:1 straightforward:1 very:1 wave:30 prog:1 nieto:7 condition:1 entire:1 y1:2 hamiltonian:7 did:1 tanh:10 michael:1 solution:3 integrated:1 solved:1 convenience:1 annihilates:1 1r:1 employing:1 zk:1 miller:1 cosh:16 second:3 further:3 brackets:2 section:9 pandey:1 henceforth:1 above:5 new:3 consisting:1 satisfy:9 full:1 ibid:1 here:3 sinh:15 others:1 represented:1 xα:1 equations:24 change:1 obtained:9 buch:1 receive:1 studied:1 soliani:1 drt:1 yˆ:1 p2:1 resulting:2 fernandez:1 conveniently:1 york:1 hermite:1 ipo:1 eiωt:1 proceed:1 levine:1 eυ:1 positive:1 brittin:1 next:2 tm:3 m1:3 therefore:4 m3:19 calgary:2 themselves:1 type:3 theoretical:1 more:4 gop:2 operators:22 odinger:26 appendix:2 normalized:2 known:1 jˆ2:10 cases:3 md:1 integrating:1 equation:27 work:1 oscillator:14 mj:1 values:2 ms:1 following:6 example:1 reserved:1 indicated:1 give:3 calculation:1 states:36 indicates:1 dropped:1 council:1 respective:2 united:1 s3:4 s2:2 s1:3 six:1 write:1 how:3 pure:2 acta:1 ordinary:7 sin:5 fp:1 algebra:24 may:1 ladder:2 earlier:2 mapping:2 hence:2 representations:2 types:1 man:1 natural:1 sp:1 explicit:4 su:3 extremal:10 so:1 representation:3 sa:3 acknowledges:2 order:13 superscript:1 restriction:1 indeed:1 over:1 paper:1 mentioned:1 satisfies:1 its:3 derive:1 group:1 ln:2 fix:1 solving:3 gen:2 parts:1 systems:17 messer:1 main:1 prime:1 docs:1 material:1 walls:1 they:3 now:2 realize:1 reemphasize:1 2t:9 eigenvalue:1 february:1 2p:1 2q:1 2r:26 e2ν:5 university:2 2e:1 2f:3 2g:7 each:7 found:3 2n:3 cliffs:1 2h:7 2i:2 subset:1 hausdorff:1 weyl:1 ei:1 formulate:1 energy:2 displacement:2 related:2 used:5 combining:2 laboratory:1 summary:1 eq:44 special:3 canada:2 simplify:1 space:3 nuovo:1 rev:5 denotes:1 fx:1 reader:1 gov:1 ref:6 b285:1 math:15 1n4:1 after:1 theory:2 2h1:1 2h3:1 standard:2 reason:1 mmn:2 california:1 term:1 mizrahi:1 subalgebras:1 w1c:2 definition:3 r1:3 r3:5 could:2 turn:1 consequence:2 2ωt:5 first:13 initial:1 xo:13 symmetry:4 number:14 xe:3 xx:6 wronskian:4 done:2 relations:6 xp:1 george:1 given:10 necessarily:2 needed:1 introduction:3 eqs:11 system:2 construct:6 their:7 appl:1 too:1 siam:1 final:1 williams:1 relationship:1 continuous:1 x2:16 x3:18 x1:14 coefficients:1 iωt:2 showed:1 require:1 normalizing:1 classes:2 were:1 symmetries:3 ann:2 mind:1 spectrum:1 generalization:1 conjugate:2 close:1 any:1 viewed:1 lie:5 mappings:2 convenient:1 latter:1 note:3 decomposing:1 take:2 kerner:1 heisenberg:1 begin:1 shall:3 algebraic:2 definitions:1 acknowledgements:1 class:2 eigenfunctions:1 calculated:1 t2n:1 ko:1 exp:62 dot:1 quantity:2 2m3:1 show:4 spaces:1 relation:2 solutions:6 analogue:1 find:2 ground:2 q1:3 q3:6 parameters:2 commutators:2 state:35 should:1 jan:1 only:5 explicitly:1 employed:3 hamiltonians:10 hall:1 greenberger:1 do:1 handle:1 cheng:1 dependent:9 db:1 expectation:1 arranged:1 dt:9 ds:2 closure:3 πs2:1 differential:12 yield:1 method:4 nθ:1 dodonov:1 contain:1 fixed:1 set:5 schreiber:1 computed:1 national:1 2c:1 j1:14 j3:32 campbell:1 see:8 result:2 discussions:1 terms:6 theoretic:1 y3:2 subject:1 satisfying:1 commutation:7 case:1 written:2 subscript:1 recently:1 however:1 jr:1 jj:2 analyzed:1 come:1 both:3 cos:8 last:2 taking:1 according:3 chosen:1 casimir:1 rodney:1 expression:2 baltimore:1 cj:1 groups:1 facts:1 ca:1 corresponds:1 ωx2:1 exploit:1 adjoining:1 nψn:1 polynomial:1 table:8 described:1 transformations:4 basis:1 three:8 been:2 oξ:1 arxiv:1 interest:2 4q3:1 ph:7 algebras:7 austriaca:1 po:11 define:1 corresponding:4 quantities:4 kanai:1 argument:4 coherent:21 c3:20 c1:4 present:2 applied:2 exponential:4 pacs:1 truax:11 straight:1 engineering:1 evaluated:1 transformation:3 will:4 while:2 squeezed:22 procedure:2 klauder:1 ix:1 unitary:2 mexico:1 characteristics:3 refs:4 thus:2 need:1 different:2 grant:1 generic:1 same:3 clearly:1 complex:4 quant:7 φj:1 constructed:1 subalgebra:7 composition:2 φn:11 higher:2 literature:1 prentice:1 kim:1 normalization:1 schr:26 fully:1 well:1 analysis:1 academic:1 solve:3 chemistry:1 usual:1 ny:2 being:1 when:3 obtain:18 αj1:2 differentiation:1 doss:1 eigenstates:2 k3:1 conjugates:1 sciences:1 transparent:1 other:1 hat:1 remaining:1 real:11 iθ:25 iν:1 iξ:4 possible:1 spanned:1 harmonic:2 using:7 englewood:1 helpful:1 follows:3 reduces:3 specific:4 abdalla:2 iξx:1 arbitrary:2 reduced:1 wilkens:1 therein:1 yeon:1 because:1 methods:2 noting:1 coddington:1 some:3 cs:2 examples:3 nonzero:3 provided:1 eiθ:5 integration:2 subclass:7 2c3:2 does:1 ucalgary:1 yields:3 hasse:1 demonstrated:1 refer:3 2q2:1 2q3:3 2q1:2 martin:1 although:2 imaginary:2 unpublished:1 simpler:1 integers:1 about:1 constraint:4 commun:1 discussed:2 dependence:1 o:56 wolf:2 ox:1 os:17 op:1 perelomov:1 forwardly:1 h2:1 h3:1 into:3 h1:2 obtaining:1 isomorphic:3 equality:2 appropriate:1 references:2 operator:6 schrodinger:1 span:1 support:1 there:2 transform:2 specifically:1 los:2 quadratic:2 way:2 ψn:14 was:3 function:21 leach:1 elsewhere:1 form:6 nφn:1 pe:2 but:1 gaussian:1 repeated:1 construction:1 hn:3 squeeze:2 true:1 raising:1 partially:1 compute:1 ωt:10 us:1 um:1 below:2 problem:3 called:1 constant:2 computing:1 defined:6 certain:1 describe:1 am:1 general:12 single:1 our:3 formalism:1 dγ:1 defines:1 again:1 functions:21 cim:1 reiθ:1 detail:2 application:1 setting:2 details:2 department:2 theor:1 applications:2 ξx:14 ξp:25 symbol:2 shown:1 commutator:2 important:2 bounded:1 ξo:3 variable:1 ξe:11 structure:4 independently:1 bch:1 algorithm:1 assume:1 baker:1 lanl:1 sˆ2:2 fung:1 4q:1 mass:3 fact:2 4h:1 time:18 firstorder:1 4g:1 starting:2 once:1

quant-ph9911094.txt \|@word consider:2 results:3 types:1 follow:1 relationships:1 depend:1 calculate:1 similar:3 alamos:2 tq:18 citing:1 tm:18 yˆ2:1 alberta:1 division:1 rise:1 wave:7 prog:1 nieto:7 difference:1 condition:1 differentiated:1 hamiltonian:5 υe:7 υd:1 list:1 damped:3 large:9 solved:1 υx:1 small:3 wronskian:7 cosh:42 past:1 second:3 obey:1 what:2 t2n:1 section:5 intimate:1 goes:3 new:1 method:1 satisfy:3 respectively:5 here:4 growing:1 focused:1 sinh:48 equations:15 change:6 obtained:13 buch:1 soliani:1 drt:1 yˆ:1 p2:3 products:3 fernandez:1 examining:1 regardless:1 hermite:1 sign:8 replace:1 apply:1 total:1 linearly:1 derivatives:2 use:3 feb:1 levine:1 recalling:1 positive:8 eχ:25 contains:1 finally:2 few:1 m1:1 therefore:1 m3:1 calgary:2 type:2 theoretical:1 more:1 becomes:3 operators:6 odinger:15 appendix:6 particular:1 jˆ2:8 cases:8 iii:2 must:2 recall:2 equation:22 work:5 oscillator:4 mj:1 values:17 ms:1 following:5 making:1 example:4 figure:7 give:9 states:31 indicates:2 minimum:2 council:1 magnitudes:1 united:1 s3:2 verify:1 s1:2 six:1 write:1 how:3 varies:1 acta:1 ordinary:2 sin:79 oscillatory:2 product:1 algebra:4 after:2 derived:2 mapping:1 produce:1 constants:1 curve:9 natural:1 dynamical:1 third:1 slightly:2 sk:1 so:4 s2:33 acknowledges:2 order:2 developed:1 paper:3 through:2 y1:3 y3:1 its:2 roots:1 derive:1 rapidly:1 singular:1 ln:142 solving:1 decreases:2 actually:1 systems:16 messer:1 ours:1 defining:1 τp:2 eventually:1 them:1 matches:3 docs:1 hamilton:1 they:5 now:3 discuss:1 2t:4 february:1 2r:24 e2ν:1 university:2 wronskians:1 2d:1 2e:3 magnitude:1 each:10 went:1 cliffs:1 2h:3 2i:17 characterized:4 differential:3 ei:8 michael:1 energy:1 related:1 obtains:1 combining:4 quantum:1 laboratory:1 eq:34 xp:1 canada:2 shown:3 space:1 restricted:3 furthermore:1 since:1 rev:5 research:1 looking:1 eprint:4 reader:1 gov:1 ref:4 b285:1 math:8 shows:1 1n4:1 turning:1 linear:1 standard:1 mmn:2 california:1 rises:2 beginning:1 backwards:1 r1:2 r3:2 ds2:1 motion:7 exponentially:7 hence:1 first:4 initial:4 xo:24 symmetry:5 variables:3 number:10 reaches:4 xx:2 another:1 thick:3 given:12 1r:1 similarly:2 introduction:2 eqs:8 system:29 needed:1 attack:1 listed:1 man:3 too:1 authors:2 x2:12 x3:12 x1:12 begins:3 was:1 zero:1 classes:3 were:1 gives:1 result:1 seminal:1 symmetries:3 nuovo:1 curves:2 conjugate:3 apparently:1 their:8 lie:10 depending:3 note:1 sciences:1 investigations:1 object:1 algebraic:4 regular:1 acknowledgements:1 class:13 considered:1 calculated:1 ko:3 principle:1 exp:32 dot:1 slope:1 show:2 timedependent:2 solutions:32 substituting:1 d2:2 find:5 q1:4 q3:4 should:2 only:3 going:2 generators:1 constant:1 hamiltonians:5 cheng:3 notation:2 dependent:19 compiled:1 expectation:13 combinations:1 applying:2 dt:2 gen:2 evolution:1 arxiv:1 yield:1 dodonov:3 set:1 schreiber:1 computed:2 national:1 j1:2 j3:2 relative:2 see:7 w2:11 w1:11 kerner:1 satisfying:1 state:8 various:1 between:3 subscript:1 approach:1 email:2 terms:1 extend:1 nature:2 complement:1 ln2:12 wt:2 ws:3 jj:1 distinguish:1 2po:6 restrictions:1 cos:100 always:1 many:1 taking:4 uncertainty:4 equal:1 chosen:1 connection:1 figures:1 rodney:1 finds:1 τe:2 point:3 ca:1 corresponds:1 exploit:3 respect:3 transformations:1 basis:2 three:12 been:3 damping:1 prentice:1 ph:5 algebras:7 austriaca:1 po:24 corresponding:2 oω:6 both:3 kanai:1 coherent:16 observe:1 c3:12 c2:5 c1:5 case:24 look:2 exponential:1 tanh:6 truax:8 straight:1 examine:1 value:1 will:7 near:5 momentum:1 iγ2:1 squeezed:15 procedure:1 identical:1 unitary:2 mexico:1 ii:4 eighteen:1 ie:10 different:3 grant:1 make:1 unity:2 complex:10 quant:5 φj:1 several:1 subalgebra:1 composition:1 φn:1 independent:2 used:2 upon:5 parametrized:1 recent:1 weakly:1 schr:15 well:1 solve:2 position:1 chemistry:1 being:2 obtain:9 tables:7 conjugates:4 hall:1 setting:2 transformation:3 iχ:6 real:8 lanl:1 know:1 using:3 englewood:1 sizes:1 follows:2 performing:1 specific:7 abdalla:2 yields:4 either:1 martin:1 specifies:1 because:1 methods:4 classical:5 coddington:1 some:1 growth:1 examples:7 table:20 oscillations:2 nonzero:1 demonstrates:2 normal:1 subclass:1 assuming:1 ucalgary:1 hasse:1 refer:1 2q2:1 2q3:1 2q1:1 s12:21 continuing:1 although:1 2n:3 about:1 discriminant:1 discussed:2 o:71 eυ:5 2iχ:2 euler:1 os:10 other:2 own:1 h3:1 into:2 h1:1 isomorphic:2 negative:12 appropriate:4 references:1 operator:2 brittin:1 lastly:1 uncertainties:4 support:1 there:5 specifically:1 los:2 quadratic:5 ψn:1 sections:1 function:8 leach:1 elsewhere:1 form:6 but:9 hn:4 line:7 illustrative:1 compute:3 maximum:3 us:1 foresight:1 below:4 demonstrate:2 problem:9 subclasses:1 strongly:1 required:1 associated:4 up:2 certain:1 abstract:1 am:1 proven:1 general:6 engineering:1 our:5 constructed:1 again:2 functions:39 cim:1 when:9 detail:1 interested:1 papers:1 department:2 theor:1 dashes:3 conclusion:1 ξx:6 separate:1 ξp:6 polynomials:1 important:1 variable:4 structure:3 dτ:1 interval:2 sˆ2:1 fung:3 4q:2 mass:2 time:47 4a:7 starting:4 having:1 once:1

quant-ph9911095.txt \|@word consider:1 maximum:1 results:8 prefix:1 comments:1 computation:1 parameterization:1 relationships:1 alamos:2 tt:2 technique:1 tq:3 presents:1 tm:3 indicate:2 under:1 alberta:1 indicating:1 division:2 returning:1 wave:3 entries:1 emphasized:1 condition:1 ωto:13 hamiltonian:4 list:2 solution:3 large:2 solved:1 convenience:1 wronskian:7 oscillation:4 dealing:4 sign:4 second:4 further:6 what:1 sub:3 t2n:1 section:7 above:1 new:3 increasing:1 method:1 satisfy:6 subdivided:1 hµ:10 exchange:1 respectively:6 here:2 ranges:2 sinh:15 consideration:1 coupling:1 equations:18 implicit:1 change:2 obtained:8 studied:3 allows:1 drt:1 p2:1 accomplished:1 products:3 complicated:1 implement:1 useful:3 fµ:9 classification:2 namely:1 prefer:1 derivatives:4 use:5 calculation:1 bases:1 m1:1 therefore:3 m3:1 calgary:2 associated:3 type:6 theoretical:1 more:1 initial:4 operators:9 envelope:2 odinger:17 appendix:16 particular:5 jˆ2:7 cases:5 must:2 recall:2 equation:25 work:3 oscillator:9 values:14 thin:2 ms:1 ato:3 following:2 making:1 trans:1 example:5 compare:1 figure:6 give:9 process:1 states:16 indicates:2 numbers:2 council:1 arise:1 respective:2 united:1 end:2 quantph:1 s3:1 verify:1 s1:2 six:1 write:2 how:5 occasionally:1 ordinary:2 divides:1 oscillatory:1 product:2 algebra:4 may:1 derived:1 mapping:2 applications:1 2iχ:2 representations:1 constants:1 natural:1 dynamical:1 third:1 ss:2 explicit:2 generic:1 so:3 acknowledges:2 order:1 superscript:1 holds:1 displayed:1 paper:5 tto:8 motions:1 y0:13 satisfies:1 its:5 before:1 τo:32 derive:1 τh:4 ln:54 solving:1 conjugation:1 writing:1 systems:42 listing:1 derivative:1 main:1 defining:1 h0:3 versus:2 them:1 greater:1 yn:1 hamilton:1 they:1 now:5 discuss:1 2t:8 eigenvalue:1 february:1 2p:2 2r:6 e2ν:1 university:2 wronskians:2 identified:2 establishing:1 2g:3 each:4 went:1 cliffs:1 2h:3 differential:7 another:1 michael:1 energy:1 reduce:1 related:2 frequency:2 obtains:4 combining:1 laboratory:1 eq:23 thick:2 special:5 out:1 canada:2 shown:3 space:6 furthermore:1 research:1 eprint:2 reader:4 gov:1 ref:7 b285:1 math:3 1n4:1 hankel:4 mmn:2 california:1 york:1 subalgebras:1 e2:7 backwards:1 derivation:1 starts:1 1v:2 motion:8 place:1 hence:1 support:1 first:6 origin:1 already:1 xo:37 symmetry:2 variables:13 powerful:1 number:11 xx:2 smaller:1 done:3 directly:1 xp:2 y02:2 given:10 their:7 introduction:2 eqs:13 system:42 relations:4 1a:1 needed:1 attack:1 listed:4 calculations:4 normalization:2 scheme:1 cite:1 gives:2 relationship:1 required:1 πz:4 nieto:4 x2:5 kept:1 cosh:9 specify:2 kind:2 see:11 computations:1 classes:14 amplitude:2 were:2 powers:3 w2:1 motivation:1 symmetries:4 ann:1 coddington:1 argument:1 conjugate:1 need:2 seen:1 demonstration:1 complete:3 lie:6 subsystems:2 zero:1 depending:5 note:3 sciences:1 take:1 forces:1 modulus:2 formulas:1 begin:1 shall:2 2to:34 falls:1 algebraic:1 involving:1 phase:4 acknowledgements:1 class:7 eigenfunctions:1 clear:3 sometimes:1 principle:1 exp:8 fact:1 dover:1 lebedev:2 show:2 timedependent:3 solutions:27 substituting:4 d2:1 find:3 based:1 σo:10 parameters:14 written:1 should:1 jan:1 increasingly:1 only:3 going:1 generators:1 coefficients:2 employed:1 hamiltonians:4 notation:4 means:1 dependent:19 expectation:9 dw:1 dt:3 gen:1 prime:1 arxiv:1 yield:2 investigate:1 fixed:1 valid:1 set:3 computed:1 national:1 j0:14 j1:1 j3:1 depends:2 result:2 w1:1 existence:1 commutation:1 µz:1 subsequent:1 review:2 yet:1 state:7 determined:1 various:3 between:2 subscript:1 conditions:1 email:2 terms:5 extend:1 nature:1 however:1 ln2:1 jn:1 wt:3 article:1 nonconservative:1 both:2 cos:15 σh:2 last:1 always:2 iγ2:1 taking:1 uncertainty:5 according:1 chosen:1 figures:1 context:1 designations:1 distinction:1 rodney:1 simple:1 ca:1 corresponds:1 decreases:2 cs:2 respect:2 j02:2 complication:1 described:3 transformations:1 basis:3 union:2 trajectory:1 three:7 been:1 wz:2 belongs:1 iy0:1 interest:2 basic:1 combine:1 ph:2 algebras:5 po:37 choose:1 corresponding:1 quantities:1 coherent:6 observe:1 determination:1 c3:15 c2:6 c1:6 general:6 present:2 case:17 truax:5 straight:1 engineering:1 value:4 iτ:2 will:4 while:2 applies:1 squeezed:8 procedure:2 unitary:3 ve:1 mexico:1 vh:4 refs:2 thus:2 ii:1 ie:3 different:5 grant:1 perform:1 recursion:3 same:5 unity:2 complex:10 quant:2 emphasize:1 φj:1 composition:1 higher:2 independent:2 trivially:1 upon:4 i4:1 prentice:1 parametrized:1 kim:4 identity:1 recent:1 schr:17 reflection:1 nevertheless:1 well:1 analysis:3 solve:3 applying:1 position:4 chemistry:1 being:1 obtain:7 identify:2 differentiation:2 regardless:1 eigenstates:1 previous:1 tables:10 hall:1 iω:6 interested:1 transformed:2 guarantees:1 transformation:6 momentum:4 real:11 read:1 possible:3 harmonic:1 increases:1 silverman:1 using:3 englewood:1 necessary:2 helpful:1 follows:12 reduces:1 performing:2 specific:7 yields:1 martin:1 become:1 because:1 methods:1 classical:7 discrete:2 some:2 examples:1 table:28 oscillations:1 ignore:1 demonstrates:1 toto:1 subclass:1 ucalgary:1 bessel:5 demonstrated:2 refer:5 obey:1 power:3 plot:3 illustration:2 constructive:1 substitution:1 eiω:2 plots:2 refers:2 properties:1 about:1 carried:1 column:3 discussed:2 o:65 addition:1 range:1 a2:1 wσ:2 os:5 contrariwise:1 h3:1 into:15 h1:5 obtaining:2 isomorphic:2 appropriate:5 references:1 significantly:1 uncertainties:5 assumed:1 apparently:1 there:4 specifically:1 los:2 quadratic:4 way:1 ed:1 forward:1 was:2 naturally:1 function:8 elsewhere:2 form:4 forming:1 becoming:1 hj:1 construction:1 line:4 partially:1 made:1 compute:1 whether:1 up:2 us:1 entails:1 below:2 jµ:5 problem:8 define:1 subclasses:5 calculated:1 regimes:2 later:2 constant:5 defined:14 recognize:1 describe:2 denote:1 examine:1 our:12 formalism:1 constructed:2 again:1 functions:46 no:1 yµ:5 when:13 detail:1 ny:1 other:2 details:1 department:2 ns:1 conclusion:1 ξx:6 separate:1 ξp:6 symbol:4 4i:2 important:2 variable:5 structure:1 longer:1 partitioned:1 assume:1 lanl:1 sˆ2:1 dσ:3 together:1 mass:2 dot:1 time:32 sin:21 original:1 once:1

quant-ph9911096.txt \|@word gs:3 consider:1 remarkable:1 particular:5 truncated:2 results:25 leads:2 roy:3 computation:1 gn:3 expressions:5 gl:1 2r1:1 whose:4 hertog:1 const:2 schiff:2 technique:1 charge:2 monotonically:1 those:1 timedependent:1 aris:2 analogous:1 hereon:2 indicating:2 divergent:1 division:1 updated:1 r12:1 δρb:2 straightforward:1 orthogonal:2 far:2 frequencies:1 continues:1 2rc:1 springer:1 focus:1 electron:4 difference:2 exact:42 abandoned:1 generalised:2 four:1 school:1 impressive:1 hamiltonian:4 diverging:1 proc:5 tokyo:2 υa:6 solution:25 υc:3 υb:3 large:3 discrete:3 convenience:1 burke:1 shows:1 optics:1 equation:19 υr:1 zl:2 δfa:1 concise:1 direct:3 literature:1 approximation:6 generalisations:1 second:4 plenum:1 evaluated:3 further:3 3z1:1 odd:2 gm:2 quite:1 theory:12 even:4 will:10 errors:1 developed:1 chem:2 iterating:1 complexities:1 section:16 symbolically:2 current:3 version:2 above:1 waals:13 obvious:1 appeal:1 method:29 contrast:1 body:2 edited:2 dictates:1 led:1 perdew:1 respectively:3 b136:1 here:9 atoms:5 behaviour:1 desired:4 operating:1 cos2:7 separation:2 others:2 directions:1 slater:4 along:1 strong:1 equations:6 z1:3 z2:6 hass:2 obtained:11 search:2 dashed:3 spite:2 cg:1 involved:2 study:2 studied:1 experience:1 prior:1 survey:1 decouple:1 proof:1 studies:2 der:13 involves:1 plotted:2 via:4 sticky:1 merely:3 dedicated:1 replace:1 dobson:2 zeits:1 summation:2 unit:1 readily:3 formalised:1 use:9 additive:1 would:2 electrostatics:3 continuous:1 contains:2 uniqueness:1 tabulated:3 ψj:1 few:3 call:2 therefore:1 m2:1 taken:1 associated:2 type:3 theoretical:2 possible:1 more:8 fractions:3 formally:1 becomes:2 operators:1 odinger:1 tested:1 berlin:1 dirichlet:1 excellent:1 known:7 testifies:1 iii:7 must:2 none:1 include:1 integrating:1 originally:2 work:11 oscillator:1 kleppner:1 theories:7 remain:1 values:3 den:1 determining:1 following:9 making:1 sci:1 example:3 numbers:2 f1:2 compare:1 wang:1 give:3 calculation:4 expanding:1 cited:1 table:11 rc:6 states:6 sphere:1 chin:1 performed:1 employs:1 hydrogen:14 r22:1 axis:1 information:1 respective:1 z22:1 rather:1 verify:1 dalgarno:3 six:2 write:1 polarizabilities:3 ψg:2 answer:1 absolute:1 beach:6 sin:1 badly:1 levy:2 may:1 after:2 derived:5 long:1 factored:1 makarov:1 fa:15 levi:2 fc:5 physik:1 date:2 fi:1 derives:1 fl:1 response:2 constants:15 workstation:1 interscience:1 dynamical:3 third:1 sets:1 6th:1 explicit:1 lost:1 sk:21 provide:1 complexity:1 so:9 correlation:7 definitions:1 order:28 furnish:1 lieb:3 least:1 dx:2 schwartz:2 noteworthy:1 subtracting:1 indeed:1 over:4 displayed:1 facilitated:1 mathematicians:1 experiments:1 through:1 sham:2 y1:3 satisfies:1 y2:4 its:6 before:1 superior:3 derive:3 lb:1 lc:1 ln:7 interesting:2 invoked:1 solving:3 lj:2 2zj:1 coordinates:3 better:1 attraction:1 systems:10 hidden:1 main:1 pointed:1 versus:1 treating:1 non:4 good:4 motivated:2 combination:1 numerically:1 amenable:2 operator:5 number:1 mention:3 simplifies:1 they:17 nov:1 now:8 discuss:9 wiley:1 densities:5 easily:8 february:1 hereafter:1 2r:3 verifying:1 university:2 υj:4 identified:2 applied:1 xxiv:1 2z1:1 each:2 found:8 soc:5 higher:3 rk:3 referred:1 em:1 el:1 differential:5 directly:1 formulate:2 series:3 energy:28 principles:1 numeric:1 inverted:1 inhomogeneous:3 ξj:6 frequency:1 static:3 quantum:4 our:19 approximated:1 beyond:1 special:2 out:6 ultimately:2 jackson:1 matrix:6 solved:3 furthermore:1 since:4 rev:7 acting:1 ra:1 rb:7 reader:1 formula:1 correct:1 rj:8 thereupon:1 earlier:4 linear:6 interactions:4 ri2:1 standard:2 difficulty:2 approaches:1 cartesian:1 york:4 e0:4 r4:1 r5:1 r6:4 interaction:14 r0:1 r1:3 r2:6 r3:2 recast:1 qm:3 could:2 πe:1 programming:1 fb:8 ql:2 silicon:1 produce:1 leading:1 hence:2 generalizations:1 first:14 xj:1 variationally:1 already:1 symmetry:1 laguerre:5 thereafter:1 symbolic:2 redefine:1 rank:1 multiplying:1 simplified:1 fast:1 quadrupole:6 electronic:1 researched:1 given:17 perturbation:6 guaranteeing:1 their:19 introduction:2 dft:10 top:2 zk:1 mcgrawhill:1 system:8 approximately:1 obtainable:1 attack:1 inversion:1 observations:1 calculations:4 eqn:45 variational:9 behaved:1 final:1 interests:1 ξj2:1 shell:1 a34:1 l3n:1 exactly:3 extended:2 somewhat:1 manipulation:1 x2:4 x1:3 than:3 coefficients:12 center:1 distance:3 scheme:1 unfortunately:2 yj:1 ninham:1 approximations:8 iteration:3 rate:1 project:1 matter:2 determined:3 historical:1 were:4 providing:1 xk:1 motivation:1 fluctuation:1 topics:1 modern:2 curves:3 dash:1 say:1 mcgraw:1 need:2 seen:5 seem:1 any:7 wilson:3 strength:1 smallest:1 thoroughly:1 latter:4 able:2 converges:3 note:14 sciences:1 ideal:1 forces:9 green:3 concern:1 accuracy:10 cl:1 subscripts:2 begin:1 added:1 a3:2 though:1 who:2 molecule:12 alexopoulos:2 victoria:1 asymmetric:1 most:4 involving:1 connected:1 but:10 significant:2 successive:9 remarks:2 ncts:1 future:1 especially:1 lines:1 calculated:5 later:6 curvatures:2 ks:2 a140:1 points:1 generalising:1 principle:2 built:1 χm:2 physics:4 decimals:4 fact:2 particularly:1 show:8 lewis:3 atom:3 terminate:1 converge:2 soluble:4 attempts:1 solutions:3 hohenberg:2 substituting:2 longer:1 trivial:1 find:1 ground:8 based:2 knowledge:2 parameters:1 character:1 should:4 failed:1 only:5 explicitly:1 subsection:4 essence:1 cautioned:1 truncation:7 local:11 interested:1 do:1 dominant:1 notation:1 di:2 dependent:4 secular:1 a233:1 db:4 dc:4 da:3 famous:1 cannot:1 nearly:2 closely:1 dy:2 during:2 nasty:1 meir:1 dr:2 qs:4 continuum:3 textbooks:1 conditions:1 arxiv:1 expansions:2 yield:4 paper:10 common:1 contain:1 analytical:1 london:7 fixed:1 discussing:1 require:3 view:1 kernel:1 requirement:1 set:6 computed:24 exists:2 achieved:1 national:2 still:1 relative:2 δρa:1 see:10 electrostatic:1 full:1 result:7 discussions:1 insoluble:1 alternative:4 best:3 techniques:1 hilbert:1 exploited:1 learnt:1 mentioned:1 define:1 subsequent:3 review:1 definite:1 dipole:7 state:8 unable:2 various:5 closed:2 between:3 progress:1 boundary:3 approach:3 αn:5 terms:12 ability:1 nature:1 confusion:2 subject:1 however:7 neverthless:1 hill:1 concentrate:1 orbitals:10 hydrogenic:6 rapidly:1 thank:1 suggested:2 both:5 cos:3 stages:1 last:1 many:5 differs:1 readers:1 previously:1 energies:1 became:1 figures:5 pde:3 expression:3 ansatz:4 4z1:1 detailed:1 ci:1 relevant:1 afterwards:1 conclude:2 appeared:1 cb:1 ca:1 margenau:2 period:2 except:1 dimensional:3 m12:1 path:1 polynomial:1 respect:4 throughout:2 considering:2 late:1 unusual:1 decoupling:1 basis:2 addition:2 due:3 been:5 implicit:1 pb:4 pc:3 much:2 slowly:1 treat:1 interest:3 electrodynamics:1 ph:1 ann:1 partial:1 fig:22 box:1 determinant:1 arises:1 truncations:9 am:10 natl:1 essentially:3 connections:1 neumann:1 determination:1 systematic:4 graphics:1 general:5 present:5 case:9 ǫb:2 ǫa:6 uncertain:1 look:1 unlike:1 solid:3 ǫj:2 straight:1 single:1 value:6 employ:3 while:2 error:3 expertise:1 procedure:2 seven:1 larger:6 satisfying:2 coupled:1 vol:2 vi:2 thus:5 yk:1 surface:1 iv:5 ii:6 middle:1 itself:1 owing:1 helium:7 normalisable:1 different:2 lengthy:1 develop:1 thereby:3 author:6 perhaps:2 distributions:1 lett:2 same:3 orders:5 shorter:1 complex:3 quant:1 widely:1 evaluate:1 units:2 proved:1 finite:1 φl:1 φm:1 φn:4 difficult:2 used:5 upon:2 effect:3 hand:1 choice:5 moment:1 compared:4 hospitality:1 infinite:3 pioneers:1 hartree:4 cr:1 normalization:1 recent:2 schr:1 whereby:1 nevertheless:5 changes:1 well:7 academic:1 without:1 solve:3 components:1 convenient:3 very:3 chemistry:2 spherical:1 distances:8 lda:3 mathematica:7 proposed:2 less:1 being:5 accurate:5 obtain:7 product:1 differentiation:1 useful:2 taiwan:2 yet:2 previous:3 tables:1 memory:1 density:52 thinking:1 point:2 had:2 lhs:1 capabilities:1 improvement:1 internuclear:2 cc:1 book:1 treatment:5 theorem:1 necessarily:1 excited:3 identical:4 australia:1 iξ:2 situation:1 advances:1 breaks:1 term:4 corresponds:2 early:3 background:3 crossed:1 press:2 using:12 new:5 bev:1 apart:1 minimised:1 modifications:1 necessary:2 like:3 particle:5 follows:1 reduces:2 resorted:1 noted:2 ignore:1 collect:1 yields:4 integrals:4 arbitrary:2 output:1 unperturbed:2 decimal:5 mathematical:1 acad:1 pauling:9 classical:2 formulas:1 e02:1 spheres:3 some:3 somehow:1 towards:1 export:1 b2:2 normalisation:3 kohn:6 specific:1 scale:1 australian:1 bottom:5 demonstrates:1 avoid:1 shall:37 integration:3 does:3 superiority:1 yielded:1 inserting:1 core:2 varying:1 thirring:1 run:1 power:1 bl:1 equivalent:2 wavefunctions:5 agreement:5 expansion:4 variation:2 substitution:1 plots:3 imaginary:1 properties:4 gained:1 about:3 central:1 carried:2 extension:1 constraint:1 eqns:2 dependence:2 o:2 melbourne:2 ǫc:1 ξk:6 ensure:1 greatly:1 2x1:1 choy:4 observation:1 slightly:1 converging:1 outset:1 own:1 firstly:1 h2:8 intl:1 into:7 integral:9 functional:21 usa:1 lies:1 appropriate:8 schemes:1 thorpe:2 laplacian:1 determine:1 elementary:1 pairs:2 next:7 methods:9 outline:1 acknowledgements:1 van:13 strictly:1 there:6 question:2 approximate:7 stark:1 sides:1 dispersion:9 start:2 accordingly:4 physicists:1 way:3 editions:1 was:8 etc:2 function:30 considerably:1 form:16 hs:1 regard:1 amongst:1 change:1 hk:2 camb:1 hn:4 hl:3 hm:2 convergence:13 pg:1 line:1 δρc:1 considerable:1 he:5 directed:1 made:3 algorithm:1 places:4 instructive:1 proceeds:1 wish:1 up:7 us:4 until:1 considered:2 below:1 hsinchu:1 ωm:2 today:1 sum:3 demonstrate:2 problem:20 2y1:1 similar:1 mechanics:3 phil:1 constant:6 classic:1 defined:3 certain:1 universal:2 b3:2 influence:1 convergent:2 dξ:7 fixes:2 presented:1 exist:1 running:1 dθ:1 viewpoint:1 check:1 constructed:1 effected:1 again:1 functions:4 codes:3 completeness:2 courant:1 dotted:1 no:3 fixing:1 whereas:1 wavefunction:9 when:4 detail:1 ny:1 other:9 details:1 investigations:2 quantities:1 electrons:3 applications:1 dashes:5 conclusion:1 poor:3 polar:1 briefly:1 elements:6 denote:1 a10:1 calculating:1 condens:1 agx:1 problems:2 shown:10 polynomials:5 a0:1 kirkwood:4 a2:2 nucleus:3 suited:1 χn:2 needed:1 source:1 ago:1 lm:2 difficulties:1 coulomb:1 assume:1 dτ:2 required:2 curve:11 rule:1 having:1 investigated:1 appendix:2 came:1 5r2:2 time:2 n2:2 original:1

quant-ph9911097.txt \|@word concept:1 consider:1 remarkable:1 leads:4 entropy:14 go:1 inverse:1 calculate:1 finally:1 monotonically:1 th:1 under:2 supported:1 advantage:1 print:1 putting:1 difference:1 fractal:1 condition:4 gg:1 presented:1 issue:1 list:1 large:4 yale:1 small:1 configurations:10 employing:1 consistent:2 zero:1 cat:1 zq:1 canonical:17 intimately:1 what:1 plays:1 abe:2 celebrated:1 consistently:1 above:1 new:2 increasing:1 method:1 edited:1 justification:1 respectively:2 here:4 understanding:1 believed:1 consideration:1 balian:2 logarithmic:8 obtained:2 naval:2 conviction:1 reason:1 suggests:1 resulting:1 appropriately:2 via:1 prefer:1 replace:1 order:1 total:2 conventional:1 usa:1 probabilities:1 positive:1 uniqueness:1 program:1 m1:2 therefore:4 m2:1 taken:1 type:1 formally:1 becomes:1 normalized:2 biblio:1 known:1 goes:1 logarithm:2 science:2 equation:4 mn:1 modified:2 theories:1 values:1 concepts:1 following:2 example:4 arise:1 states:1 professor:1 numbers:3 allowed:1 counting:17 ratio:1 end:1 s2:1 discussion:4 holds:1 dependent:2 instead:1 ordinary:6 constraints:2 parameter:1 ensemble:12 mat:1 mendes:1 may:4 thermodynamic:3 derived:2 applications:1 summarize:1 law:4 journals:1 stress:1 introduced:1 sq:6 sn:1 fundamental:1 acknowledges:1 s1:3 office:1 developed:2 over:2 through:1 same:2 statistical:8 japan:1 jaynes:1 its:5 thank:1 ln:25 sα:3 actually:3 microscopic:2 systems:9 covered:1 defining:2 non:3 yn:25 mention:1 now:4 university:4 identified:1 micro:1 sumiyoshi:1 each:1 found:5 identifies:1 referred:1 energy:1 principles:1 related:1 combining:1 our:2 eq:38 special:2 shown:3 furthermore:1 crucial:1 research:2 mα:5 denoted:1 reexamination:1 ref:4 shows:1 foundation:1 theory:10 interactions:1 completely:1 sbf:1 longrange:1 definition:1 derivation:2 turn:1 support:1 first:1 probability:5 tsallis:7 number:4 specifically:2 another:2 precisely:1 given:8 indicate:2 introduction:1 leading:1 eqs:6 system:5 construct:1 their:2 assumption:2 escort:1 htm:2 speaking:1 rajagopal:2 part:1 authors:1 x1:1 haven:1 wide:1 kind:1 determined:1 result:2 rewrite:1 boston:1 ann:1 mind:1 emphasizing:1 need:1 seen:1 demonstration:1 lim:3 note:2 generalized:6 finding:2 replicas:1 who:1 most:1 boltzmann:2 letter:1 class:3 appear:2 observation:1 calculated:1 partition:1 physica:1 counted:1 points:1 principle:5 exp:3 mechanical:1 physics:1 fact:3 quantity:5 nonuniqueness:6 show:2 labels:1 converge:2 relation:2 substituting:1 find:2 based:4 extensivity:2 should:2 explicitly:1 employed:1 oct:1 establishes:1 df:1 expectation:3 aα:1 words:1 regarding:2 arxiv:1 europhys:1 roger:1 ascertain:1 sho:1 achieved:1 physically:1 cbpf:1 see:1 college:2 descriptions:1 existence:1 discussions:1 subject:1 satisfying:2 probable:1 currently:1 definite:1 identification:1 between:4 conditions:1 available:1 various:1 plastino:3 attention:1 however:2 multiplier:2 configuration:1 both:1 beck:1 braz:1 taking:1 equal:3 connection:2 gibbsian:1 context:2 whole:1 otherwise:1 relevant:1 point:2 lagrange:2 cq:4 throughout:1 descents:1 pq:8 basis:5 interest:1 ph:1 corresponding:1 careful:1 present:2 case:1 multi:1 exponential:1 pacs:1 value:6 will:2 property:1 concomitant:1 chaotic:1 refs:1 thus:1 cond:1 technology:2 disappear:1 belong:1 lévy:3 unity:1 quant:1 gibbs:4 finite:2 http:2 comprehensive:1 hand:1 v2:1 arose:1 normalization:2 thought:1 consistency:3 arising:3 drawing:1 obtain:2 macroscopic:2 yet:1 chiba:1 alternate:1 seems:3 thermodynamics:1 priori:3 lett:2 theorem:5 extensive:1 take:1 identical:2 around:1 rules:2 showing:1 press:2 using:3 unique:4 brought:1 like:1 follows:4 microcanonical:7 translates:1 imposes:1 essential:1 reidel:1 some:2 nonextensive:6 provided:1 lead:2 memories:1 nihon:2 gnedenko:2 funabashi:1 power:3 equivalent:1 br:2 properties:1 about:2 central:4 would:2 origins:1 constraint:1 dependence:1 o:1 range:1 mean:3 consequently:1 considerations:1 equally:2 cambridge:2 into:1 washington:1 lies:1 references:2 bjp:1 statistics:1 additional:1 assumed:1 strictly:2 there:2 question:1 long:1 accordingly:2 way:1 was:1 function:5 usp:1 but:2 true:1 wish:1 maximum:5 us:1 work:1 below:1 limit:10 steepest:1 distribution:6 similar:1 average:1 mechanics:5 associated:3 defined:1 certain:2 universal:2 general:2 examine:2 exist:1 laboratory:1 balazs:1 formalism:2 distributions:2 physical:5 compared:1 no:1 index:1 whereas:1 generally:1 ny:1 other:2 role:1 shannon:1 papers:1 mathematics:1 arithmetic:3 conclusion:1 stat:1 kinds:1 gross:1 deriving:1 important:2 bounded:1 structure:1 algorithm:2 assume:1 rule:13

quant-ph9911098.txt \|@word represent:1 consider:4 remarkable:1 limited:2 rev:5 magnetic:1 dynamic:3 results:3 kernphysik:1 leads:4 mild:1 entropy:4 cases:11 whose:1 certainly:2 inverse:1 depend:2 integral:1 paris:1 superficially:1 critical:1 indicate:2 those:1 th:3 under:5 cumulants:5 mehta:1 p2:4 supported:1 mixte:1 evolves:1 very:8 brownian:1 reader:1 swallows:1 account:1 induce:1 focus:1 sons:1 fall:1 specific:1 matrices:3 exotic:1 orifice:1 entire:7 induced:1 gue:3 level:6 did:3 ref:2 nucl:1 solution:3 large:4 evy:4 porter:1 yale:1 small:7 relation:1 numerically:1 solutions:1 concluded:1 smaller:2 force:4 tem:1 consistent:1 literature:3 zirnbauer:1 past:1 likely:2 perspective:1 correlator:7 further:1 dynamics:18 positivity:1 odd:3 hopefully:1 canonical:2 even:15 aim:1 what:5 sud:1 adds:1 stands:1 brackets:1 deeply:1 exactly:1 selected:3 near:1 reasoning:1 exchanged:2 experiment:1 suspect:1 fractional:3 new:10 learned:1 increasing:1 ever:1 method:1 publications:1 exchange:6 never:2 modify:1 here:7 sink:2 address:1 concluding:1 path:2 along:1 strong:1 equations:3 change:3 box:1 spite:1 noticeable:1 technical:1 involved:1 study:2 studied:4 formalism:1 completely:3 later:1 amount:1 action:1 suitable:2 changes:1 elongated:1 uniquely:1 emerge:1 scales:1 merely:1 x02:3 order:1 put:1 sloane:1 aimed:1 perhaps:2 angle:1 planck:1 unit:1 fed:2 would:19 prove:1 sake:2 played:1 flights:4 france:1 predict:1 linear:2 call:1 averaging:2 taken:1 postfach:1 exhaustive:1 stage:1 type:7 theoretical:3 more:7 introducing:1 becomes:1 apparent:1 odinger:1 surprisingly:1 connecticut:1 reversible:1 particular:12 known:5 hole:1 effort:3 circumstances:1 states:1 keeping:1 defines:3 equation:15 work:5 oscillator:1 modified:1 mk:1 theories:1 mt:1 assumptions:1 obvious:1 temperatures:1 universe:34 arrive:1 example:3 claim:1 distortions:1 solved:1 process:1 allowed:3 lindblad:1 purposes:1 accept:1 high:2 collision:1 minimum:1 something:1 sense:3 interpreted:2 mn:2 occur:1 huge:2 needs:1 requirements:2 rather:4 discussion:1 moves:1 evidently:1 how:3 strategy:1 pure:2 answer:1 instead:1 parameter:1 ensemble:2 simplicity:1 description:4 information:1 max:1 oscillators:4 earlier:2 derived:1 lengthy:1 applications:1 fb:1 end:1 choice:1 constants:1 namely:2 natural:1 collective:1 consequently:2 sq:1 spectra:1 perform:1 fictitious:1 negligible:1 specifying:1 allow:3 correlation:4 looking:2 counterpart:1 typical:4 neto:1 restriction:1 wigner:1 reservoir:10 cumulant:2 over:3 move:1 vary:3 choose:2 cohen:1 years:1 held:1 thermal:2 through:2 looks:1 statistical:2 mentioned:3 kinetic:8 its:6 refs:1 expansion:1 kusnezov:6 derive:1 symmetry:1 chosen:3 interesting:4 translation:2 complex:14 coordinates:2 ds:1 better:1 h2:1 absence:3 production:1 microscopic:5 systems:14 derivative:1 main:1 might:10 alter:1 non:3 qualifier:1 than:3 washington:2 outlined:1 amenable:1 processes:1 functional:2 mention:2 tails:1 they:2 nov:1 now:2 maxwellian:3 discuss:3 bigger:1 ωk2:1 term:5 several:1 always:2 university:2 drop:1 into:1 reasonable:3 cannot:1 kl:3 2m:6 universit:1 characterized:1 fractals:1 subsystem:14 lifted:1 significantly:1 ed:1 energy:7 einstein:1 gaussian:3 t3:1 arrives:3 expect:1 entering:1 measure:1 quantum:24 laboratory:1 eq:4 special:2 out:8 emerges:2 shown:1 matrix:17 space:2 goe:4 integrates:1 since:2 inadequacy:1 chaos:1 particles:1 comprehensive:2 surprise:2 rea:1 forth:1 correct:2 math:2 lutz:1 theory:6 barrier:2 localization:1 dealt:1 attempt:1 possibility:1 standard:1 ex:1 reason:3 salient:1 surely:1 york:2 besides:3 ask:1 inconsistent:1 universally:1 incorporates:1 pairs:1 interaction:6 derivation:4 locations:1 could:12 motion:5 strange:1 length:4 εl:2 exponentially:1 austin:1 first:2 origin:1 connotation:1 initial:3 probability:1 guessing:1 variables:1 number:7 reaches:1 done:1 adopted:1 another:3 open:7 illustrate:1 given:4 perturbation:1 temperature:5 width:3 introduction:3 eqs:1 behaves:2 system:30 least:2 their:1 master:1 1d:3 leggett:6 final:1 too:2 free:1 mostly:1 completed:1 continuous:1 serve:1 obtained:6 weakly:1 somewhat:3 review:1 x2:2 schr:1 x0:15 believe:1 representing:1 haven:1 coefficients:2 diffusion:5 wide:2 kind:2 wilkinson:2 roles:1 double:3 require:1 thermodynamic:2 transferred:1 matter:5 determined:1 supposed:2 were:1 dang:6 gives:1 powers:1 pirner:1 exert:1 banded:2 ann:3 spectrum:1 say:1 manner:1 qualitatively:2 need:1 seen:3 seem:5 apparently:5 any:10 solitons:1 relatively:1 forced:3 subsystems:4 implemented:2 genuine:1 convenient:1 self:1 physique:2 isolated:1 mechanism:1 swallowing:1 emphasis:2 potential:6 εk:2 band:2 weidenm:5 so:9 4x0:1 kac:1 spectral:2 play:1 added:1 fundamental:2 shall:7 techniques:1 falls:1 react:1 most:5 mazur:1 germany:1 significant:2 nothing:3 homogeneous:3 ford:1 extremely:1 class:1 singled:1 deviations:1 reduces:1 consequences:1 considered:1 average:3 sometimes:1 dof:7 repeated:1 physica:1 doe:1 feynman:3 part:2 place:1 exp:4 mechanical:1 velocity:3 usual:2 typically:6 notion:1 fact:7 incorporate:1 emerging:1 intensity:1 show:2 random:12 recipe:1 friction:5 gauge:2 fermions:3 keywords:1 especially:1 longer:1 fine:1 find:4 q2:2 resemblance:1 parameters:1 dissipative:9 writes:1 should:5 only:11 explicitly:3 black:1 indeed:1 parabolic:1 adequate:1 equilibrium:4 meant:1 do:11 dk:1 notation:1 means:3 dependent:1 de:4 brink:1 ko:1 satisfied:1 made:1 reversal:1 devising:1 combinations:1 2mk:1 du:1 dr:1 neither:1 evolution:12 textbooks:1 approach:15 arxiv:1 bandwidth:2 stuff:1 boring:1 analytical:1 qk:1 fixed:2 view:2 ignored:1 set:1 exists:1 achieved:1 inquiry:1 turbulent:3 see:4 decided:1 heavy:4 conductivity:1 closer:1 caldeira:6 neuman:2 satisfying:1 capacity:1 interacting:2 temptation:1 ways:2 away:1 enough:1 difficulties:1 various:7 between:13 boundary:1 conditions:4 tent:1 preserve:1 ends:1 terms:2 reproduced:1 nature:2 confusion:1 complement:1 attention:2 weak:7 however:8 p2k:1 vernon:3 py:1 modeling:1 come:1 distribution:9 concentrated:1 both:4 recherche:1 reverse:1 limits:2 many:3 density:10 according:1 display:1 verbaarschot:1 sketchy:1 section:1 distinction:2 argue:2 nearby:1 ck:2 strongly:1 unclear:1 necessary:1 point:4 simple:7 had:1 narrower:1 period:1 community:1 ized:1 simply:7 stretched:1 article:1 moreover:4 trust:1 points:1 forms:1 described:5 second:3 source:2 px:2 locally:1 atomic:2 due:2 been:12 quickly:1 much:4 devoting:1 interest:5 fluctuation:1 expected:7 degrees:3 ph:1 hardly:1 universal:2 define:2 faced:1 direction:1 relations:1 corresponding:2 innocent:1 retrospective:1 quantities:1 subscripts:1 essentially:3 ik:1 else:2 kramers:1 understand:1 external:4 general:1 spin:1 present:6 case:16 pacs:1 conserved:1 value:1 excited:1 will:4 while:5 kick:1 behavior:2 situation:1 tunneling:2 unsatisfactory:1 generate:1 coupled:2 phenomenological:2 characteristics:1 von:2 thus:9 them:1 reads:1 seattle:1 technology:1 conserve:1 underlining:1 different:6 jargon:1 generic:3 80b:1 make:1 lett:5 same:7 parts:1 quant:1 arguments:4 widely:1 universality:1 physical:1 development:1 independent:4 calculation:1 used:5 singapore:1 laboratoire:2 trajectories:1 drives:1 hand:2 sys:1 moment:1 strength:2 infinite:1 realm:1 invariance:2 prescribed:1 drain:1 shortly:1 center:2 framework:1 modeled:1 well:11 analysis:3 obviously:4 academic:2 without:2 gse:4 consistency:1 coordinate:7 quantitative:1 model:5 parametric:2 dimension:1 justify:1 routinely:1 just:1 being:2 able:1 guided:1 puzzle:1 resolution:1 rest:35 press:2 shape:1 relevant:2 thanks:1 world:1 uller:5 alternative:2 yet:3 down:1 previous:2 unique:2 dqq:1 infinitely:2 seems:2 bell:1 character:3 except:1 weiss:1 confirmed:2 quadratures:1 thermodynamics:1 add:1 other:7 developments:1 versa:1 input:1 extensive:1 heidelberg:1 momentum:8 real:3 easily:2 evaluate:1 iγ:1 possible:2 harmonic:6 eorique:2 nor:1 judge:1 using:5 accepted:1 ruled:1 imposed:1 like:7 particle:8 follows:2 qualitative:2 shapes:1 flux:1 steps:1 either:3 integrals:1 arbitrary:3 become:1 works:1 reduced:3 specifies:1 sketch:1 because:1 dimitri:1 classical:11 reveals:1 some:15 back:1 calculated:1 choosing:2 respect:2 differences:1 ourselves:1 reasons:2 embodied:1 describing:3 lead:1 umr:1 leak:1 avoid:1 though:6 langevin:2 contributing:1 does:5 assuming:1 demonstrated:1 refer:1 limitations:1 noise:2 scientific:1 power:2 rep:1 problems:1 equivalent:1 use:1 vanishing:1 host:1 diosi:1 found:2 refers:1 super:1 properties:5 simpler:2 about:3 usa:2 freedom:5 based:1 discussed:3 dependence:1 o:2 practical:1 distinct:1 extensions:1 stand:2 act:1 introduced:1 slightly:1 bˆatiment:1 own:2 markovian:1 presence:3 previously:2 spreading:2 within:1 obtaining:2 satisfactory:1 bath:1 accommodate:1 remarks:1 overkill:1 references:1 determine:1 apologize:1 proportional:2 outskirts:1 orsay:1 bulgac:6 rely:1 institut:1 few:1 assumed:6 strictly:1 there:11 transform:1 long:1 why:3 start:1 quadratic:2 low:1 way:5 was:7 δln:1 δlm:1 function:1 medium:3 arise:1 form:4 governs:1 δkn:1 attempted:1 δkm:1 but:12 somehow:1 volume:3 hk:1 heat:5 line:1 irreversible:2 illustrative:1 partially:1 commun:1 october:1 surprising:2 characteristic:2 characterization:1 up:1 us:6 ur:1 limit:17 approaches:3 fluctuations:3 problem:1 similar:4 called:4 obtains:1 mechanics:1 ab:1 proved:1 contributors:1 certain:1 abstract:1 describe:5 influence:6 textbook:2 inferred:1 single:1 guessed:1 our:8 controlled:1 hamiltonian:15 distributions:1 check:1 regime:3 again:2 functions:1 entirely:2 no:15 when:9 field:6 interested:1 role:2 spatial:1 department:1 really:1 mock:1 deviation:1 briefly:1 elements:2 models:2 finite:1 kt:2 june:1 2n:3 includes:2 nucleus:1 allowing:2 suited:1 dissipation:6 structure:3 suffers:1 implies:1 coupling:18 coulomb:1 vice:1 assume:2 physics:7 confirm:1 kinetics:3 rule:1 naively:1 overline:1 portion:1 lying:1 time:11 far:5 nuclei:2 requires:1 having:3 once:1

quant-ph9911099.txt \|@word ibid:4 code:1 wigner:1 valid:1 pointing:1 feb:1 moroz:5 hamburg:2 bandgap:1 photonic:6 known:1 determine:1 experiments:1 relation:1 atomic:1 lewenstein:1 sufficiently:1 differs:1 still:1 depending:1 based:1 hold:1 depend:1 thank:1 zone:1 density:1 true:1 less:1 distributed:2 vicinity:2 exhibits:1 edge:7 fortran:1 only:3 k0:2 lett:4 my:1 factor:1 employed:1 freely:1 local:2 achieve:1 within:5 therefore:2 material:1 original:1 often:1 band:8 electron:1 bykov:2 brillouin:1 vacuum:3 part:1 exact:1 alexander:1 entire:1 qs:1 netherlands:2 like:1 should:1 arxiv:1 kruislaan:1 vector:1 predicted:1 universal:1 knight:1 universit:1 fixed:1 essential:1 www:1 averaged:1 financial:1 qed:5 r33:1 higher:1 hypothetical:1 phenomena:2 approximation:1 tip:1 second:1 frequency:2 quantum:1 close:1 approximated:1 eq:1 scientific:1 shown:1 distribution:1 exponent:1 crystal:1 cavity:1 slight:1 rev:6 ωk:1 research:3 cell:4 probed:1 enough:1 europhys:1 weighted:1 fom:1 boundary:1 cause:1 contrast:1 shows:1 available:1 foundation:1 notice:1 theory:1 notoriously:1 interactions:1 uniformly:1 error:1 use:1 atoms:4 approaches:1 huang:1 address:1 fluorescent:3 chen:1 jetp:1 upon:1 properties:2 change:1 calculate:1 obtained:1 remark:1 radiatively:1 weisskopf:1 influential:1 shift:3 discussed:2 o:1 sov:2 sensitive:1 length:1 edges:1 isotropic:4 usually:1 germany:1 changes:1 first:2 exotic:2 among:1 already:1 features:1 probability:1 presence:1 radical:1 others:1 matter:1 number:5 except:1 homogeneously:1 references:1 least:1 applicability:1 article:1 amsterdam:1 complex:1 unit:4 significantly:1 conventional:1 institut:1 asymptotic:3 glauber:1 support:1 there:1 theoretische:1 been:1 dispersion:1 their:2 however:1 much:1 1d:2 calculations:1 anisotropic:1 ph:1 john:8 was:1 minima:2 const:1 function:1 direction:1 complete:2 some:1 toader:1 photon:3 emission:2 gap:3 optical:1 atom:6 worthwhile:1 cases:1 given:1 considerations:1 than:1 present:1 especially:1 case:1 ii:1 made:2 zhu:1 pacs:2 approximations:1 when:2 zero:1 value:1 ur:1 institute:1 near:6 determined:2 behavior:3 were:2 agarwal:1 ωc:5 anomalous:1 spontaneous:2 called:2 strongly:1 lowest:1 program:1 wang:4 coupled:2 calculation:1 electrodynamics:1 abstract:1 surprisingly:1 generalization:1 states:1 discussions:1 minimum:2 predictions:1 allowed:1 crystals:2 ldos:11 work:1 lamb:1 capture:1 nl:2 minimally:1 no:1 derived:1 latter:1 radiation:1 isolated:1 polarization:1 html:1 quant:2 papers:1 more:2 difficult:2 independent:1 quang:2 models:2 earlier:1 molecule:2 possible:1 average:1 involving:1 propagate:2 physik:1 position:4 measured:1 subsequently:1 structure:2 recent:1 independently:1 organization:1 modes:1 described:1 considered:2 k20:1 interval:1 request:1 order:2 sj:1 filed:1 materials:2 so:1 fundamental:1 dos:6 model:4 starting:1 dimension:1 se:5 maxima:1

quant-ph9911100.txt \|@word consider:6 priori:1 caused:3 magnetic:2 theoretical:6 results:4 leads:2 attracted:1 expressions:2 contributions:1 optical:2 whose:1 certainly:1 inverse:1 zone:1 collisions:2 paris:1 γt:2 environment:14 finally:2 does:2 γn:8 under:5 stochastic:2 analogous:2 sent:2 iνn:2 case:28 supported:1 straightforward:1 orthogonal:1 very:5 frequencies:3 springer:2 choice:1 puzzles:1 drever:1 every:2 traced:1 resonant:3 experimentally:6 difference:3 condition:5 randomness:2 squares:1 beginning:1 vibrational:6 hamiltonian:15 turns:1 t2:3 solution:2 t1:3 large:4 small:4 optics:1 leibfried:1 possibility:1 work:2 pragmatic:1 oscillation:12 consistent:3 uef:1 prediction:5 pulse:11 ǫn:12 approximation:2 second:6 dissipation:1 dynamics:2 estimated:2 leakage:1 linear:3 even:4 errors:1 detuned:1 apparatus:2 clock:3 giving:1 section:7 selected:1 dephasing:2 expressed:1 waiting:1 experiment:20 above:4 fractional:1 new:3 woodbury:1 increasing:2 acknowledgments:1 contrast:4 edited:2 evolving:1 full:1 lef:1 exchange:1 applies:1 here:2 atoms:5 reported:1 identifications:1 ramsey:9 cos2:1 relaxation:2 concluding:2 consideration:1 along:1 standard:3 equations:1 appears:2 change:1 obtained:7 delle:1 davidovich:1 shift:7 study:2 studied:4 leaving:1 suggests:3 procedure:1 situations:1 usually:1 opinion:1 tτ1:1 changes:1 york:1 uniquely:1 via:2 depart:1 stray:3 νt:1 problematic:1 explained:2 private:3 highly:1 scaled:1 coinciding:1 gradshteyn:1 apply:3 counts:2 planck:1 unit:2 use:5 takes:1 would:8 positive:2 contains:1 negative:2 periodically:1 few:2 ψi:1 call:1 therefore:10 those:1 vi:1 taken:1 means:4 dλλ:1 today:1 more:4 separated:1 flat:1 becomes:6 line:2 visibility:2 berlin:2 train:1 normalized:3 particular:2 known:2 cases:6 iii:2 must:5 logarithm:1 high:4 account:3 crosses:1 quantized:1 equation:10 averaged:7 ρn:2 remain:1 fock:2 crossed:1 three:1 evolved:1 tracing:2 following:10 roos:1 example:4 purity:1 ions:4 lτ:2 transition:4 modulation:2 give:3 process:3 expanding:1 allowed:1 neglected:1 haroche:1 states:9 assumptions:4 performed:6 aspect:1 sense:1 david:1 ωeg:2 ratio:2 lamb:4 information:2 celoria:1 νn:3 end:1 varied:2 destroying:3 get:4 l1n:1 write:1 pure:1 instead:2 ordinary:1 parameter:14 sin:1 circular:3 description:3 may:3 max:1 ω2r:3 fed:1 derived:4 mapping:1 stefano:1 consequence:1 tries:1 suppl:1 inst:1 ρmix:3 verified:1 law:9 data:3 concerns:1 constants:1 diagonal:4 introduced:2 outline:1 effective:4 joint:1 whenever:1 light:1 schneider:1 acknowledged:1 yielding:3 thorne:1 neglect:1 generic:1 cannot:3 so:10 fundamental:1 correlation:1 representation:2 order:9 typical:2 interpretation:2 kiefer:1 numbers:1 developed:2 over:8 eqs:7 mainly:1 satisfied:1 produced:1 attitude:1 experiments:7 through:3 statistical:5 satisfies:2 still:2 pointer:1 its:7 before:1 derive:5 group:1 decay:12 interesting:5 greatly:1 decreases:1 according:3 degrees:3 systems:4 rabi:35 main:1 might:1 h0:4 ideal:1 non:20 good:2 evolution:40 investigated:1 scaling:12 walls:1 quantenoptik:1 detunings:2 effects:3 they:5 sweeping:1 univocally:1 now:4 mysteries:1 easily:3 february:1 gets:3 always:4 presented:2 sideband:1 identified:1 sufficiently:2 fringes:4 mode:14 l0:2 each:3 crossing:1 found:2 universit:2 higher:1 side:2 characterized:3 mean:15 em:1 en:1 ei:2 significantly:1 series:1 energy:10 try:1 gaussian:11 molecular:1 frequency:25 obtains:1 configuration:1 measurement:3 separating:1 our:6 approximated:3 recognizable:1 eq:48 out:2 iλb:1 matrix:11 driving:1 res:1 nuovo:1 since:2 rev:7 denotes:2 replacing:2 adapt:1 rb:1 print:2 induced:5 ref:19 independence:1 shows:1 inevitably:1 after:1 theory:6 written:1 fisica:2 free:1 quite:2 difficulty:1 completely:3 term:1 estimate:6 e1:3 e0:1 milburn:2 e2:3 definition:1 interaction:28 derivation:1 r2:7 ion:7 impose:1 times:13 counterpart:1 place:2 eigenbasis:1 hence:1 dipartimento:2 first:7 origin:2 there:2 probability:19 laguerre:1 rydberg:9 variables:2 number:9 approximate:1 restrict:1 clear:3 smaller:2 least:1 another:5 bonifacio:3 reached:1 dispersive:5 given:5 necessarily:3 rewritten:1 table:1 introduction:1 adjoint:1 behaves:1 2ωr:4 system:27 approximately:1 2ωn:1 needed:1 assumption:4 master:7 observations:1 realization:1 rates:4 white:2 perfectly:1 ranging:1 recovered:2 gives:2 imperfect:1 trapped:8 relative:2 continuous:2 murao:1 environmental:1 larger:1 part:1 values:5 authors:2 stamatescu:1 than:1 intrinsically:1 population:1 diffusion:1 observed:15 kind:1 scheme:3 trel:2 measured:3 see:10 iωz:1 annihilation:1 determined:2 contrary:3 assumes:2 nonresonant:1 sec:2 interferometry:3 integrals:1 perturbative:1 raman:7 generality:1 rewrite:1 fluctuation:3 unchanged:1 damped:5 turned:1 argument:1 regime:1 correspond:1 randomly:2 already:1 multivalued:1 seen:4 tτ:5 nτ2:5 apparently:1 any:1 duration:2 strength:4 able:2 essentially:2 self:1 responsible:1 isolate:1 isolated:6 note:2 fitting:2 internal:5 generalized:3 analogy:1 negligible:2 coincide:3 subject:2 explanation:2 blue:1 added:1 antihermitian:1 shall:8 decreasing:1 joos:1 most:2 involving:2 importantly:1 cummings:2 preliminary:1 remarks:2 pais:1 extremely:1 considered:5 average:9 flow:1 exhaustive:1 accounted:1 exp:8 aip:1 velocity:4 physics:1 sum:1 fact:20 quantity:3 precise:1 particularly:2 phenomenon:1 intensity:5 show:3 raithel:1 random:21 implying:1 relation:2 king:1 ωz:2 find:2 paradoxes:1 excitations:1 based:2 just:3 parameters:4 dissipative:9 explain:4 state:14 jan:1 giulini:1 only:15 stand:1 ien:1 constant:2 zeh:1 kτ2:1 meant:1 do:2 itano:1 mixture:1 di:6 dependent:4 zurek:1 overall:1 infm:3 soon:1 beam:1 ones:1 preparing:1 closely:1 despite:1 during:2 dt:4 quantifies:1 positivedefinite:1 differentiating:1 runs:1 caves:1 heaviside:1 approach:16 arxiv:1 motion:1 yield:1 tuned:1 bad:1 paper:6 common:1 though:1 characteristic:2 pulses:3 lasers:3 reference:1 imposing:2 cimento:1 comparable:2 lett:3 ωt:3 detection:2 depends:2 injecting:1 discussions:1 recently:2 limiting:1 ieee:1 acquires:1 phases:4 satisfying:1 interacting:2 resonantly:1 varcoe:1 jaynes:2 knight:1 definite:2 dap:1 originated:1 lτ1:1 tool:1 il0:1 between:15 ωm:1 previous:1 conditions:4 brune:4 preserve:1 notice:4 terms:8 nature:1 initially:1 however:12 understanding:1 suggested:4 both:2 cos:7 iωn:1 2n:1 ila:2 many:5 taking:3 uncertainty:5 equal:2 attributed:2 agree:1 ilt:4 raimond:3 variance:3 whole:1 finds:1 experimental:19 otherwise:1 unitarily:1 mechanics:3 relevant:3 jitter:1 fields:3 timescale:1 reasons:1 character:2 ca:1 corresponds:2 simply:2 scully:1 polynomial:1 moreover:4 ae:1 considers:1 considering:4 tint:10 described:6 cavities:3 basis:2 narducci:1 due:11 been:12 imperfections:1 reduction:2 describes:1 interpret:1 interest:4 expected:1 intensities:2 ph:3 fig:8 field:2 direction:2 corresponding:9 dashed:1 quantities:1 concerning:1 coherence:4 photon:7 modelization:1 spectrum:1 determination:1 present:9 applied:6 hωr:1 replaces:1 laser:9 exponential:5 kupsch:1 appearance:1 conserved:2 value:8 excited:1 will:1 hωa:1 while:4 replaced:3 walther:4 behavior:2 error:3 situation:3 property:3 characterizing:3 unitary:10 averaging:1 refs:1 them:2 iv:2 ii:8 reads:1 properties:5 il:2 madonna:1 ib:2 demolition:1 monroe:1 different:10 recover:1 italy:2 perform:1 make:2 intrinsic:1 expect:1 same:4 shifts:1 attributing:1 quant:3 arguments:1 pag:3 units:2 dimensionless:1 finite:3 events:2 difficult:1 independent:7 used:2 numerical:1 effect:3 hand:2 driven:1 v1:4 levels:1 resonance:1 entanglement:5 changing:2 arb:1 identity:1 recent:3 lower:2 supports:1 off:3 center:1 zagury:1 expression:5 nonetheless:1 well:12 analysis:2 academic:2 without:1 studying:1 quantitative:3 model:8 plotted:2 usual:11 comment:1 µsec:8 proposed:2 moments:1 when:11 wagner:1 obtain:1 rest:1 sources:2 λa:1 ch:1 atomic:11 predicts:2 integer:2 eigenstates:1 cn:5 rapid:1 signal:1 generator:2 density:15 similarities:2 seems:2 dicke:4 arctg:2 confirmed:2 simple:4 valid:3 treatment:1 easy:1 natl:1 semigroup:7 transformation:1 take:1 identical:1 rescaled:4 fluctuating:13 aspects:1 around:1 lacking:1 rules:1 advances:1 innsbruck:1 possible:4 period:1 dark:2 vibrations:2 provide:1 background:2 vacuum:1 press:1 using:11 mod:1 meaning:4 loss:1 imposed:1 like:1 δv:3 follows:1 δt:5 velocities:2 camerino:3 immediately:1 unified:1 specific:1 yields:4 sezione:1 arbitrary:1 evolutions:1 become:2 reduced:2 therein:1 because:9 qed:7 classical:12 orlando:1 plausible:1 some:6 back:1 understood:1 examples:1 sight:1 respect:4 oscillations:14 neglecting:1 matching:1 nonzero:4 provided:2 describing:5 trace:1 lead:1 cavity:36 opposite:1 microwave:10 behave:1 tends:1 peg:11 proc:1 durations:1 trap:1 measuring:4 run:2 reasonable:2 power:8 coincides:1 oscillating:1 agreement:2 expansion:3 qnd:2 step:1 references:1 zimmermann:1 repeating:1 asymptotic:1 rodolfo:1 actual:1 world:1 algebraic:1 freedom:3 waist:1 fringe:3 discussed:1 dependence:4 o:2 range:2 r1:7 evident:1 ot:2 gamma:1 subsystem:1 markovian:1 wineland:3 communication:3 into:4 within:7 integral:3 uncontrolled:1 phase:6 hermitian:1 right:2 accounts:1 determine:2 operator:16 proportional:2 theoretically:1 detectors:2 institut:1 log:3 prepare:1 area:7 assumed:1 initial:7 detuning:2 dispersion:4 width:4 much:1 low:1 way:4 sections:1 eg:4 uncontrollable:1 naturally:1 function:18 dispersively:1 form:11 differences:1 ryzhik:1 but:10 repeated:1 properly:1 matematica:1 atom:13 injection:1 level:1 irreversible:2 proposal:1 partially:2 infn:1 paolo:1 made:3 micromaser:3 rate:2 ωr:11 maximum:1 us:3 ur:1 limit:10 ωl:1 ωn:15 continuously:1 fluctuations:18 distribution:14 similar:4 called:2 distance:1 aa:1 khz:6 lanl:2 associated:3 interrupted:2 introducing:1 defined:7 milano:3 universal:1 describe:2 linearity:1 general:10 quantum:10 single:3 proves:1 predictions:2 flight:5 formalism:10 archive:2 triangles:1 physical:2 again:10 compared:2 no:5 liouvillian:1 whereas:1 generally:2 detail:1 meekhof:2 arctan:1 application:1 other:4 role:1 picture:3 elements:4 kinds:1 superposition:2 gas:2 preceding:1 berman:1 prepared:2 generated:3 a2:1 technol:1 variable:10 quadrupole:1 source:2 sandberg:1 implies:3 assume:4 thermalization:1 interval:3 implied:2 mass:1 fitted:4 time:76 understand:1 decoherence:35 flexible:1 starting:1 original:1 once:1

quant-ph9911101.txt \|@word represent:1 consider:6 illustrates:1 forbidden:2 lack:1 results:3 four:5 roy:1 generalize:2 gb:6 children:28 issues:1 eiα1:1 gases:2 dα1:3 re:4 tt:3 tr:1 answered:1 tail:1 does:1 th:3 under:4 teaching:1 analogous:1 must:5 magnetic:2 subtleties:1 straightforward:3 returning:2 very:1 multi:1 splitting:2 electron:2 sons:1 experimentally:1 emphasized:1 matrices:11 condition:5 identity:1 gg:8 level:2 turns:4 mb:3 list:1 applicable:6 discrete:1 vector:5 annihilates:1 manifestly:1 sleep:2 referred:1 eiα2:1 dαk:3 smaller:2 mg:2 likely:19 bg:6 enhancement:3 spontaneously:1 linear:2 even:6 what:10 stands:1 incompatible:1 dr1:2 fact:1 section:1 selected:13 brief:1 expressed:1 uniform:1 3k:2 above:13 new:3 contrast:1 coefficient:2 condensed:1 exchange:2 respectively:3 answers:2 understanding:1 symmetrizations:3 objects:4 sink:2 along:1 knowledge:2 obtained:4 boy:18 search:1 antisymmetric:1 independences:1 study:4 studied:2 reason:1 drk:2 usually:2 advantages:1 studies:1 dices:1 blackbody:1 via:2 regardless:1 griffiths:2 extra:1 merely:2 outcomes:11 brought:1 support:2 rarely:2 planck:1 unit:4 feb:1 distinct:9 chi:1 coins:20 generate:1 classically:1 taken:1 scope:1 reflects:1 more:9 separated:1 introducing:2 sharing:1 asterisks:1 becomes:1 operators:2 curriculum:1 berlin:1 appendix:6 normalized:1 sharply:2 particular:5 known:1 cases:4 iii:10 maryland:1 fermionic:4 md:1 none:1 word:1 ρf:4 recall:2 des:2 theories:1 recast:1 labeled:5 ρr:3 values:1 mp:1 following:6 male:1 example:9 f0:8 f1:2 stated:2 arise:1 share:1 parameterize:1 states:33 sphere:2 assumptions:1 caution:1 degenerate:3 sense:4 distinguishable:12 occur:2 νk:5 νj:2 information:2 respective:1 end:2 mutually:1 provide:1 discussion:5 holds:1 far:1 ρn1:1 answer:11 instead:4 allowable:11 axis:1 sin:8 simplicity:1 product:2 de:1 description:2 huge:1 may:3 fz:3 after:5 factored:1 expectation:4 applications:4 tries:1 law:1 constants:3 namely:1 introduced:1 natural:3 light:1 acknowledged:1 correspond:1 ones:1 negligible:2 fundamental:1 order:1 dramatically:1 exclusive:1 stowe:2 interpretation:1 over:1 move:2 satisfied:1 paper:3 through:1 enumeration:1 statistical:14 gender:4 mentioned:2 satisfies:1 agrees:1 its:1 before:7 derive:1 exclusion:2 chosen:3 zˆ:1 expectations:2 conjugation:1 absence:2 compelling:1 systems:16 listing:3 main:1 puzzle:1 renaming:1 symmetrization:3 them:13 affected:1 combination:6 rewritten:1 mention:2 tails:1 effects:1 they:4 half:2 oxford:1 now:5 discuss:1 wiley:1 rj:2 easily:5 february:1 several:1 dirac:8 name:1 2r:2 always:6 university:1 hamiltonian:1 factorizable:1 courses:1 each:11 found:4 soc:1 cliffs:1 rk:7 2k:4 domain:1 duxbury:1 energy:4 gaussian:1 dωc:5 literature:1 expect:1 presumed:1 quantum:80 our:5 girl:3 beyond:1 eq:7 event:1 special:1 out:10 matrix:15 space:3 since:10 projected:1 research:1 particles:29 reformulate:1 acting:1 term:1 formula:4 ref:1 occurs:1 independence:8 shows:1 foundation:1 philosophy:1 theory:7 interactions:2 given:7 standard:3 approaches:2 a112:1 complicated:1 bayes:4 remainder:2 finite:1 care:10 definition:1 interaction:1 r1:5 r2:1 locations:1 so:5 turn:2 isotropic:1 hence:4 onto:1 condensate:3 first:7 organize:1 probability:43 number:6 crib:5 obeying:6 set:4 long:2 another:4 precisely:1 electronic:1 angular:1 little:2 necessarily:1 heads:7 temperature:4 needed:1 introduction:1 interact:1 girls:5 system:5 least:5 their:4 confirming:1 fermions:4 realization:1 quanta:1 john:1 recovered:2 gives:3 fraction:2 exactly:2 park:1 immediate:1 optical:1 manifestation:1 believe:2 than:4 coefficients:3 peaked:2 polarized:1 zero:1 annihilation:3 matter:1 express:1 determined:1 doubly:2 ber:1 genders:2 outcome:4 distinguished:1 rewrite:1 cohen:1 measure:1 spectrum:2 generalization:1 randomly:3 manner:1 seen:1 occupied:1 clearly:1 studying:2 verlag:1 note:3 extracted:1 emphasis:1 potential:2 generalized:2 analogy:1 finding:3 destroy:2 reproducing:1 subscripts:1 akad:1 unless:2 who:1 most:7 beta:1 but:5 letter:1 coin:8 measured:1 why:2 appear:1 give:2 observation:1 hk:5 considered:1 clear:3 adopt:1 coincides:1 underlined:1 part:1 electrons:1 principle:3 mechanical:3 left:4 physics:6 sum:1 lying:2 laws:1 thomas:1 selection:7 particularly:1 show:2 random:4 analogously:1 spaces:1 tend:1 thirds:1 find:1 ground:3 rf1:1 rf0:1 ratio:1 dice:16 written:2 should:2 only:14 factor:2 interested:1 hall:1 do:5 quantentheorie:1 fraser:2 goes:1 familiar:1 between:16 overall:1 antisymmetrization:2 ρcl:5 famous:1 cannot:1 preparing:2 words:3 combinations:12 dr:7 clearest:1 dp:5 die:6 settings:1 textbooks:5 seldom:1 arxiv:1 imposed:2 implication:1 enhances:1 omission:1 predicts:1 reference:1 physically:1 correlations:1 depends:1 college:1 result:6 discussions:5 close:1 wonder:2 phases:4 satisfying:2 probable:2 fn1:2 tackling:1 nuclear:1 label:1 symmetric:1 state:29 simplest:1 prentice:1 αj:5 conditions:2 notice:2 terms:3 statistically:6 roe:2 however:8 gratefully:1 york:2 hypothesis:1 here:2 analyzed:2 bose:10 atoms:3 distribution:16 both:13 essentially:2 realizable:3 last:1 met:1 many:1 taking:1 readers:1 equal:1 etc:1 connection:1 passing:1 photons:2 experimental:1 cos2:2 ck:3 among:3 simple:3 high:1 dimensional:2 anti:3 testable:1 forecasted:1 described:3 asks:1 three:7 been:3 much:2 anisotropic:1 ph:1 topics:1 empty:1 define:3 dots:1 terminologies:3 direction:1 observable:2 subspace:1 cos:5 gap:1 dramatic:1 external:3 systematic:2 child:13 spin:6 case:3 intriguing:2 value:5 rectangular:1 will:14 while:4 evaluating:1 applies:1 situation:1 procedure:1 real:8 larger:1 violating:1 iv:11 ii:8 focus:1 shorthand:1 different:4 grant:1 make:1 indistinguishable:2 same:8 any:8 unity:2 complex:4 quant:1 emphasize:1 pauli:2 evaluate:1 fill:1 events:1 higher:1 independent:8 used:4 infinity:1 see:3 trivially:1 upon:1 effect:1 hand:6 doublets:2 levels:3 introduce:1 necessity:1 opportunity:1 normalization:5 off:2 center:10 scenario:1 well:2 analysis:4 obviously:1 academic:1 without:1 solve:1 jersey:1 components:1 convenient:2 position:1 usual:1 ρbe:4 less:1 being:13 when:3 removed:2 rest:1 λf:1 questions:7 world:1 useful:1 rn1:1 macroscopic:2 previous:2 polarization:1 density:26 regarded:1 except:1 day:10 thermodynamics:1 add:1 valid:1 location:2 easy:2 remaining:12 momentum:1 take:1 identical:12 aspects:1 around:2 read:2 bands:1 possible:15 increases:2 englewood:1 entangled:2 presume:1 press:2 integer:4 like:2 counterintuitive:6 appearing:1 particle:22 lost:1 alternatively:1 reduces:1 manifest:1 specific:1 remind:1 either:1 arbitrary:1 simply:1 spins:3 accessible:6 often:3 classical:12 conditional:16 some:2 springer:1 understood:1 examples:7 curious:1 total:3 describing:3 dimensions:1 lead:1 sufficiently:1 cavity:2 undergraduate:4 measurements:4 behave:2 provides:1 tends:1 proc:1 equipartition:1 obey:3 bb:12 wavefunctions:5 agreement:1 clarendon:1 projection:3 departures:1 2m:1 zur:1 getting:3 discussed:5 practical:1 probabilities:12 carries:1 a2:2 ensure:2 terminology:1 chow:1 mixed:5 mean:2 consequently:1 other:16 dθj:3 equally:20 angles:5 into:2 disentangled:1 due:1 lies:3 einstein:6 operator:7 lesson:1 lastly:1 bosonic:7 statistics:35 fluctuate:1 strictly:1 there:15 question:20 specifically:2 start:2 bosons:6 low:3 way:7 analyze:2 was:1 function:2 north:1 enough:1 understandably:1 attempted:1 differences:5 denoting:2 keung:1 ht:7 principles:1 hj:4 boys:15 hh:14 properly:1 atom:3 fg02:1 true:2 tossed:1 intuitive:1 whether:1 variations:2 up:3 us:2 wiss:1 projecting:1 fermi:5 integrating:1 highlight:2 problem:15 similar:1 called:1 mechanics:9 θj:11 ab:4 constant:1 θk:4 defined:1 ak:3 aj:1 general:1 single:5 ar:11 formalism:5 check:1 physical:4 again:6 nj:3 nk:10 know:1 no:3 deserve:1 nb:1 wavefunction:1 tossing:8 field:2 priori:10 spatial:3 department:2 really:1 elements:1 superposition:1 separate:1 setting:2 problems:4 a1:3 chance:1 important:2 massachusetts:1 rolling:1 correlated:1 implies:1 longer:1 using:3 assume:1 changed:1 delta:1 incomplete:1 time:1 n1:12 n2:15 n3:1 having:1

quant-ph9911102.txt \|@word limited:2 unavoidable:1 consider:1 represent:1 rev:9 forbidden:1 results:9 existing:1 four:2 eds:2 scalar:1 entropy:4 research:1 issues:1 whose:1 b42:1 braginsky:1 subband:1 crest:1 kν:1 case:3 supported:1 amplitudes:1 rise:2 account:1 readout:1 electron:7 wishes:2 mixing:1 difference:2 matrices:1 condition:8 fukuoka:1 hamiltonian:20 applicable:1 large:2 vector:1 small:6 relation:3 upper:3 smaller:2 renormalized:1 consistent:1 literature:1 aip:1 approximation:2 second:1 evaluated:3 dynamics:2 estimated:1 established:1 apparatus:12 section:2 expressed:1 current:1 experiment:1 above:2 new:3 waveguide:1 contrast:3 satisfy:1 full:1 respectively:1 here:9 ranges:1 desired:1 represented:1 strong:2 change:1 knowledge:2 obtained:6 remarks:1 shift:5 changed:1 published:1 fujita:2 composed:3 appropriately:2 modulates:1 semiconductors:1 explained:1 total:1 univ:2 use:1 proceed:1 would:3 positive:3 physics:1 therefore:6 taken:2 means:2 more:2 becomes:2 about:1 validity:1 controlling:2 particular:4 known:2 cases:2 must:7 evolves:1 keeping:1 tokyo:3 science:4 equation:1 work:4 itself:3 values:4 following:4 meet:1 example:9 decoupled:1 control:3 figure:1 give:1 relativistic:1 states:7 performed:1 sakaki:2 sharp:1 standard:1 occur:1 verlag:1 information:14 quantph:1 technology:2 breaking:2 necessary:1 ensemble:3 simplicity:1 description:1 may:2 derived:8 diagram:1 wrong:4 designed:3 fk:3 meaningful:1 response:6 types:2 dynamical:1 effective:10 light:4 element:1 cannot:4 so:2 fundamental:10 correlation:4 representation:1 order:3 haus:1 words:1 indeed:1 over:2 satisfied:5 course:1 paper:2 through:1 statistical:2 meguro:1 japan:3 satisfies:1 its:4 before:1 nonlinearities:1 probability:1 la:1 energies:1 interesting:2 forms:7 detected:1 systems:7 mail:1 τt:1 alter:2 τp:5 virtually:1 non:2 nonideal:1 was:3 ukℓ:3 evolution:2 operator:1 landau:1 walls:1 effects:1 oxford:2 nov:1 discuss:2 easily:1 dirac:1 name:1 fully:1 university:1 porta:1 possibilities:1 realistic:1 magnitude:4 each:1 found:1 another:1 ed:1 energy:5 principles:3 related:3 constitute:1 interferometer:2 used:2 measurement:45 quantum:40 wavelength:1 operation:1 eq:8 out:3 shown:2 ezawa:1 matrix:1 3rd:1 furthermore:3 since:6 interference:3 denotes:3 increase:4 denoted:1 induced:2 ref:5 correct:10 foundation:1 log2:1 theory:6 interactions:10 free:2 quite:1 completely:1 yuri:1 milburn:1 interaction:17 could:1 motion:1 tempting:1 hence:7 first:1 initial:3 symmetry:2 variables:1 number:12 clear:1 philosophical:1 directly:3 impossible:2 precisely:2 given:2 introduction:1 system:17 relations:3 unruh:1 their:5 constants:2 hypothetical:1 structures:1 murayama:1 gives:4 a32:1 imperfect:2 calculations:1 evolutional:1 accurately:1 employ:1 optical:3 pulse:2 yurke:1 than:4 coefficients:1 wide:1 kind:1 polarized:1 determines:1 unfortunately:2 double:1 namely:6 annihilation:1 matter:1 determined:8 a43:1 were:5 contrasted:2 distinguished:1 peierls:1 function:1 electrodynamics:1 unchanged:1 mind:1 argument:1 conjugate:3 need:1 seen:4 any:6 strength:4 ideas:1 note:1 ideal:4 potential:3 absorbed:1 generalized:3 detector:5 strengths:2 measures:1 jst:1 most:3 phase:6 accepting:2 measured:8 chap:1 eigenfunctions:1 consequences:1 calculated:1 detectors:1 points:1 electrons:3 principle:3 ku:1 normally:1 specification:1 fact:2 b44:1 drastically:1 particularly:1 intensity:3 show:1 absorbing:1 probe:2 notations:1 gauge:12 εba:7 carefully:2 d4:1 find:1 photodetector:4 based:1 proposed:1 explain:1 less:1 state:3 should:7 only:10 going:1 local:1 pointed:1 achieve:1 do:1 viewpoint:1 get:4 dependent:1 simplest:2 nanostructures:1 beam:1 ones:2 preparing:2 closely:2 invariant:1 during:2 justified:1 processes:1 arxiv:1 photodetectors:1 including:1 limitations:1 requirement:2 set:7 physically:5 undergoes:1 unpublished:1 depends:2 sec:1 result:4 discussions:2 disturbing:1 uncorrelated:1 quantizing:1 preparation:2 wire:2 commutation:3 definite:2 enough:4 classes:1 various:1 between:7 drawn:1 boundary:1 caves:1 conditions:1 controllability:1 available:2 terms:1 nature:4 weak:4 okuda:1 jp:1 however:11 analyzed:1 observable:5 hits:1 limits:8 many:4 region:2 uncertainty:4 according:1 quantization:1 berry:1 whole:1 comes:3 among:3 reconsidered:2 conclude:1 simple:2 corresponds:2 semiclassical:1 concluding:1 simply:1 moreover:1 throughout:1 ps:1 leads:3 due:1 been:2 ai:2 reduction:1 interest:1 basic:2 ph:2 komaba:1 fig:3 direction:1 both:1 quantities:2 photon:16 dramatic:1 decreased:1 present:3 applied:1 ǫb:2 ǫa:4 reliable:1 ij:3 ǫn:3 value:4 heidelberg:1 will:1 while:1 optimization:3 ǫw:1 error:7 property:2 taking:2 nonrelativistic:1 detailed:1 unitary:1 a28:1 refs:4 thus:2 examined:2 conf:1 elsevier:1 claimed:3 demolition:2 currents:1 nmax:4 different:3 perform:4 suggest:2 make:5 d18:1 same:2 clearly:2 imoto:1 quant:2 arguments:1 schematic:1 finite:6 independent:2 wires:4 see:3 hand:3 levels:2 uses:1 changing:1 invariance:4 lower:3 well:1 analysis:3 academic:1 without:5 uniquely:2 just:2 akira:1 accurate:2 obtain:3 ozawa:1 haug:1 yamamoto:1 modulate:1 previous:4 rapid:1 conclusions:1 absorption:1 photons:3 point:2 seems:2 except:1 mathematically:1 lett:2 easy:1 excited:1 real:2 evaluate:1 possible:4 know:3 using:2 mod:1 loss:1 pollicott:1 imposed:1 semi:1 reduces:1 specific:1 imposes:4 either:1 essential:1 because:6 often:1 classical:3 some:11 springer:1 strongest:1 examples:1 proper:1 confirm:1 electromagnetic:1 measurements:3 ak:4 does:3 tends:1 moderate:1 proc:2 demonstrated:1 measuring:10 core:1 instabilities:1 conventional:1 expansion:1 qnd:17 although:4 properties:1 limitation:9 actual:1 getting:4 dependence:1 range:6 backaction:14 slightly:1 gamma:1 mechanics:3 cambridge:2 device:2 references:1 elementary:8 proportional:2 devices:1 prepare:1 assumed:7 there:4 approximate:1 occupy:1 quadratic:1 quanta:1 low:3 way:1 sections:1 assumes:1 lowest:2 commutes:1 complete:1 form:13 but:5 hi:25 aµ:3 hc:2 true:6 longer:2 made:1 intuitive:1 us:1 books:1 limit:19 demonstrate:1 distribution:2 similar:3 called:1 strongly:4 ac:1 constant:4 int:1 certain:2 abstract:1 detuning:1 ergodic:2 textbook:1 general:5 fujii:1 duration:2 conserved:3 balazs:1 commuting:1 regime:2 dotted:1 no:1 corporation:1 whereas:2 wavefunction:2 when:2 slusher:1 virtual:2 field:10 other:7 role:1 bℓ:4 department:1 shimizu:9 realize:1 conclusion:4 draw:1 excitation:3 a12:1 time:1 problems:2 variable:2 structure:1 acknowledgment:1 correlated:3 coupling:5 typically:1 governed:1 confinement:1 nmin:4 demonstrates:1 walker:1 observables:5

quant-ph9911103.txt \|@word default:1 consider:7 lack:1 desirable:1 results:7 leads:1 edu:2 equiprobable:1 content:3 terms:1 disposal:1 tr:1 send:1 presents:1 does:2 those:1 resources:1 wjm:1 worse:1 advantage:2 orthogonal:5 very:8 experimentally:1 ending:1 exact:1 generalised:2 presented:1 noiseless:4 small:1 upper:1 approximately:1 hillery:1 second:4 value:1 implemented:2 machines:3 linear:1 even:3 employ:1 what:8 effort:1 access:1 transmit:1 above:6 ongoing:1 increasing:1 notions:1 never:3 here:6 ranges:1 correlating:1 situation:5 alone:1 consideration:1 strong:1 extreme:2 obtained:2 incoming:1 involved:1 studied:1 allows:3 ignoring:1 amount:6 schumacher:1 usually:1 involves:1 buˇzek:1 useful:4 marginal:1 put:1 singlephoton:1 achievable:2 counts:2 total:1 readily:2 environment:2 fed:2 would:4 intense:1 positive:2 hilbert:1 few:2 depicted:1 monotonically:1 opposed:1 centre:1 australian:1 reflects:1 more:12 introducing:1 knows:1 successful:1 becomes:2 ρˆn:2 berlin:1 basically:1 particular:2 known:3 cases:5 producing:2 must:3 entangle:1 high:2 springer:1 valued:1 science:1 equation:3 ρn:2 itself:2 obvious:2 following:1 example:1 figure:5 give:2 process:2 introduces:1 share:1 states:13 something:1 council:1 occur:2 information:14 destroying:1 get:1 machine:3 how:6 varies:1 vital:1 answer:1 gate:2 parameter:4 simplicity:1 utilise:1 barnum:1 may:3 use:1 applications:2 produce:1 improving:1 destructive:2 types:1 physical:2 effective:3 whenever:2 register:2 lines:2 rather:2 so:6 allow:1 correlation:2 order:1 typical:1 operations:1 help:1 ith:3 produces:1 over:5 mainly:2 produced:3 paper:1 through:1 mentioned:2 still:2 pointer:1 its:3 before:1 perfect:6 regions:1 acknowledge:1 actually:3 better:3 detected:1 microscopic:1 systems:5 potentially:1 might:2 easier:1 non:2 good:4 greater:3 combination:1 outlined:1 practice:2 evolution:1 effects:2 they:2 optimal:1 nov:1 now:5 hall:1 represents:1 february:1 finite:1 fully:1 university:1 realistic:2 theory:1 each:1 found:2 2n:1 macchiavello:1 schemes:6 another:1 reduce:1 idea:1 begun:1 measurement:11 quantum:32 beyond:1 extract:1 shannon:3 out:2 large:1 shown:4 matrix:1 space:1 restricted:2 since:4 rev:5 research:2 increase:1 replacing:1 contained:1 after:1 log2:1 aˆi:4 possibility:1 quite:3 approaches:2 carried:1 ask:2 jozsa:1 generate:1 could:1 feasible:1 creates:1 due:1 first:4 initial:2 probability:14 coding:1 number:5 employing:1 simplified:1 least:1 proposing:1 message:1 quality:1 given:4 unitarity:1 unknown:1 system:8 construct:1 their:1 intermediate:1 scheme:19 gives:4 inevitable:1 imperfect:8 lot:2 relationship:1 somewhat:2 authors:1 qld:1 copy:6 than:11 relative:2 supposes:1 wootters:2 determines:1 fuchs:2 ators:1 kraus:1 preparation:1 matter:1 future:3 were:1 naturally:1 distinguished:2 result:5 fig:2 failing:1 correction:1 seen:3 any:4 relatively:2 depending:1 efficient:4 lim:1 latter:1 note:5 equipment:1 ideal:1 take:1 deuar:5 finding:1 destroy:1 detector:13 effectiveness:1 smolin:1 added:2 fundamental:1 opposite:1 who:2 reach:1 most:1 said:1 drummond:1 significant:1 dummy:2 treats:1 considered:4 average:1 later:1 detectors:17 tech:2 physics:3 fact:4 bell:2 random:3 sion:1 defended:1 attempts:1 registers:1 threshold:1 current:1 photodetector:1 parameters:1 situations:1 entangling:3 written:1 controls:1 only:3 pretty:1 probabilities:3 do:1 gains:3 cryptography:1 means:1 spurious:2 syst:2 zurek:2 simplest:2 overall:1 ones:2 words:1 new:2 processes:2 arxiv:1 circuits:1 though:1 photodetectors:4 london:1 fixed:1 discussing:1 available:1 set:4 observer:3 achieved:6 acquired:1 unpublished:1 maximum:2 detection:28 depends:3 cloning:1 enhanced:2 close:1 best:1 subject:1 fails:1 detect:2 ways:1 state:20 determined:1 various:2 jth:2 correctly:1 between:5 caves:2 approach:1 email:2 preserve:1 recently:1 creating:2 nature:1 qubits:2 however:2 efficiency:26 incident:6 concentrate:1 distinguish:1 article:2 come:1 improve:1 both:5 improved:1 always:6 many:1 equal:1 against:1 logic:1 expression:4 finds:1 comes:1 otherwise:3 arbitrarily:1 bruß:1 conclude:2 simple:1 address:2 ease:1 described:1 aˆ:3 create:1 copier:29 copies:12 been:4 defined:1 much:2 interest:2 basic:4 pj:5 inefficiencies:1 ph:1 pi:3 isolating:1 controlled:4 photon:20 requires:1 observers:1 uqcm:1 external:1 former:1 present:2 case:10 laser:1 solid:2 examine:2 evaluated:1 will:9 while:1 suppose:3 error:1 irrespective:1 property:1 layer:1 larger:1 thus:2 them:1 entangler:1 im:12 leaving:1 technology:1 different:2 perhaps:1 things:1 make:2 same:3 quant:1 copying:11 gets:1 infer:1 independent:5 used:3 upon:4 effect:2 hand:1 levels:2 uses:1 entanglement:1 frequently:1 totally:2 identity:1 modeled:2 well:3 analysis:2 obviously:2 concrete:1 without:1 firstly:2 model:4 ekert:1 degrade:1 just:1 less:2 brisbane:1 generally:1 half:1 macroscopic:1 yet:1 adding:2 photons:2 point:1 improvement:3 priori:3 combine:1 lett:1 theorem:1 input:18 5a:1 transformation:3 5b:1 identical:3 australia:1 easily:1 possible:11 dark:3 possibly:1 increases:2 provide:1 unseen:1 vacuum:7 using:11 mod:1 imposed:1 like:1 admittedly:1 signal:1 separately:1 either:1 arbitrary:3 become:1 essential:1 depend:1 because:3 often:3 classical:5 foreseeable:1 some:14 somehow:1 ranking:1 examples:2 happens:1 specific:1 measurements:4 extensively:1 per:2 efficiencies:5 measuring:1 noise:6 equivalent:3 confidence:1 although:2 output:1 properties:1 noisy:2 gained:1 about:4 working:1 extension:1 certainty:3 discussed:2 meaning:1 practical:1 mutually:3 act:1 mixed:1 introduced:1 slightly:3 block:1 ηe:1 follows:2 previously:1 into:2 photodetection:3 obtaining:1 three:2 usefulness:1 queensland:1 appropriate:1 determine:1 ηp:2 operator:3 rely:1 support:1 there:2 question:2 low:1 way:3 forward:1 was:8 iˆ:3 function:2 decoded:1 enough:1 registered:1 but:2 failure:4 gain:3 encoded:1 line:1 trying:1 entered:1 count:5 made:2 originals:2 whether:1 wish:1 implementing:1 uq:2 up:1 us:2 limit:3 similar:2 clear:1 detailed:1 promises:1 computing:1 povm:2 certain:2 measure:1 general:3 single:6 au:2 surmise:1 mutual:5 no:10 amounts:1 dashed:1 whereas:2 when:9 detail:1 application:2 other:7 department:1 realisable:1 poor:2 briefly:1 superposition:1 divincenzo:1 symbol:1 prepared:1 chance:2 additionally:1 included:1 munro:2 assume:1 values:2 required:3 time:2 far:2 4b:1 original:11 4a:1

quant-ph9911104.txt \|@word mind:1 simultaneously:1 consider:1 show:1 indeed:1 bagchi:1 obtain:1 bring:1 underlying:1 statistical:1 constants:1 ψeven:1 expressions:1 ros:1 scattering:1 its:1 controllable:1 parameters:1 hint:1 supersymmetric:1 conclude:1 seems:1 should:1 forms:1 only:2 explicitly:1 choose:1 factor:1 usage:1 derivative:1 hamiltonians:2 reversal:1 match:1 5b:1 real:13 case:2 non:2 rev:2 propose:1 express:1 springer:1 results:2 early:1 cannot:1 dx:2 isical:1 emphasized:1 now:1 possess:1 normalizable:1 2u:1 thus:2 obvious:1 excluding:1 semi:1 hamiltonian:5 exploiting:1 university:1 arxiv:1 yield:1 discrete:1 investigate:1 n1:3 chandra:1 common:1 further:1 found:2 nice:1 communicated:1 parity:1 www:1 en:1 energy:10 under:2 zero:6 differentiable:1 b2:3 table:2 quantum:1 terms:1 odd:1 mimicks:1 borne:1 even:1 savage:1 cooper:1 µx:19 definite:1 detailed:1 denotes:1 symmetric:4 state:3 indian:1 above:1 between:1 new:5 3a:1 contributes:1 either:1 sinh2:2 notice:1 recently:1 whose:1 enforcing:1 however:2 possibility:1 acharya:1 following:2 york:1 sinh:1 trunk:1 concreteness:1 imaginary:1 publication:1 obtained:1 both:1 roychoudhury:1 weisskopf:1 institute:1 practical:1 addition:1 connection:2 levels:2 eigenvalues:4 shared:1 behaviour:1 other:2 road:2 andrianov:1 appropriately:1 mechanics:1 relevant:1 symmetry:1 point:1 substitution:1 requirement:1 negative:1 hermitian:1 references:1 construct:1 isospectral:2 respect:1 unit:1 illustrate:1 considering:2 given:2 asymptotic:1 sake:1 there:1 system:2 been:2 sech2:7 vol:1 3b:1 normalization:1 bender:3 ph:2 consistent:1 gives:2 function:3 main:1 relations:1 2ab:1 form:1 raj:1 expose:1 future:1 but:2 part:1 known:2 ugge:1 level:1 2ib:1 potential:6 those:1 applied:2 wide:1 none:1 made:1 tanh:3 work:1 see:2 us:1 choices:1 will:1 states:1 classes:1 values:2 znojil:2 sech:5 continuously:1 demonstrate:1 boettcher:2 example:1 fernandez:1 result:1 exhibit:1 f1:2 ac:1 associated:1 choosing:1 defined:1 certain:1 abstract:1 india:2 dash:1 footnote:1 our:2 partner:1 tan:1 ernet:1 functions:3 ib:1 end:1 whereas:1 when:1 lett:3 guardiola:1 note:2 complex:12 quant:2 details:1 forming:1 department:1 mathematics:2 text:1 e2i:1 eµx:1 literature:1 problems:1 different:1 meisinger:1 a2:3 purpose:1 letter:1 potentials:4 phase:1 representations:1 wave:1 fl:1 class:1 coinside:1 eigenfunctions:5 task:1 nov:1 especially:1 corresponding:1 light:1 clear:1 spectra:6 well:1 correspond:1 feshbach:1 furnish:1 time:1 n0:3 calcutta:3 physics:1 possesses:1 fact:2

quant-ph9911105.txt \|@word limited:1 consider:11 chain:11 induces:2 results:16 unmeasurable:1 founded:1 commute:1 ψ1m:2 consists:1 follow:1 gk:1 gj:1 localized:3 rd:5 supposedly:1 amplification:1 depend:1 superpositions:1 ferrite:1 pˆj:2 contained:1 send:1 environment:3 citing:1 program:1 indicate:1 excluded:1 marks:1 stochastic:1 analogous:9 include:4 fukuda:1 penetrating:1 springerverlag:1 applied:2 random:1 amplitudes:1 orthogonal:1 very:4 collision:1 springer:1 induce:3 wave:3 umezawa:1 electron:6 crosses:1 experimentally:1 difference:4 exact:2 σyi:1 common:1 evi:1 radiated:1 whitaker:1 obvious:1 quantized:1 level:3 t2:2 applicable:1 t0:5 t1:6 large:7 convenience:1 leninsky:1 demonstrated:1 science:2 small:1 biological:1 suppress:1 upper:1 zn:1 approximately:1 mi:3 consistent:3 measurable:1 approximation:1 surrounding:2 second:1 settled:1 reflected:1 qualitatively:1 copenhagen:1 estimated:1 incompatible:1 quite:4 linear:4 even:8 index:1 contradicts:2 rate:1 ρp:1 sum:3 axes:1 analogously:3 expressed:1 current:7 experiment:3 d0:4 above:2 relational:5 un:1 ground:5 multitude:1 condensed:1 full:2 simultaneously:2 exchange:1 never:2 here:8 atoms:14 shouldn:1 objects:7 ansatz:1 excess:1 dissipated:3 consideration:2 along:1 strong:3 z0:3 appears:3 change:1 z3:1 obtained:5 sending:1 property:2 incoming:1 splitting:1 shift:1 study:4 vectors:1 experience:1 σx0:3 tempting:1 amount:3 substituted:1 through:1 permit:2 principally:10 opinion:2 suitable:2 studies:1 options:1 mutual:1 thermofield:1 via:6 useful:1 divide:1 ρij:1 sgi:1 weaker:1 contradictions:2 rρ:2 stern:2 apply:1 should:5 synthese:1 wouldn:2 predicted:1 use:4 additive:2 projector:1 would:1 prove:1 formulated:1 continuous:1 univers:2 finally:1 next:3 ψj:2 few:1 automata:1 pˆr:1 msk:1 ψm:4 taken:1 ψf:6 start:1 more:8 chapter:2 formally:3 initial:15 operators:15 under:1 conducting:1 deserve:1 berlin:2 correspondingly:1 rigid:2 broke:1 particular:15 known:1 cases:3 hold:1 xn2:1 must:11 bremsstrahlung:1 reconstructed:2 account:3 hamiltonians:1 mc:5 permits:1 decay:1 equation:4 ρm:3 suggestive:1 london:1 theories:1 mt:3 macroscopically:1 obstacle:1 values:4 three:1 ms:43 starts:3 following:4 perturbs:1 example:10 imitation:1 control:1 compare:2 computers:1 impacts:1 give:2 process:4 magnet:2 accept:1 states:51 selfinteraction:5 slit:2 performed:5 reconstruct:1 sense:3 unphysical:1 exclude:1 newly:1 verlag:1 information:50 needs:4 hoc:1 memorize:7 turn:1 rather:1 s2:3 s1:4 di:3 clarification:1 fermion:2 makes:1 till:3 pure:20 answer:1 acta:2 coleman:1 memorization:13 ensemble:3 simplicity:2 product:3 description:8 flip:1 may:1 demonstrates:1 after:12 inessential:1 mapping:1 dc:16 tries:1 pr:1 inst:1 stipulate:1 waves:1 cambridge:1 representations:2 destructive:4 monoatomic:1 attempt:1 collective:6 effective:3 attracts:1 spectra:1 correspond:1 su:1 ziman:1 discussing:1 spectral:1 σzi:1 so:32 fundamental:2 verify:2 representation:5 discussion:3 talk:1 typical:1 restriction:1 acts:1 interpretation:3 produces:2 september:1 developed:1 amplifying:1 insight:1 flips:1 interpreted:1 produced:3 brain:11 thermal:1 paper:8 including:5 looks:2 penetrate:1 differs:3 existence:1 imitate:1 still:2 excitations:7 its:27 prompted:1 before:2 destructively:1 emits:2 derive:1 how:1 interesting:1 ll:17 h2:1 noninteracting:1 microscopic:9 systems:5 stiff:1 mail:1 main:2 spreading:1 ideal:2 maximal:2 eventually:2 them:5 propose:2 material:2 regarding:1 introduce:1 number:2 framework:2 walls:1 nonzero:1 effects:9 they:6 half:3 oxford:1 strates:1 nov:1 now:5 discuss:3 shadows:1 eigenvalue:2 february:1 finite:5 contains:1 always:4 hamiltonian:4 v0:5 identified:2 crudely:1 realistic:6 reasonable:5 each:7 heinemann:1 accompanied:1 interfering:1 characterized:2 mean:3 domain:1 directly:4 density:1 energy:5 ferromagnetism:1 principles:2 elementary:1 altogether:1 extended:1 obtains:2 measure:11 quantum:25 our:34 operation:1 transitions:1 eq:2 event:2 special:1 try:1 shown:7 matrix:1 space:16 restricted:1 surrounded:1 interference:9 semiconductor:1 acting:1 vector:6 performs:2 denoted:1 σyj:1 get:2 ref:1 ri:2 relations:4 shows:1 occurs:2 perception:8 theory:9 interactions:1 hf:2 derived:1 given:3 free:2 standard:6 admits:1 completely:2 complicated:4 int:3 dynamics:3 eigenvalues:1 put:1 indicates:1 estimate:3 implication:1 forbids:1 definition:8 interaction:15 r0:1 automatic:1 route:1 omit:1 decohering:1 motion:2 matrices:1 length:1 produce:2 isn:5 δij:1 distinctions:1 consequence:1 neglect:1 first:8 xi:2 xn:1 features:4 relate:1 parted:1 production:2 philosophical:1 done:1 least:6 another:3 changing:1 impossible:5 array:2 open:2 aperture:1 differ:1 toy:2 exists:3 their:11 introduction:1 unknown:1 interact:7 b2:7 system:13 dfs:5 glauber:3 passed:1 postulate:1 structures:1 final:13 store:3 gives:2 speculates:1 ashtekar:2 inevitable:1 collapse:27 moscow:1 observable:10 albert:1 gas:1 part:2 enigma:1 authors:1 x2:1 probably:1 x1:1 oversimplified:1 dynamical:2 distance:1 kind:4 polarized:1 holland:1 penrose:1 breuer:3 pointers:2 gji:1 finiteness:2 discriminating:1 speaking:1 deserving:1 tion:1 russia:1 acquisition:4 prospect:1 permitted:1 mind:1 lahti:1 turned:1 argument:1 generalization:1 already:1 alike:1 further:4 need:2 sees:1 border:3 any:25 accounted:5 functioning:5 cascade:1 self:2 able:1 ideas:1 mechanism:1 polarization:2 decomposing:1 percept:1 internal:11 take:1 analogy:3 new:7 detector:8 subject:1 channel:2 heisenberg:3 memory:1 oscillate:1 exactly:2 multiple:1 trace:2 object:1 molecule:1 algebraic:3 regular:1 connected:1 ht:4 significant:1 definitions:1 device:2 acquired:2 measured:13 why:1 tensor:3 hj:1 don:11 reduces:1 consequences:1 considered:2 clear:2 partition:2 implications:2 reaction:2 electrons:4 principle:6 lpi:1 lays:1 velocity:1 left:2 physics:2 fact:9 laws:4 sector:2 lebedev:1 restore:1 hm:1 scattered:1 appearing:1 scattering:1 destroy:2 attempts:1 helv:2 relation:4 gerlach:2 wigner:1 magnons:2 d2:1 find:2 paradoxes:1 d1:1 impact:1 rev:4 slow:1 based:2 consciousness:1 parameters:2 rovelli:5 irreversible:3 explain:1 loinger:1 outside:3 operational:8 only:27 he:5 local:2 over:3 regularly:1 do:1 mixture:1 unavailable:1 subspaces:4 means:11 df:7 zurek:2 express:1 stop:1 expectation:2 criticized:2 joint:2 tachiki:1 ones:1 closely:3 despite:5 combinations:2 during:1 selfinteracting:1 chips:1 uneven:1 evolution:19 resolve:1 qu:2 conclusion:1 course:3 conditions:3 arxiv:1 preliminarily:1 b0p:1 factorization:2 investigate:1 scientist:1 qe:2 qd:1 pulses:1 finishing:1 qm:22 cells:1 qo:3 transforms:1 reveals:1 set:2 observer:41 phenomenologically:1 physically:1 frame:1 correlations:2 packet:2 transferred:3 relative:7 see:2 computer:5 nonperturbative:2 result:11 close:1 espagnat:1 analog:1 points:1 commutation:3 µz:15 phonons:3 pointer:4 review:1 rings:1 artificial:1 yet:5 state:96 proof:3 closed:1 between:11 incompatibility:1 progress:1 mathematical:1 previous:1 approach:9 supposed:1 available:1 notice:2 terms:5 adding:1 initially:2 processes:1 attention:1 analyzer:1 hypothesis:3 extent:1 separately:1 b2p:1 restrictions:14 interpretations:1 memorized:3 many:2 taking:3 uncertainty:1 assumed:3 constructed:1 quantization:1 fulfilled:1 etc:2 connection:2 decompose:4 distinction:3 argue:1 disappears:1 photons:5 experimental:2 otherwise:1 unitarily:1 strongly:1 ch:16 excites:1 conclude:1 simple:4 had:1 unitary:2 corresponds:4 except:2 dimensional:1 ψi:2 simply:1 confirmed:1 numbers:2 dependent:1 moreover:3 dislocation:1 throughout:2 considers:1 ad:1 considering:1 sensible:1 most:1 described:15 transformations:1 basis:3 addition:1 discrimination:1 ing:1 due:14 ai:7 reduction:2 much:1 slowly:1 pj:1 degrees:1 ph:2 σz0:4 box:5 describe:6 corresponding:6 both:5 influence:2 transferring:1 subspace:9 coincides:1 observers:6 finished:6 understand:1 external:6 demand:2 presented:1 spin:17 manifolds:1 selforganization:1 case:9 look:1 solid:4 appearance:3 conserved:1 value:11 excited:2 will:15 suppose:6 promising:1 σxi:4 properly:2 σxk:1 loop:4 landauer:1 resolved:1 detailed:2 studied:3 ve:1 coupled:1 phenomenological:2 vi:1 thus:1 equal:1 itself:2 properties:1 reports:1 busch:1 interacts:1 conserve:1 currents:2 binary:4 different:8 cji:1 italy:1 multiphoton:1 perform:5 make:2 belong:1 radiation:9 lett:1 same:9 dγ:2 beside:1 complex:1 quant:2 φf:2 φi:2 defines:2 independent:2 used:5 everett:1 trajectories:1 effect:2 effectively:2 moment:2 purpose:2 entanglement:2 paradox:3 single:4 destruction:1 eigenvectors:1 lower:1 correspondent:1 kept:1 reflection:1 largely:1 nevertheless:1 changes:3 obstacles:2 well:2 roughly:1 analysis:1 obviously:2 solids:1 without:4 matsumoto:1 simulated:1 coordinate:1 position:1 model:40 entangled:3 distances:1 construct:2 manifold:4 proposed:2 cj:2 observed:3 obtain:1 rest:1 ne:3 stored:2 atomic:4 human:5 macroscopic:3 eigenstates:6 mittelstaedt:1 projection:2 note:8 inelastic:1 mirrors:5 conclusions:3 regarded:6 bnp:1 seems:5 lake:1 evidences:3 lattice:6 potential:4 transformed:1 choice:1 easy:1 ρ0m:2 input:2 iσ:1 eigenstate:1 real:7 journ:3 depends:1 demands:1 dissipative:1 dislocations:1 decomposed:2 possible:4 spanned:1 know:1 ψ0m:1 vacuum:5 world:7 bit:1 stable:2 coincide:4 formal:2 improper:1 necessary:4 like:12 particle:4 follows:6 signal:10 performing:1 specific:1 collect:1 arbitrary:2 slits:2 soft:1 essential:1 spins:3 therein:1 because:5 qed:5 classical:5 sequence:2 absolutely:1 successfully:1 some:35 back:1 donald:1 b1:2 complete:7 mirror:2 proper:1 neglecting:1 dc0:4 bell:1 xn1:2 ignore:1 total:1 describing:5 electromagnetic:6 avoid:1 measurements:9 stops:2 decomposition:1 assuming:6 nondestructive:2 particles:2 chains:3 o2:2 o1:3 measuring:4 conference:1 dcm:1 obey:1 bm:4 jumps:1 processing:8 bi:2 bj:1 packets:1 prohibited:1 references:1 found:4 analyses:1 hilbert:11 asymptotic:1 gained:1 comparison:4 about:7 extending:1 freedom:1 discussed:5 o:159 reduced:1 compatible:1 range:1 important:4 obeys:5 neighbor:2 mixed:24 introduced:1 consequently:3 processor:2 considerations:1 perturbed:1 own:5 nonequivalent:3 previously:1 into:13 h1:1 integral:1 jγ:4 down:1 dissipation:2 hermitian:5 right:2 accounts:1 imitates:1 operator:25 amsterdam:1 reabsorbed:1 often:3 schrodinger:5 statistics:1 additional:3 comparing:1 aren:1 transfer:2 strictly:2 there:5 u0:4 long:1 avail:1 strict:10 restricts:1 describes:4 way:1 conceivable:1 analyze:1 was:8 function:9 ef:8 north:1 irreversibility:3 form:6 metastable:1 hs:2 regard:5 but:37 idea:1 subjective:6 reminds:2 neutral:1 hi:11 hn:1 ho:4 hl:1 atom:1 photon:6 hc:4 true:8 utilizing:1 hd:2 amplify:1 consist:4 wish:1 inside:7 uq:1 up:1 us:2 crystal:5 below:2 decays:1 ui:3 verification:1 observation:2 demonstrate:1 problem:8 define:1 character:1 called:3 chip:1 expect:1 mechanics:2 ac:4 conserves:1 hepp:2 defined:7 detectors:5 abstract:1 measurement:59 linearity:1 doesn:5 general:8 chap:6 reliability:1 exist:1 reflecting:1 formalism:7 check:1 physical:6 again:1 functions:2 compared:1 discriminate:7 no:7 asymmetry:1 dc2:2 nc:6 when:4 phonon:2 reality:1 members:2 field:14 other:12 role:2 branch:1 becomes:2 theor:3 unobservable:14 expected:1 gaining:1 picture:1 elements:2 kinds:1 superposition:2 excitation:1 models:25 excite:2 a18:1 includes:3 a1:8 a0:1 meaning:1 a2:7 n1:1 included:1 needed:1 structure:16 regime:1 probabilistic:1 practically:1 assume:2 normally:1 changed:2 interacting:1 d26:1 ments:1 reversible:1 weights:1 procedure:1 b1p:1 time:10 observables:5 decoherence:16 starting:2 restored:1

quant-ph9911106.txt \|@word camacho:12 measurements:11 consider:8 rev:6 preparations:1 results:2 eds:2 concept:2 controversial:1 gm:2 instantaneous:3 whose:1 depend:1 calculate:3 equivalence:1 braginsky:3 finally:2 those:3 under:2 include:2 case:26 hibbs:1 very:5 account:4 atoms:1 wave:3 surprise:1 coulombian:1 difference:1 condition:2 disturb:1 level:2 lanz:1 proposals:2 solution:2 small:2 equation:3 heinz:1 zh:1 direct:1 cosh:3 feasibility:1 zero:2 further:1 dynamics:1 expressions:1 linear:3 even:4 what:1 plays:2 appear:3 current:1 experiment:6 above:1 international:2 learned:1 acknowledgments:1 justification:1 presilla:1 honour:1 here:7 understanding:1 behaviour:1 believed:1 free:2 sinh:1 path:12 vorontsov:2 appears:7 change:1 deduced:1 operational:1 remark:1 remarks:1 institute:1 involved:1 study:1 allows:2 sternwarte:1 hospitality:1 involves:2 65th:1 emerge:2 family:4 elaborated:1 dedicated:1 sliced:1 analyzing:1 total:1 propagators:1 readily:2 would:2 probabilities:4 contains:2 predictions:2 imω:1 noting:1 therefore:3 m2:5 taken:3 associated:3 type:1 theoretical:2 more:3 outputs:4 company:1 validity:1 tested:2 berlin:1 particular:1 known:1 4am:1 cases:1 must:4 topic:1 mg:3 word:1 rβ:1 der:1 work:5 oscillator:5 ρl:1 renders:1 pioneered:1 example:1 compare:1 process:10 sense:3 1980s:1 performed:1 allowed:1 absolute:7 information:2 monitoring:4 technology:1 discussion:1 reuter:1 feature:4 located:2 nontrivial:1 stemming:1 xxxi:1 answer:1 instead:1 parameter:1 sin:2 b72:1 may:12 immersed:2 after:5 containing:1 hence:2 mac:1 birthday:1 trapping:1 coming:2 choice:2 response:1 gaussian:3 remember:1 light:1 approximation:3 grant:1 acknowledged:1 thorne:1 element:1 so:3 fundamental:2 definitions:1 looking:1 order:5 interpretation:1 words:4 noteworthy:2 indeed:4 over:1 course:1 experiments:2 through:1 experimentally:1 mentioned:1 satisfies:2 its:3 before:4 tending:1 probability:14 img:1 how:1 chosen:2 interesting:2 khalili:3 fruitful:1 better:1 resort:1 systems:1 schmidt:1 decades:1 weber:1 non:1 orthodox:1 evolution:1 introduce:3 effects:6 they:3 now:4 easily:1 finite:1 name:1 always:3 university:2 hamiltonian:2 prosperi:1 2g:32 l2:2 each:3 2m:14 mean:1 domain:2 differential:2 sosa:1 weight:9 series:1 idea:3 related:2 inhomogeneous:5 frequency:2 expect:1 measurement:24 quantum:33 our:11 avoided:1 es:1 out:2 shown:1 restricted:1 nuovo:2 since:1 lagrangian:1 denotes:2 astrophysikalisches:2 hill:1 formula:1 issue:1 shows:2 8i:2 theory:2 mσ:2 found:1 mω:7 liebscher:1 possibility:2 standard:3 york:2 regarding:1 r2:1 geometry:1 could:11 bears:1 american:2 βg:1 nondemolition:4 consequence:3 teor:1 first:3 already:7 neccesary:1 features:1 render:1 striking:1 opez:1 radical:1 variables:8 xx:1 employing:1 done:4 another:5 comprises:5 impossible:1 given:1 colella:1 smaller:1 rewritten:1 hyperbolic:1 introduction:1 system:2 their:1 cooling:1 statement:2 postulate:1 gives:1 collapse:1 continuous:5 peculiar:1 traps:2 distance:2 kind:4 determines:1 kindly:1 princeton:2 cimento:2 see:4 charges:1 determined:2 were:3 galv:3 rainer:1 rewrite:1 ann:1 modern:4 conjugate:4 seen:1 cosmology:1 any:1 seminar:1 paths:4 realm:3 able:1 gravity:3 instance:3 potential:2 gσ:1 take:1 measurability:1 sakurai:1 coincide:1 canonical:4 heisenberg:1 allow:1 gα:1 most:2 germany:1 ht:2 device:4 analytically:1 measured:8 why:3 exico:1 considered:2 calculated:4 neutral:1 feynman:3 proceedings:2 principle:2 exp:12 mechanical:1 a262:1 physics:7 fact:6 quantity:2 precise:1 emerging:1 supported:1 purely:1 relation:3 earth:4 find:6 help:1 aσ:1 dehmelt:1 explain:2 b114:1 should:1 only:8 explicitly:1 school:1 employed:1 do:2 his:1 means:2 de:1 mgl:2 mgr:1 ones:1 aforementioned:3 new:3 dt:11 coth:1 processes:2 approach:2 arxiv:1 grav:1 d55:1 qd:7 analytical:1 reference:1 ωt:4 namely:7 radius:2 result:2 discussions:1 paul:3 subject:3 said:1 8a2:1 functionals:1 difficulties:2 between:2 conceptual:2 geometric:1 reading:1 conditions:2 email:1 notice:4 latin:1 complementary:1 importance:2 omn:1 4m2h:2 vanishing:2 jetp:1 endows:1 thank:1 observable:2 cos:2 last:5 uncertainty:1 equal:1 against:1 fulfilled:1 fiz:1 connection:3 context:1 hσ:2 contribution:1 σp:1 expression:15 experimental:8 arbitrarily:1 onofrio:3 relevant:2 co:2 afterwards:3 point:10 simple:1 wonder:1 harmonic:5 hm2:2 dimensional:4 werner:2 comprehension:1 respect:2 ct:2 considering:1 described:1 publishing:2 simplification:2 been:10 reduction:1 pa:1 pe:1 ph:1 choose:3 addison:1 direction:2 corresponding:7 concerning:1 else:1 assert:1 2im:4 understand:1 stems:2 present:4 2ia:1 p2:4 extracted:1 laser:2 tanh:12 defining:1 appearance:1 aip:2 will:3 near:2 momentum:3 error:4 situation:6 barchielli:1 mensky:6 century:1 von:1 them:1 surface:2 reads:3 demolition:3 disappear:1 begining:1 different:1 author:1 perform:1 make:1 same:6 clearly:3 complex:2 quant:1 viola:2 physical:2 difficult:1 independent:1 finish:1 overhauser:2 bristol:1 singapore:2 trajectories:1 upon:4 effect:2 iop:1 moving:4 kleinert:1 task:1 center:1 nevertheless:3 deal:1 academic:1 without:2 solve:1 position:7 model:2 possesses:1 comment:2 proposed:1 less:1 being:1 newton:1 trigonometric:1 obtain:5 momenta:1 underline:1 4m2:12 disturbance:1 monitored:3 4a2:1 gmm:2 conclusions:1 had:1 mathematically:2 source:4 add:2 conacyt:1 lett:7 relevance:1 match:2 idealization:2 around:1 possible:4 know:6 press:2 world:2 emergence:2 mod:6 necessary:2 like:1 particle:15 follows:2 future:1 performing:1 audretsch:1 integrals:3 output:5 works:1 orozco:1 page:2 mathematical:3 shed:1 classified:1 neumann:1 classical:4 some:5 springer:1 hacyan:1 polymer:1 understood:1 deduce:1 election:1 uspekhi:1 duration:2 matching:1 electric:2 happens:1 αa2:1 dehnen:1 avoid:1 unavoidable:1 integration:3 planck:2 does:6 measuring:17 conference:1 dittrich:1 measurment:1 equivalent:1 qnd:14 wesley:1 substituted:1 lasts:1 gm2:1 tanh2:1 perspectives:1 comparison:1 about:4 carried:2 simplify:1 instantaneously:2 graw:1 discussed:1 practical:1 remains:2 a2:45 trajectory:1 introduced:2 cambridge:2 inclusion:1 h2:5 into:4 integral:8 functional:9 lies:1 references:1 sov:1 operator:2 cuevas:1 letts:1 statistics:1 institut:2 additional:2 there:8 question:2 philadelphia:1 class:1 intention:1 restricts:2 much:1 way:2 ed:1 scientific:2 analyze:2 was:5 propagator:7 function:5 form:2 differences:1 jun:1 but:10 formalisms:1 repeated:1 magnitude:1 hm:1 eksp:1 proposal:1 interferometer:1 characteristic:4 gravitational:11 up:1 us:9 4im:1 limit:15 d20:1 continuously:2 problem:8 similar:1 called:4 mechanics:5 constant:7 certain:2 abstract:1 measure:3 single:1 journal:1 formalism:1 defines:2 again:3 functions:2 antenna:1 no:8 na:1 when:5 vanishes:1 field:11 other:6 role:2 potsdam:4 becomes:3 test:3 a14:3 elements:1 a12:1 4i:1 problems:2 meaning:2 important:2 variable:12 coupling:2 penning:2 interval:1 having:3 4m:3 mass:7 time:4 far:1 decoherence:1 resolution:5 original:1 once:3

quant-ph9911108.txt \|@word ibid:1 represent:1 logarithms:1 quarks:3 partial:1 consider:11 similarity:1 rev:6 results:2 existing:1 leads:2 scalar:24 ga:2 sci:2 sation:1 certainly:1 depend:2 isosinglet:1 tr:3 petersburg:4 under:1 analogous:1 include:2 b147:1 belonging:1 nσ:2 g2:1 advantage:1 rise:1 rqcd:3 dokl:1 matrices:2 discovered:1 school:1 dominate:1 level:1 proc:2 solution:2 trf:6 large:1 vector:9 small:1 gauge:2 upper:2 work:2 zh:1 renormalized:1 za:1 sign:1 approximation:2 second:1 mφ:5 zu:2 dynamics:1 implemented:1 b138:1 victor:1 even:1 aim:1 what:1 nonlinear:3 appear:1 giving:1 expressed:3 d3:1 current:1 axial:2 experiment:1 new:2 increasing:2 method:1 coefficient:1 lef:13 fiz:2 eksp:1 shankar:1 here:2 understanding:1 asymmetry:3 groups:4 represented:1 consideration:1 strong:6 equations:1 appears:1 change:3 obtained:1 study:2 reason:1 leaving:1 resulting:1 published:1 action:13 suitable:1 changes:1 gluons:1 scales:2 gluon:9 anomalies:1 condensates:10 m2φ:6 total:1 tools:1 use:5 takes:1 would:1 covariant:1 positive:5 eχ:1 contains:2 france:1 nucl:1 renormalisation:2 qcd:5 theoretical:3 ψd:1 more:3 composite:29 becomes:2 known:1 chiral:7 dim2:1 account:2 ma:1 integrating:4 equation:2 des:1 theories:1 fock:5 following:1 arrive:1 example:3 f0:1 compare:1 renormalization:1 give:2 states:1 effectively:1 dxl:3 numbers:3 standard:1 quark:21 provide:1 157b:1 get:4 instead:1 parameter:2 description:3 may:4 after:1 inessential:4 containing:1 wrong:1 sankt:1 mψ:2 dynamical:6 effective:12 higgs:1 correspond:1 st:3 dilaton:4 so:2 fundamental:1 representation:2 first:4 order:5 gµν:12 origin:1 breaking:2 dx:2 produces:2 over:10 held:1 paper:1 through:3 existence:1 kinetic:5 its:5 derive:1 group:6 symmetry:3 decay:2 ln:3 masses:4 lm:2 decreases:1 lv:1 absence:1 degrees:6 systems:4 derivative:1 main:3 into:5 maximal:1 non:3 thereby:2 ya:1 practice:1 operator:1 break:1 framework:1 they:1 nov:1 now:1 yu:15 discuss:1 developments:1 chromodynamics:1 represents:1 term:3 φk:1 dirac:2 name:1 invariants:1 university:2 presented:1 m2a:3 identified:2 fπ:2 mode:1 l0:3 found:3 higher:1 2i:2 ei:1 another:1 weight:1 3fπ2:1 generation:1 ed:1 energy:11 related:2 bosonization:1 used:1 isospin:1 interplay:1 entering:1 combining:1 quantum:22 our:1 beyond:1 out:6 space:6 nuovo:1 lagrangian:19 particles:4 got:1 induced:12 evaluation:1 integrated:1 math:2 earlier:1 theory:9 interactions:2 fondation:1 differ:1 quite:2 approaches:3 yuri:1 definition:3 interaction:5 longwave:1 language:2 widths:1 omit:1 moment:1 david:1 corrections:2 quadratically:1 teor:2 zφ:2 integrand:1 xj:1 there:1 features:1 probability:1 variables:18 number:2 reaches:1 minimum:2 directly:1 wadia:1 calculational:1 given:3 perturbation:1 zψ:9 πd:1 their:3 introduction:1 condensate:8 system:5 relations:2 needed:1 assumption:1 fermions:6 gives:1 novozhilov:19 moscow:1 electroweak:1 part:5 constituent:1 july:1 than:2 coefficients:1 m3:1 see:2 matter:5 classes:2 were:3 russia:1 ann:1 modern:2 measure:3 argument:1 akν:1 curved:2 zero:1 depending:1 self:1 gravity:4 mechanism:1 internal:2 take:2 bogolubov:1 jacobian:3 zs:3 elias:1 spectral:2 though:1 trφ:1 most:1 g2µν:1 class:1 constructed:1 considered:2 coincides:2 graphs:1 proceedings:1 exp:13 shirkov:1 physics:4 fact:1 slope:1 phenomenon:3 show:1 supported:1 notations:1 colors:1 relation:4 carefully:1 find:4 decade:1 impact:1 knowledge:3 parameters:7 explain:1 should:6 only:5 explicitly:1 ambiguity:1 factor:2 integrate:2 local:1 hope:1 do:1 2mq:2 vainstein:1 zeldovich:2 viewpoint:1 means:2 simplest:1 expectation:1 a2ν:1 pions:1 cannot:2 words:1 soloviev:1 combinations:1 aν:11 qq:2 volkov:1 fields:27 arxiv:1 common:1 characteristic:2 diquarks:1 φei:1 namely:2 bare:1 result:2 dµ:3 acquires:1 interacting:1 ways:2 review:1 functionals:1 state:2 identification:2 between:3 b225:1 invariant:5 approach:10 nambu:2 terms:11 πei:1 however:1 vanishing:1 jetp:1 τk:4 both:3 qft:4 many:3 salpeter:2 la:1 etc:1 forgotten:1 contribution:7 disappears:1 schroedinger:1 comes:1 relevant:1 reconsidered:1 point:1 simple:1 lagrangians:1 cg:3 corresponds:1 qgq:1 path:8 respect:2 cq:2 indefinite:1 pseudoscalar:4 speak:1 conference:1 isotriplet:1 described:4 transformations:2 z0:2 create:1 radiative:1 due:4 int:1 describes:2 microscopic:2 ph:1 universal:1 compositeness:16 generating:1 arises:3 corresponding:2 scalars:5 noninvariance:1 2g12:1 external:6 denote:2 present:4 case:12 look:1 103a:1 value:2 transformation:3 will:3 euclidean:1 while:3 dν:1 viii:1 situation:1 conformal:1 region:7 loop:2 3nc:2 metric:3 thus:5 them:1 iw:1 mqq:1 fermion:3 disappear:1 rfbr:1 different:6 pis:1 develop:1 φu:3 grant:2 radiation:1 same:5 φa:4 complex:3 quant:1 pauli:1 finite:5 composition:1 difficult:1 independent:3 extended:3 running:2 purpose:1 necessity:1 changing:1 invariance:3 normalization:1 lower:1 task:1 gv:1 well:2 2ga:1 without:1 solve:1 consistency:1 model:12 reintroduce:1 λs:4 restore:1 just:1 newton:1 obtain:1 actions:1 reviewed:1 λa:1 underlying:2 σnc:1 unesco:1 flavor:2 ldx:1 macroscopic:1 enters:2 wef:4 conclusions:1 zakharov:1 dhar:1 add:1 potential:7 lett:10 iπ:3 remaining:1 depends:1 easily:1 background:8 vacuum:10 necessary:2 vν:4 mod:1 δz:2 particle:6 identifying:1 follows:1 collective:21 sakharov:2 serves:2 separately:1 integrals:1 decrease:1 composites:1 reduces:1 replacement:1 acad:2 b343:1 classical:6 creation:1 some:1 zz0:1 understood:1 einsteinian:1 choosing:2 normalisation:1 scale:22 describing:3 lead:1 malization:1 separate:1 integration:8 mesons:11 does:5 provides:1 closely:1 demonstrated:1 run:1 rep:1 equivalent:1 quarkonia:1 broken:1 2m:1 refers:1 properties:2 about:1 column:1 freedom:5 b351:1 pronko:1 meson:2 introduced:2 consequently:2 kaons:1 cutoff:1 mixture:1 dyson:2 within:1 integral:9 functional:12 andrianov:6 appropriate:1 ussr:1 references:1 einstein:1 elementary:4 fortsch:1 rows:2 additional:2 vassilevich:3 initial:4 transform:2 why:1 width:1 bosons:1 low:8 way:2 was:4 function:2 considerably:1 irreversibility:1 form:3 phenomena:1 but:3 aµ:2 line:1 adler:2 absent:2 made:1 mat:1 whether:1 minkowski:1 gravitational:1 up:3 us:5 bethe:2 bogolyubov:2 shifman:1 fluctuations:3 problem:2 similar:2 mechanics:1 required:1 constant:7 defined:7 abstract:1 describe:2 influence:1 lasinio:2 general:1 loops:2 single:2 guessed:1 exist:2 scadron:1 nonleptonic:1 formalism:1 regime:4 compared:1 cim:1 dressed:1 nc:9 when:10 schwinger:2 field:41 jona:2 other:3 nat:1 department:1 picture:1 briefly:1 superconductivity:2 models:3 problems:1 polynomials:1 includes:1 substract:1 a0:1 ξn:2 variable:3 honour:1 gets:1 structure:1 hayashi:1 independently:1 coupling:7 pion:1 assume:3 requires:1 proposed:1 rs:1 rather:1 together:1 mass:12 2mψ:1 vestnik:2 starting:1 original:1 vµ:2

quant-ph9911109.txt \|@word passively:1 consider:1 illustrates:1 rev:15 activated:1 results:4 four:5 avalanche:1 broader:1 reasoning:1 localized:1 maximally:1 depend:1 calculate:2 nonlocal:1 supported:1 finally:1 compensate:1 device:1 preserved:3 stable:3 tb:1 sent:1 ta:1 case:6 labels:1 amplitudes:2 advantage:4 peaks:3 hughes:1 splitting:1 chooses:1 stays:1 difference:8 condition:1 leads:3 swapping:1 pbs:2 presented:1 did:1 pacs:1 t0:4 prototypes:1 large:2 discrete:2 detected:5 phase:5 red:1 indices:1 chemically:1 smaller:4 pulse:15 second:5 noise:2 pass:1 manipulating:1 repetition:1 port:3 shows:1 even:1 nonlinear:2 stands:1 rate:2 bo3:1 labeled:2 access:1 experiment:3 above:1 utkenhaus:1 new:5 increasing:2 public:1 contrast:1 counters:1 opposition:2 quenched:1 respectively:4 never:1 circulator:1 teleportation:1 behaviour:2 following:1 asymmetry:1 intercept:1 free:1 path:4 table:4 change:2 separating:1 technical:1 leaves:1 vulnerability:2 leaving:1 simultaneous:1 simply:1 bob:18 york:1 composed:1 control:2 via:6 stabilization:1 secure:2 explained:1 modifying:1 herzog:2 inequality:1 decrease:1 establish:1 bangalore:1 use:3 refers:1 ieee:2 working:1 probabilities:1 faint:4 arms:2 loops:1 error:2 therefore:1 indistinguishable:1 type:2 more:5 separated:1 introducing:3 knows:3 india:1 emission:4 visibility:2 tested:1 controlling:1 furusawa:1 cases:4 producing:1 must:2 franson:2 stabilized:1 mm:2 science:2 setup:6 work:1 nonmaximally:1 attacks:1 mw:2 renders:1 morgan:1 growing:1 drops:1 example:1 point:2 weaker:1 boschi:1 coincident:2 mirrors:1 process:4 bennett:2 neglected:1 stressing:1 states:18 really:1 degenerate:1 bechmann:1 keep:1 occur:1 ratio:1 information:1 end:2 varied:1 technology:1 travel:3 holds:2 located:1 consist:1 instead:2 guarantee:1 brassard:3 fs:1 overall:2 fed:1 containing:1 applications:2 wrong:2 demonstrating:1 fits:1 wave:1 data:1 bouwmeester:2 ambiguous:1 short:9 remember:2 whenever:2 light:8 sp:6 complexity:1 so:2 enter:1 sb:3 sa:3 operate:1 order:6 pulsed:1 developed:2 over:5 years:2 stability:1 paper:2 pulses:11 looks:1 eavesdropping:2 mentioned:2 peterson:1 still:3 fwhm:1 its:3 before:2 perfect:2 horizontally:1 group:1 thank:1 la:3 energies:2 interesting:1 window:1 fig:6 lp:6 quant:3 photodiodes:1 focussed:4 them:5 combination:2 evolution:2 introduce:1 number:6 they:2 half:2 oxford:1 nov:1 now:7 silver:1 nos:1 ribordy:2 always:2 university:1 gautier:2 infer:1 possibilities:1 transmission:1 fringes:1 transmitted:1 mode:1 each:4 inherent:1 polzik:1 ports:3 mean:4 domain:1 engendered:1 detect:3 generation:2 energy:24 idea:2 manifests:1 interferometer:15 frequency:1 gates:1 measure:4 quantum:27 our:8 eq:2 special:1 out:1 travels:1 shown:1 furthermore:1 since:7 interference:3 acting:2 rg:1 dominated:1 reader:1 mattle:3 electronics:1 issue:1 interchanging:1 singlemode:1 zeilinger:4 fiber:11 telecommunication:1 found:3 birefringence:1 perfectly:2 possibility:2 standard:1 small:6 base:7 advantages:1 conditioning:1 besides:5 detecting:1 jozsa:1 generate:1 publication:1 pairs:10 michler:1 created:2 computers:1 messages:1 times:6 filter:1 turn:1 length:5 place:1 including:1 unknown:2 hence:4 onto:1 first:4 jennewein:1 owens:1 major:1 initial:2 probability:4 coding:1 reflected:1 traveled:5 improvements:1 long:9 another:2 michelson:3 dispersive:1 passes:1 given:2 temperature:3 leading:5 system:1 approximately:1 circumvented:1 their:1 attack:2 assumption:1 rates:9 scheme:5 bits:2 speaking:1 eavesdrop:1 behind:2 wavelength:2 exactly:2 tapster:1 optical:5 somewhat:1 herself:1 than:6 coefficients:1 distance:4 kind:2 polarized:1 fuchs:2 depends:1 rarity:1 collinear:1 absence:1 townsend:1 impinge:1 sister:1 enables:2 spectrum:1 already:1 idler:1 increment:1 seen:2 weinfurter:5 demonstration:1 any:5 geneva:2 zero:1 depending:1 note:5 instance:4 absorbed:1 take:2 griffiths:1 finding:1 detector:11 continuous:1 investigations:1 measures:2 most:5 errors:5 connected:1 waveplates:1 unmeasured:1 pair:5 deviations:1 especially:1 average:2 detectors:9 kn:1 km:1 face:2 braunstein:1 proceedings:1 principle:1 mechanical:1 left:4 physics:4 fact:3 quantity:1 intensity:1 show:2 violation:1 diode:2 random:1 infrared:1 serving:1 relation:1 dimension:1 find:7 slot:2 based:7 popescu:1 implementation:1 bobs:1 state:4 only:6 bases:4 pasquinucci:1 eibl:1 emitting:1 pointed:1 do:1 his:2 cryptography:11 dd:1 de:1 db:4 probably:1 during:1 resend:2 processes:2 places:1 settings:1 fields:1 arxiv:1 seperated:1 yield:1 consisting:1 europhys:1 she:6 switzerland:1 through:1 fixed:1 arrival:1 decides:1 fascinating:1 correlations:4 lett:14 detection:10 see:2 actively:1 sec:3 operated:1 uncorrelated:2 arm:8 best:1 phases:6 downconverted:3 inequalities:2 placed:1 subsequent:4 complementary:2 please:1 label:1 µm:1 pump:21 between:6 progress:1 preserve:1 terms:2 statistically:1 nature:2 emitted:3 weak:1 however:5 cut:1 key:12 rapidly:1 come:1 problem:2 both:13 providing:1 last:4 desired:1 rhodes:1 taking:1 equal:2 against:2 agree:1 chosen:2 pdl:1 context:1 polarizing:1 contribution:1 whole:1 experimental:3 otherwise:1 arbitrarily:1 ch:1 afterwards:1 characterization:1 wootters:1 corresponds:2 coincidence:2 dimensional:1 maintained:2 qber:8 sequences:1 respect:2 slots:2 conference:1 passive:1 ensures:2 described:2 particulary:1 basis:7 addition:1 create:1 three:6 been:6 strategy:2 secret:3 describes:1 deposited:1 oriented:1 pj:2 ph:3 pi:1 systems:3 sanders:1 generating:2 tittel:8 sorensen:1 concerning:2 coherence:2 photon:36 bulk:1 controller:1 ensuring:2 understand:1 niu:1 isolator:1 denote:1 assigning:1 present:2 applied:1 exception:1 novel:1 laser:7 look:2 publicly:1 brendel:5 bb84:1 kimble:1 value:1 will:8 intercepts:1 situation:1 property:1 opt:1 losses:6 almost:1 thus:6 non:5 discrepancy:1 ii:1 coupler:3 coincidences:5 itself:2 triple:3 faraday:1 different:10 martini:1 fibers:1 cross:2 same:11 tells:1 pad:1 split:2 mor:1 several:1 events:10 pan:2 european:1 satellite:4 used:4 phasematching:1 optic:1 welsh:1 inbetween:2 codes:1 entanglement:7 changing:1 implement:2 recent:3 implements:1 interferometers:6 lower:1 nevertheless:1 adapted:1 min:1 well:7 roughly:1 obviously:1 person:1 without:3 swiss:1 circulators:1 chosing:1 know:1 distances:4 lb:3 protocol:1 proposed:1 being:5 guided:2 germanium:1 distant:1 world:2 previous:1 polarization:4 enters:1 trigger:2 photons:18 bell:12 favouring:1 signals:2 source:3 lets:1 treatment:2 input:1 remaining:2 build:1 real:1 march:1 around:8 evaluate:1 showing:2 possible:1 dark:1 increases:2 entangled:5 press:1 using:12 bit:3 projects:1 necessary:1 like:6 particle:1 hardy:1 exploiting:1 signal:2 alice:19 serves:2 controllers:1 detections:2 mhz:1 either:2 follows:1 output:4 security:1 works:1 cooled:1 mathematical:1 right:5 schematics:1 deal:1 sequence:1 sends:1 creation:1 some:1 back:1 moreover:2 duration:1 dense:1 lead:2 per:4 efficiencies:4 visibilities:1 demonstrated:1 refer:3 measuring:1 mimicking:1 who:1 quantph:2 power:2 slight:1 equivalent:3 processing:1 combines:1 clarendon:1 eiφ:1 article:2 exciting:1 properties:1 about:2 central:3 would:1 eavesdropper:7 o:1 kwiat:1 ensure:5 equalize:1 introduced:1 allowing:1 muller:1 beamsplitter:1 presence:2 communication:4 into:11 within:8 due:6 down:1 contrasts:2 appropriate:1 schemes:3 parties:1 revealing:3 additional:1 her:2 support:1 there:5 fast:4 accordingly:1 appl:1 quanta:1 low:2 actuator:1 was:4 hz:1 runs:1 complete:1 enough:3 differences:1 denoting:1 but:2 weihs:1 delivery:1 hk:1 injection:1 he:1 count:4 made:2 intuitive:1 whether:1 inside:1 up:5 crystal:6 converted:1 mature:1 demonstrate:1 distribution:9 geiger:1 similar:1 called:3 gisin:10 khz:2 cirac:1 constant:1 certain:1 measurement:4 decrypt:1 ist:1 general:2 peres:2 complementarity:2 single:5 mostly:1 laboratory:3 controlled:1 huttner:1 commuting:1 compared:2 encrypt:1 nm:2 no:3 ekert:3 when:4 detail:1 preventing:1 application:2 prism:1 other:6 test:1 ns:1 sufficient:1 branca:1 conclude:1 simon:1 accidental:1 prepared:1 important:1 peak:4 describing:1 zbinden:7 max:1 correlated:9 values:5 required:1 coherent:1 observe:1 time:30 international:1 resolution:1 having:4

quant-ph9911110.txt \|@word concept:1 crucial:1 leads:1 eds:1 scalar:3 follow:2 rot:1 issues:1 depend:1 aug:1 charge:3 aut:1 under:2 analogous:1 divergent:2 p2:10 fond:1 choice:2 puzzles:1 matrices:3 condition:3 presented:1 did:1 irreducible:1 leave:1 solved:1 vector:7 science:2 indices:1 eigenvalues:1 der:1 concluded:2 work:1 zj:1 htm:1 unpolarized:1 sign:1 zero:2 substitute:1 theory:3 index:1 what:1 giving:1 interactions:1 current:3 fock:1 mexican:1 above:4 new:3 equivalent:3 that2:1 coefficient:1 full:2 ibid:2 honour:1 here:2 possibility:2 consideration:2 november:1 equations:23 change:2 obtained:2 antisymmetric:4 leaves:1 studied:1 stressed:1 usually:2 opinion:1 therein:1 makes:1 useful:1 merwe:1 9b:1 ipl:1 ipr:1 contradictions:1 reχ:2 coester:1 derivatives:2 indicated:1 would:4 finally:2 substitutions:1 few:1 nucl:1 therefore:1 m2:2 taken:1 nonpotential:1 theoretical:1 ramond:2 becomes:1 factor:1 aware:1 ip2:1 ip3:2 particular:1 known:1 foundations:1 account:1 monopoles:1 room:2 electrodynamic:1 equation:9 fµν:4 iα0:1 theories:3 assumptions:1 publications:1 following:2 my:3 mx:2 claim:1 prohibiting:1 imχ:2 relativistic:2 states:2 lorentz:3 firmly:1 information:1 acts:1 symposium:1 parameter:1 pub:1 ft:1 description:1 singular:1 may:8 after:7 derived:2 confirmed:1 consequence:1 explored:1 sistema:1 multiplication:1 representations:2 law:1 sz:3 sy:3 sx:3 dynamical:1 light:2 explicit:2 correspond:1 si:1 used:2 fundamental:1 definitions:2 subsequently:1 operations:1 xj:1 interpretation:1 indeed:1 mainly:1 satisfied:1 interpreted:1 course:2 paper:5 through:1 looks:1 mentioned:1 its:3 before:1 derive:1 group:3 la:1 chosen:1 interesting:1 ll:1 boson:1 actually:2 meantime:1 misunderstandings:1 mail:1 might:1 non:1 yj:1 horwitz:4 hunter:1 awarding:1 mention:1 they:7 half:1 nov:1 yu:1 discuss:1 escuela:1 dirac:2 2s:1 kpz:1 professorship:1 applied:2 good:2 found:4 soc:1 side:2 enigmatic:1 spinor:1 gersten:9 hadronic:2 series:3 energy:1 idea:1 related:3 inhomogeneous:1 weinberg:9 poincare:1 quantum:8 our:2 eq:5 ep:19 shown:1 matrix:3 space:3 gradient:1 furthermore:3 lagrangian:1 particles:4 izv:1 denoted:1 formula:1 ref:5 correct:1 math:5 foundation:1 linear:1 ast:2 ısica:1 free:1 admits:1 york:2 onoma:1 e2:1 isz:2 isy:2 isx:2 derivation:7 precaution:1 length:1 massive:1 universidad:1 hence:1 generalizations:2 origin:1 symmetry:1 zac:1 rank:2 multiplying:1 directly:1 angular:3 given:1 necessarily:1 publication:1 leading:1 system:2 relations:2 their:1 too:1 explanation:1 authors:2 translation:2 lubanski:1 toronto:1 kind:1 unfortunately:2 cimento:1 namely:3 submitted:1 future:1 were:1 a48:1 symmetries:1 ana:1 appreciate:1 ann:1 say:1 need:1 any:1 latter:1 ideas:1 note:1 instance:4 potential:1 generalized:5 so:2 coincide:1 lectures:1 play:1 broglie:1 normal:1 bruce:1 english:2 connected:2 but:3 representation:4 intrinsic:1 exico:2 constructed:1 surprising:1 considered:4 proceedings:1 ampere:1 physics:3 fact:3 laws:1 show:1 vigier:1 supported:1 gauge:3 solutions:2 wigner:1 find:1 based:2 iep:2 should:5 only:4 explicitly:1 dvoeglazov:6 boulder:1 his:5 de:5 straightforwardly:1 ahluwalia:3 famous:2 watson:1 2mf:1 words:1 during:1 years:1 aν:2 bondi:1 densities:2 textbooks:1 fields:7 arxiv:1 oppenheimer:2 imposed:1 investigate:1 europhys:1 contain:1 london:1 explanations:1 4πi:2 transversality:1 commutation:1 set:6 apeiron:1 frame:1 argued:1 see:5 cim:2 p23:1 discussions:2 chambers:1 learnt:1 tensor:5 review:1 symmetric:1 importance:1 written:1 cambridge:1 correctly:1 between:1 limit:2 terms:2 foreword:1 nature:2 zacatecas:3 however:1 jr:2 jm:6 jk:1 longitudinal:1 come:1 suggested:1 both:3 interpretations:3 last:1 0t:1 many:2 invited:1 according:1 nikitin:1 fiz:2 ernst:1 vuz:1 asked:1 comment:1 profs:2 co:1 cf:1 2nd:1 faraday:1 considering:1 forms:1 pp:1 110b:1 transformations:3 pt:3 basis:4 pz:4 px:5 py:4 thanked:1 due:1 been:6 int:1 describes:1 pk:2 ph:2 pi:2 pl:7 helicities:2 polubarinov:4 corresponding:2 cosmological:1 sufficient:1 photon:3 derivative:2 c2:2 spin:8 present:3 c4:1 case:4 p3:13 p1:9 papini:1 valeri:4 appearance:1 will:1 situation:1 procedure:4 ization:1 noether:1 a27:1 vol:2 thus:7 surprisingly:1 iv:1 ij:1 im:2 claimed:1 quantization:1 bargmann:1 acknowledgments:1 different:5 author:1 suggest:1 belong:1 another:1 parts:2 quant:1 pauli:1 several:2 higher:4 status:1 literature:3 http:1 published:1 interscience:1 hand:2 pubs:2 potentials:4 infinite:1 totally:1 normalization:4 recent:2 analysis:7 academic:2 without:1 programa:1 sets:2 coordinate:2 jean:1 ny:1 kalb:1 proposed:1 being:2 obtain:2 aspect:1 using:1 momenta:1 previous:1 kluwer:2 density:1 nacional:1 belinfante:1 add:1 book:1 lett:6 theorem:5 momentum:3 real:1 iα:5 possible:3 helicity:1 press:1 integer:2 ams:1 postal:1 decomposes:1 mod:1 theor:1 appearing:1 like:5 contradict:1 arbitrary:2 kpt:1 university:4 spins:2 mathematical:1 parity:1 right:2 old:1 classical:1 discrete:1 korff:1 some:4 pierre:1 pχ:1 moreover:1 proper:4 proofs:1 describing:1 lead:1 electromagnetic:2 recami:2 does:1 prof:1 proc:2 majorana:1 pr:8 11a:1 journal:1 symp:1 2m:9 stage:1 chapter:1 shnerb:2 discussed:1 dependence:1 greatly:1 slightly:1 considerations:1 mechanics:1 rev:7 letters:1 colorado:1 reidel:1 maxwell:13 into:1 obtaining:1 functional:1 sachs:1 references:2 sov:1 operator:3 proportional:1 guideline:2 van:1 additional:5 there:3 question:2 nova:2 dispersion:1 appl:1 way:1 ed:2 was:2 assumes:2 function:1 complete:1 form:2 gauss:1 land:1 aµ:5 removed:1 he:2 consequences:1 versions:1 whether:1 us:2 url:1 below:1 those:1 russ:1 problem:3 pm:1 similar:2 multiplications:1 detailed:1 defined:1 certain:2 abstract:2 chubykalo:1 am:1 general:3 conserved:1 formulation:1 partly:1 formalism:3 apartado:1 physical:1 functions:2 no:4 uµ:4 when:1 field:11 other:1 role:1 carrera:1 papers:2 massless:3 conclusion:3 suppl:1 separate:1 problems:1 15c:1 a7:1 lyttleton:1 111b:1 longer:1 assume:1 factors:1 mass:3 nelson:1 time:1 roy:1 nuovo:3

quant-ph9911111.txt \|@word gr:2 remarkable:1 krainov:1 varying:1 results:8 gy:1 leads:2 ρji:1 ge:5 garching:1 ikj:4 consider:6 whose:1 griffin:1 depend:1 calculate:2 γr:3 tr:1 including:1 finally:3 investigation:1 stable:1 γg:3 tc:43 applied:1 g5:4 g4:2 g3:18 presently:1 broadly:1 orthogonal:1 p0j:1 wave:5 wishes:1 every:1 axes:1 resonant:1 experimentally:2 difference:3 condition:4 treating:1 rotating:2 steeper:1 vibrational:1 level:2 transmission:1 evaluation:3 solution:3 large:1 solved:1 convenience:1 vector:4 science:2 eigenvalues:1 optics:1 der:1 degeneracy:1 kz2:1 upper:1 smaller:1 evaluating:1 estimates:1 linares:1 pulse:9 approximation:4 across:2 zero:3 evaluated:3 qualitatively:1 dynamics:3 50a:1 rough:1 substitute:2 linear:3 substantiates:1 reviews:1 nonlinear:1 unavailable:1 apparatus:1 complexities:1 section:15 selected:1 erf:1 d3:1 axial:3 experiment:4 nez:1 above:9 new:4 occupation:2 consisting:1 condensed:2 full:2 hypothesis:2 eikj:1 ibid:2 respectively:3 here:11 atoms:36 hkj:1 reported:3 cylindrical:2 variance:1 andrews:2 2kb:3 directions:1 path:1 along:6 standard:3 equations:8 appears:1 change:4 box:6 property:1 incoming:1 parameters:6 photomultiplier:1 rdr:1 involved:1 study:4 studied:3 allows:1 p2:2 chemical:1 usually:1 fourier:1 studies:1 delays:1 inference:1 explained:1 replace:2 scaled:1 electromagnetically:1 matthews:1 welch:1 apply:1 total:6 planck:1 cloud:24 plot:4 use:4 asymptotic:2 would:2 γre:1 jain:1 vg:11 predictions:1 comparing:1 a53:1 therefore:8 vi:1 taken:1 theoretical:2 today:1 clearly:1 brings:1 under:1 emission:1 correspondingly:1 particular:1 known:2 cases:3 iii:4 states:6 account:2 νr:4 cm3:2 equation:1 work:1 oscillator:13 ρn:6 reproduce:2 dej:1 itself:1 values:4 temperatures:4 transparency:1 following:6 making:1 spontaneous:1 deg:2 compare:2 chosen:1 calculation:1 organized:1 νz:9 sample:2 slit:1 numbers:1 arise:1 r27:1 ωeg:1 axis:6 caption:1 navrangpura:1 ultracold:2 write:5 hot:1 frequencies:3 circular:1 simplicity:1 pinhole:1 description:3 may:2 max:1 after:2 derived:1 davis:1 fc:3 ρee:3 ρeg:6 ahmedabad:1 fi:1 ρej:1 data:4 response:1 kurn:3 dynamical:1 effective:2 light:14 schneider:1 lines:3 correspond:2 lζ:1 rather:3 cannot:1 so:2 allow:1 representation:1 vapor:1 playing:1 developed:1 over:9 top:1 mainly:4 interpreted:1 stamper:1 thermal:4 experiments:2 through:5 statistical:4 cuts:1 mathematical:1 cold:5 still:2 excitations:1 its:3 before:2 delay:12 derive:3 group:50 thank:1 decay:2 energies:1 interesting:1 zˆ:5 coordinates:3 complex:2 dje:2 fig:14 h3:3 rabi:2 main:1 defining:1 outside:1 versus:1 them:1 affected:1 a0r:3 similar:1 outlined:1 ωlj:2 introduce:1 a0j:1 records:1 walls:1 quantenoptik:1 ωlr:2 effects:6 they:2 half:1 nov:1 now:4 discuss:3 wiley:3 susceptibility:11 february:1 gets:2 2p:1 goldstein:1 inhomogeneity:1 van:4 hamiltonian:1 magnitude:2 l2:1 trap:4 radial:3 found:6 higher:4 2i:1 scattering:2 homogeneous:2 weighted:1 determine:2 ej:1 ee:2 scheme:1 energy:9 hard:1 principles:1 semiclassical:7 applicable:1 inhomogeneous:1 frequency:8 expect:1 entering:2 measure:1 quantum:4 laboratory:1 transitions:2 eq:22 event:1 out:1 ketterle:6 emerges:1 shown:3 jackson:1 matrix:6 factors:1 gradient:1 open:1 furthermore:2 since:3 rev:12 projected:1 research:1 particles:3 re:4 rg:2 thermodynamic:3 formula:3 induced:2 suffices:1 shows:1 earlier:1 theory:3 interactions:7 abramowitz:1 mechanisms:1 free:8 quite:1 πa:1 york:4 ρij:1 region:1 estimate:6 e0:1 definition:1 ρrr:3 interaction:2 r2:3 transition:7 motion:4 appearing:3 length:2 harris:4 isotropic:1 hence:1 hussein:1 pitaevskii:1 eqs:10 first:4 grossman:1 zl:1 major:1 simplifies:1 symmetry:1 laguerre:1 number:9 transform:1 ensher:1 directly:1 ky2:1 βv:2 reached:1 tempere:1 electronic:1 causing:1 size:13 given:13 cartesian:1 temperature:50 introduction:1 fl:6 condensate:10 achieved:1 system:3 their:2 cooling:2 rates:1 observations:1 calculations:3 handbook:1 πy:2 final:4 gives:2 way:1 trapped:4 wavelength:1 larger:4 optical:12 authors:1 x2:1 july:1 representing:1 than:5 coefficients:4 population:2 plausible:1 john:3 roles:1 fundamental:1 approximations:2 rate:2 limiting:2 project:1 matter:1 bigelow:1 future:1 contrary:1 radius:6 india:1 grossmann:1 hz:8 sees:1 rewrite:2 electrodynamics:1 correction:1 argument:1 curves:4 delone:1 already:1 manner:1 disjoint:1 seen:2 orders:3 illuminated:1 rostovtsev:1 depending:1 responsible:3 polarization:6 centered:1 ideal:12 potential:10 take:2 lβ:4 canonical:1 stringari:2 raman:1 πac:1 electric:3 investigations:1 logarithmic:1 rhs:1 denominator:1 most:1 germany:1 significant:1 formulae:1 phase:1 acknowledgements:1 measured:2 kb:7 cause:1 kg:9 surprising:1 considered:1 kj:1 average:6 steady:5 order:8 kr:3 part:1 principle:1 exp:12 mechanical:3 velocity:49 effect:5 scully:3 sum:4 fact:1 dover:1 thomas:5 evaporative:2 phenomenon:4 show:1 radii:1 probe:1 motional:2 discovered:1 attempts:1 relation:6 shi:1 substituting:1 kx2:1 find:6 ground:12 slow:1 ratio:3 dividing:2 explain:2 written:1 negligible:1 should:2 only:3 fundamentals:1 factor:1 integrate:1 interested:1 equilibrium:1 do:1 means:3 dependent:2 γgr:12 beam:2 ones:2 dz:10 dt:7 dr:5 nk:3 fields:1 behroozi:1 arxiv:1 yield:1 method:1 lukin:1 investigate:2 paper:2 mewes:2 bec:1 analytical:4 pulses:2 valid:1 fugacity:1 thanks:1 cǫ:10 set:5 reference:1 hν:1 frame:1 observed:6 see:4 sec:6 discussions:1 close:1 subject:3 interacting:13 macroscopic:1 currently:1 definite:2 dipole:2 state:21 envelopes:1 between:6 fermi:5 justified:2 αl:1 comparable:2 terms:2 extend:2 nature:2 jp:1 illustrate:1 weak:1 however:8 reproduces:1 ikg:1 key:2 bose:4 understanding:1 come:1 distribution:3 originates:1 0r:3 both:1 last:1 limits:1 many:2 taking:4 sodium:5 dkz:2 according:3 dkx:2 dky:2 marti:1 propagation:3 figures:1 ωg:1 context:2 0j:2 γij:1 contribution:4 whole:2 finds:1 experimental:10 albeit:1 ck:1 among:3 druten:4 relevant:1 co:1 huang:1 cm:1 point:2 simple:2 corresponds:4 dimensional:1 ωge:1 decreases:2 article:1 respect:1 throughout:1 points:1 considering:5 devreese:1 described:1 illustrated:1 second:1 basis:4 radiative:1 three:3 been:1 detuning:2 describes:2 slowly:1 treat:2 expected:1 e0j:2 ph:1 lett:6 obtained:2 direction:4 onset:1 corresponding:5 ρgg:3 ρge:1 coherence:6 gas:30 dramatic:1 understand:1 systematic:1 iπ:1 presented:1 ρgr:1 present:3 case:22 p0:2 schmidt:1 laser:4 eit:2 exponential:1 pacs:1 solid:1 expanded:1 value:5 excited:2 will:4 2rt:2 behavior:1 hollberg:1 ultra:2 couplings:1 procedure:1 ix:1 cylinder:1 vectors:1 coupled:1 almost:1 averaging:1 thus:4 non:8 discrepancy:1 iv:2 ii:2 need:1 ij:1 cond:1 ellipsoid:1 comments:1 agarwal:1 different:3 sensitive:1 smoother:1 cross:1 same:4 any:1 shorter:1 noninteracting:1 quant:1 arguments:1 holthaus:2 finite:3 showing:2 0g:4 independent:1 used:3 dge:2 numerical:3 drives:1 hand:1 driven:1 principally:1 moment:2 levels:2 purpose:1 potentials:1 lower:4 task:1 expression:9 well:1 analysis:1 gsa:1 solve:2 comes:2 position:1 model:8 pairs:1 nc:1 being:1 stegun:1 obtain:8 lemmens:1 atomic:12 aspect:1 momenta:1 speed:1 eigenstates:2 note:4 density:26 cornell:1 workers:1 e0r:1 internal:3 transformed:1 treatment:6 e0g:1 mod:1 hau:4 aspects:4 depends:2 evaluate:8 iγ:2 term:3 harmonic:17 increases:1 kash:1 vacuum:2 confined:4 using:8 helpful:1 loss:1 necessary:1 like:1 follows:1 qualitative:2 velocities:1 δr:1 δp:1 δk:1 cooled:1 lends:1 zibrov:1 satisfactory:1 because:2 classical:2 narrow:1 some:3 mat:1 meters:1 scale:5 describing:1 dimensions:3 lead:1 bottom:1 πr2:6 measurements:1 per:2 critical:18 provides:2 assuming:4 propagating:11 demonstrated:1 l3:2 measuring:2 parkins:1 equivalent:1 each:1 agreement:2 expansion:4 polynomials:1 2m:11 yin:1 conclusions:1 kinematical:1 dze:1 simplify:1 pu:1 dependence:12 o:6 range:1 dutton:1 introduced:2 bloch:3 considerations:2 mechanics:1 h2:8 maxwell:3 into:7 within:1 integral:3 aho:2 due:2 down:1 primarily:1 einstein:1 operator:1 proportional:1 theoretically:1 statistics:1 institut:1 mkb:2 behaviour:7 assumed:2 initial:2 approximate:3 gases:4 dispersion:1 anderson:1 much:2 bosons:9 low:1 fraction:3 was:1 eg:5 function:9 considerably:1 medium:6 complete:2 form:10 metastable:1 but:1 gaussian:1 volume:5 hk:1 recoil:3 related:1 atom:9 implies:1 line:4 fry:1 2πc:1 made:3 applying:1 durfee:3 evident:1 fulfilling:1 wieman:1 inside:3 ωr:5 us:3 ur:1 2mkb:2 below:7 ωj:1 limit:12 meschede:1 problem:2 ωe:2 eigenvector:1 regimes:1 strongly:1 ac:3 defined:11 stronger:1 geometrical:1 describe:1 slowing:1 our:8 physical:1 dalfovo:1 again:1 functions:2 compared:1 nm:1 dotted:3 no:1 dashed:2 whereas:5 wavefunction:2 when:4 inset:1 field:10 naturforsch:1 other:5 giorgini:1 spatial:9 mνj:1 er:3 rt:4 distance:3 variation:7 deriving:1 a2:10 allowing:1 kz:3 included:1 meystre:2 structure:1 15n:1 condensation:1 regime:3 coupling:1 assume:2 thermalization:1 curve:5 together:1 investigated:1 mass:1 volumes:1 time:6 decoherence:1 rep:2 νr2:5 once:1

quant-ph9911112.txt \|@word represent:1 concept:1 consider:4 chain:2 caused:1 beware:1 results:6 leads:1 roy:1 childs:1 computation:1 bergmann:1 expressions:1 forget:1 increase:2 dimensionality:1 reuven:1 knill:2 technique:2 ts:1 passage:4 does:1 stable:16 breach:1 nodes:1 briegel:1 amplitudes:2 straightforward:1 far:1 frequencies:7 wave:5 orientations:1 resonant:12 experimentally:3 difference:3 condition:3 entire:2 randomness:1 incoherent:6 level:34 transmission:1 knight:2 solution:3 leave:1 vector:5 wavelengths:1 indices:1 optics:2 lines:4 upper:5 employing:1 deutsch:3 theuer:1 pulse:11 approximation:1 rate:2 traveling:1 rigorous:1 qualitatively:2 dynamics:4 implemented:1 leakage:2 even:1 employ:1 interatomic:14 nonlinear:2 stands:2 sum:1 while:5 3k:1 volatile:1 goes:2 sixth:1 new:4 contributes:1 method:9 contrast:1 satisfy:1 edited:1 degree:1 exchange:1 awschalom:1 respectively:3 realizations:1 here:6 atoms:35 spins:1 explore:1 plenio:3 relaxation:5 represented:1 strong:1 directions:1 obtained:1 great:1 antisymmetric:15 reports:1 suggests:1 resulting:1 bennett:2 akl:2 usually:1 resonance:3 makes:1 klyshko:1 king:2 appropriately:2 via:1 useful:1 stray:1 transit:4 brought:1 coinciding:1 decrease:2 issue:1 total:1 unit:2 9v:3 standing:3 use:7 takes:1 γk3:15 intensively:1 sake:1 ψs:3 laflamme:1 few:2 monotonically:1 therefore:3 ψa:3 type:2 ψg:2 more:1 applicable:1 coupled:1 populations:2 becomes:1 operators:1 under:1 benchmark:1 odinger:1 known:2 cases:2 hold:1 iii:1 insights:1 entangle:1 states:41 science:1 equation:7 work:1 remain:1 values:8 splittings:2 following:8 making:1 trans:1 example:5 ions:1 metrology:1 figure:5 process:8 channel:1 preserving:3 involve:3 application:1 employs:1 specific:1 biharmonic:3 information:4 goal:1 decaying:1 kwiat:1 rather:2 discussion:1 breaking:4 how:1 varies:1 opt:2 instead:1 parameter:3 sin:7 brassard:1 gordon:1 simplicity:2 product:2 mar:1 description:1 barnum:1 may:2 max:1 after:5 demanding:1 diagram:3 applications:1 inst:1 trapping:1 waves:2 choice:2 unentangled:2 parallel:1 types:3 efficiently:2 2σz:1 realized:2 short:1 effective:1 negligibly:2 dot:2 explicit:2 correspond:3 element:2 ψe:1 shore:1 cannot:1 so:2 realizes:1 fundamental:1 ˆz:3 tittel:1 myatt:1 order:2 restriction:2 ith:5 constituents:1 over:1 choose:2 burkard:1 years:1 produced:2 paper:4 pulses:14 holton:1 lasers:3 lattices:2 mentioned:1 existence:1 cold:1 still:5 kofman:1 decay:19 chosen:5 interesting:1 stimulated:2 decreases:1 actually:1 better:2 wineland:3 production:1 itano:3 systems:5 omitted:2 rabi:11 easier:1 τp:4 split:1 versus:2 eventually:1 them:2 good:1 thereby:1 propose:2 practice:1 heinzen:1 processes:4 introduce:2 steane:1 detunings:1 effects:1 they:1 optimal:1 now:2 realize:1 yv:1 ωk3:19 easily:3 february:1 vitanov:1 university:2 hamiltonian:2 huelga:3 identified:1 imamoglu:1 possibilities:1 sufficiently:2 magnitude:2 each:5 instability:1 macchiavello:1 characterized:2 mean:1 em:1 schemes:3 ei:1 eh:1 happer:1 populated:4 generation:2 energy:5 idea:2 related:1 lomonosov:1 deterministically:1 investigated:1 measurement:2 quantum:15 our:6 transitions:25 special:1 er:9 large:3 shown:15 fre:1 matrix:4 driving:2 space:1 res:1 since:3 induces:1 denotes:1 particles:3 collisions:1 acting:4 print:10 mattle:1 induced:9 ref:1 shows:2 provide:1 interactions:1 gardiner:2 pumping:17 free:1 cabrillo:1 small:8 approaches:1 estimate:1 e1:6 fidelities:3 e2:6 doublets:1 interaction:4 benefits:1 created:4 geometry:11 transition:13 lomonaco:1 times:2 creates:1 length:2 levels:10 speedy:1 massive:1 renes:1 transfer:7 generalizations:1 first:6 major:1 already:1 utilizes:1 symmetry:10 prevent:1 third:1 number:2 preservation:1 channels:4 another:4 n22:1 yd:1 ovchinnikov:1 interchange:2 given:6 grimm:1 errors:2 indicate:1 amsterdam:1 system:30 their:5 intermediate:6 master:6 constants:1 calculations:2 realization:5 rates:7 wootters:1 ranging:1 speaking:1 fraction:1 trapped:1 σkl:1 moscow:2 continuous:2 sanders:1 speakable:1 optical:13 superoperator:1 authors:2 wasted:1 constituent:1 sublevels:1 representing:1 than:2 population:25 wide:1 scheme:1 ben:1 unfortunately:1 horizons:1 lying:2 approximations:1 transferred:1 normalizing:1 collinear:1 crepeau:1 doubly:2 amplitude:3 were:3 f13:2 russia:1 function:4 separations:3 cohen:1 elsevier:1 need:1 seen:2 any:1 vulnerable:2 multipartite:1 conversion:1 strength:2 computationally:1 zero:3 efficient:2 latter:3 isolated:4 situated:1 k3:2 high:5 nonresonant:3 yudson:1 analogs:1 eff:4 heisenberg:1 exactly:1 multiple:1 mizel:1 though:3 reach:1 extending:1 optimized:1 said:1 significant:3 phase:4 r35:1 intrinsic:1 why:1 tensor:1 observation:1 surprising:1 considered:9 gk3:2 phil:1 differ:1 detuned:1 typeset:1 graphs:3 part:1 tech:1 exp:1 physics:4 section:1 fact:2 show:5 supported:1 degrades:2 foregoing:1 rotating:1 2g:2 αk3:6 find:1 decade:1 ground:4 based:1 parameters:10 jessen:2 situations:2 entangling:6 should:7 moments:1 only:18 going:1 indeed:1 thompson:1 employed:1 partially:1 achieve:3 do:1 above:2 cryptography:1 means:2 beams:8 zurek:1 simplest:1 overall:3 satisfied:1 ones:1 international:1 kurizki:2 during:2 dp:1 evolution:1 increasing:2 fields:6 arxiv:1 adiabaticity:1 tuned:1 garcia:1 fernandez:1 li:1 common:1 fixed:1 set:1 achieved:3 lifetimes:1 achieves:1 arimondo:1 up:1 relative:1 differs:1 see:11 computer:1 radius:2 result:3 close:1 limiting:1 fidelity:12 analog:1 concern:1 appear:3 exploited:1 interacting:11 ways:2 review:6 dipole:22 symmetric:12 state:39 various:1 between:5 conceptual:1 progress:2 caves:1 conditions:3 sections:1 barenco:1 recently:2 creating:4 extend:1 nature:2 initially:3 however:6 efficiency:2 fifteenth:1 configuration:6 suggested:1 both:9 essentially:1 last:2 taking:1 conclusions:1 according:1 called:1 fulfilled:1 sensitive:2 connection:1 iv:1 logic:1 divincenzo:2 gisin:1 whole:1 experimental:1 otherwise:1 arbitrarily:1 mechanics:1 jitter:1 point:1 simple:3 asymptotically:2 corresponds:2 active:3 cirac:4 simply:1 respect:4 throughout:2 sherwin:1 second:4 considering:1 broadening:2 described:1 geometries:6 basis:1 create:2 radiative:12 due:9 been:5 quickly:1 offers:1 slowly:1 yh:1 ph:9 pi:3 a356:1 fig:18 dots:2 concentrated:1 direction:2 controlled:2 sergienko:1 offered:4 formed:4 photon:2 precision:2 fortschr:1 zeilinger:1 coherent:10 maximally:26 former:1 present:2 case:10 wood:1 intriguing:1 novel:1 laser:40 brendel:1 solid:1 reliable:1 appearance:1 value:2 ministry:1 will:5 near:1 walther:1 error:1 situation:1 mitchell:1 procedure:1 identical:1 turchette:1 played:2 vol:1 thus:1 equal:4 ii:1 middle:1 ij:1 lifetime:1 technology:1 monroe:2 different:5 jozsa:2 combination:1 σz:1 acknowledgments:1 realizing:1 belong:1 lett:9 same:9 clearly:1 unity:2 quant:9 arguments:3 figures:2 dimensionless:2 several:2 grows:1 four:1 calculation:1 used:4 numerical:1 companion:1 driven:3 moment:2 traditionally:1 uses:4 kim:1 entanglement:14 changing:1 dark:2 lower:9 schr:1 traps:3 pellizzari:2 programs:1 well:3 analysis:1 obviously:2 solve:1 components:2 sets:1 very:2 quantitative:1 model:8 fk3:2 ekert:2 distances:7 proposed:5 less:2 being:2 rest:2 manipulation:1 stored:1 atomic:2 using:7 alternative:2 brennen:2 previous:2 adv:1 note:3 yr:3 zoller:3 grouped:1 photons:1 bell:2 had:1 dicke:8 source:2 treatment:2 easy:1 natl:1 skl:2 violations:1 disrupt:1 excited:5 real:3 saturation:1 nielsen:1 rev:18 rules:2 capacities:1 possible:4 early:1 possibly:1 working:1 quencies:1 entangled:35 mol:1 press:1 disadvantageous:1 variants:1 mod:3 loss:1 counterintuitive:2 like:1 splitting:2 qualitative:1 adiabatic:7 extremely:1 stirap:11 ignore:1 benefit:1 unstable:1 either:1 become:1 stationary:3 collective:1 preskill:1 classified:1 methods:12 yj:1 sequence:3 creation:6 some:4 neglecting:1 reasons:1 provided:1 excitation:3 lead:1 realistic:1 cavity:2 avoid:4 wooters:1 inequality:2 connecting:2 assuming:2 semiconductors:1 demonstrated:1 refer:1 presented:2 power:3 reaching:1 s13:7 s12:7 processing:2 conventional:2 step:3 revtex:1 stenholm:1 losing:1 properties:1 would:1 most:3 prove:1 discussed:2 dependence:1 practical:1 probabilities:1 involving:1 wolf:1 beige:2 efforts:1 introduced:1 homogeneous:1 soc:1 cambridge:1 final:5 previously:1 into:11 within:3 numerically:2 three:16 down:1 appropriate:1 references:1 δk3:7 operator:3 proportional:1 qed:2 additional:1 elastic:2 area:3 removing:1 strictly:1 initial:1 lond:1 long:1 much:1 low:4 way:3 was:8 opens:1 a54:1 raman:7 considerably:1 form:6 smolin:1 differences:2 delayed:1 but:3 gaussian:1 neutral:4 multilevel:1 atom:18 russian:1 stand:1 fry:1 longer:1 made:2 applying:2 prevents:1 maximum:1 us:1 kk:2 below:1 frequency:6 pumped:2 problem:1 radiatively:14 advantage:1 calculated:4 distance:9 strongly:1 shih:1 lanl:10 associated:1 computing:1 defined:1 steady:1 abstract:1 describe:1 singly:1 general:1 peres:1 single:2 periods:1 simulations:2 corresponding:19 quantph:1 jaksch:1 physical:2 again:1 mutual:2 determinacy:1 dotted:3 no:1 cos:5 whereas:1 when:9 detail:1 meekhof:1 plugged:1 field:9 other:12 role:2 details:1 papers:1 department:1 coherence:3 conclusion:1 optically:1 picture:1 perpendicular:2 elements:2 a13:7 a12:13 models:2 center:1 problems:1 includes:1 generated:1 important:3 n1:1 included:3 transfers:3 structure:1 zbinden:1 tailored:1 coupling:5 assume:5 required:1 governed:1 having:1 leibfried:2 presenting:1 time:3 dephasing:2 decoherence:1 requires:1 original:5 unspeakable:1

quant-ph9911113.txt \|@word similarity:1 magnetic:1 four:6 entropy:1 controversial:1 consists:4 whose:2 const:1 calculate:1 every:2 experimentally:1 fractal:4 solution:1 vector:3 math:1 markov:10 miller:1 consistent:1 direct:1 phipps:2 approximation:1 second:5 7th:1 qualitatively:2 implemented:1 even:8 incompatible:2 kul:1 above:9 new:10 increasing:3 simultaneously:2 never:1 equals:1 here:4 governing:1 represented:3 path:1 interpret:1 obtained:1 study:4 completely:2 guide:1 changes:4 ﬂip:2 attractor:6 discontinuous:3 plenum:5 highly:1 total:11 unit:2 would:7 phenomenological:2 program:1 therefore:6 type:5 until:2 alberto:1 odinger:3 berlin:3 must:8 springer:4 leavens:4 theories:4 macroscopically:1 install:1 my:1 example:6 impose:1 give:1 relativistic:2 preserving:1 involve:1 want:2 provide:2 recovers:1 how:10 hot:1 answer:1 ﬁeld:2 description:3 replacing:1 proach:1 after:4 barriers:3 wrong:1 jumping:1 attempt:1 effective:1 summing:1 diﬀer:1 complexity:1 vapor:1 restriction:2 interpretation:8 feedback:2 over:2 london:3 thesis:2 before:3 better:1 fig:7 hidden:6 versus:3 them:2 band:1 they:4 multidimensional:1 represents:2 each:10 side:1 mean:18 branchings:1 series:7 principles:1 semiclassical:1 applicable:2 used:5 crucial:1 particles:4 ra:2 ri:1 palao:2 foundation:2 linear:9 barrier:31 free:3 standard:6 assures:1 stochasticity:1 created:2 starts:1 enders:4 chiao:2 onto:2 condensate:1 already:1 vittorio:1 philosophical:2 another:11 illustrate:1 master:6 observations:1 diﬀerence:4 tom:1 dwell:1 john:2 fuzziness:1 collapse:1 centered:1 deﬁnitions:1 somewhat:1 princeton:1 iteration:4 zero:2 tref:2 matter:2 historical:1 perspective:1 ev:2 modern:1 seen:2 ﬁnal:2 oriented:1 forces:1 circles:2 though:1 regular:1 quantitative:3 phase:5 suﬃcient:1 observation:1 clock:1 detectors:7 vertices:1 points:3 came:1 signatures:1 vigier:1 random:8 infrared:1 subtle:1 d2:7 d1:8 lessons:1 proposed:2 spite:1 photographic:1 explain:2 ocs:2 hamiltonians:2 do:10 mixture:1 da:3 dx:2 report:2 dt:2 dp:8 runs:3 acknowledgments:1 interspersed:3 observer:1 generally:1 sensitivity:1 testing:1 observed:2 depends:6 result:6 discussions:1 evanescent:2 subject:4 exponent:1 symmetric:1 µn:2 simplest:3 approach:13 terms:2 extend:2 nature:3 weak:1 however:1 extent:1 bose:1 maneuvers:1 essentially:3 uncertainty:2 against:1 mildly:1 uni:2 2nd:1 concluding:3 wider:1 speak:1 three:3 been:4 much:1 expected:1 algebras:1 ann:1 hepp:2 families:2 indeterminacy:1 25a:2 krausz:2 coherent:1 spin:11 applied:6 near:1 suppose:1 leaves:1 a24:1 equator:1 ii:1 nonunitary:1 perform:1 suggest:1 make:2 complex:3 quant:5 several:3 grows:1 independent:1 everett:2 trajectories:2 publ:2 normalization:1 simulated:3 claims:1 left:1 just:2 photonic:1 facts:1 yes:2 yet:9 adding:2 enters:1 easy:1 5a:1 possible:8 possibly:1 boxes:2 uniﬁed:1 unique:3 advanced:1 unnecessary:1 steps:1 sparse:1 arbitrary:2 evolutions:1 invaluable:1 www:1 right:1 old:1 deal:4 dead:1 zoom:2 born:4 algorithmic:1 illustration:1 super:1 properties:1 proceed:1 chapter:1 o:1 larmor:5 sept:1 soc:1 presence:1 intellectual:1 pair:1 hermitian:1 bielefeld:2 tetrahedral:4 often:2 initial:7 why:2 width:5 physicists:1 way:8 was:10 happy:1 medium:6 form:3 piron:5 denoting:1 idealized:1 hemisphere:2 catalyst:2 true:1 contradistinction:1 maximum:1 devices:1 σtot:1 jauch:2 computing:1 abstract:2 proven:2 peres:1 exist:2 simulations:3 commuting:2 check:1 triangles:1 constructed:1 ni:6 dotted:4 no:14 when:13 landsman:1 schwinger:1 interested:4 picture:1 models:2 dissipation:1 longer:1 dψ:2 assume:2 interval:2 packets:1 governed:1 time:68 n1:1 n2:1 n3:1 n4:1 concept:1 blanchard:7 leads:3 projective:1 depend:2 finally:1 ın:1 division:1 choice:2 exact:2 presented:1 did:1 turns:1 leave:3 discrete:2 speculation:1 equation:12 upper:2 dealing:2 htm:1 sign:1 stands:1 foregoing:1 uniform:2 current:1 goes:2 understanding:1 along:3 change:9 institute:3 vectors:2 simultaneous:5 poisson:1 usually:1 useful:1 extra:3 stingl:2 marked:1 operational:1 working:1 prove:1 positive:3 predictions:1 france:2 going:1 scope:1 associated:3 theoretical:5 hauge:1 validity:1 cases:4 parameterize:1 sphere:7 avoiding:1 originally:2 modified:1 reviews:1 fock:1 values:7 following:8 making:2 arrive:1 figure:6 identiﬁed:1 allowed:3 occur:2 verlag:2 rays:1 monitoring:1 fortunately:1 discussion:1 write:1 criterion:1 pure:5 parameter:7 product:1 may:1 max:1 applications:4 birthday:1 designed:1 representations:4 data:1 grow:1 stress:1 dynamical:1 sectors:1 su:1 reﬂects:1 cannot:5 so:9 representation:1 talk:1 indeed:5 pointed:1 years:4 course:1 experiments:9 statistical:4 still:2 ieee:1 thank:1 interesting:3 decreases:1 τa:2 mail:1 τt:4 main:2 τr:3 non:18 processes:6 introduce:1 lunch:1 nov:1 now:5 discuss:5 term:5 realistic:1 instability:1 diﬀerent:8 arbitrariness:1 ed:8 gaussian:2 inhomogeneous:1 gaps:1 happen:1 avoided:1 eq:2 minority:1 living:1 shown:2 opened:1 space:16 looking:1 formula:3 shows:4 theory:28 possibility:3 quite:3 advantages:1 org:1 e0:4 derivation:1 language:1 transition:1 motion:1 think:1 first:1 xi:1 variables:7 waves:2 reductionism:1 directly:1 carry:1 impossible:3 open:3 given:12 realization:1 bits:1 speaking:1 gives:1 progr:1 mostly:1 continuous:14 x2:6 x0:2 x1:6 representing:1 than:9 wide:3 iceberg:1 spielmann:2 future:5 were:4 topics:2 turned:1 argument:1 recover:2 any:6 zon:1 ideal:1 potential:2 take:3 online:1 wonder:2 formulas:2 begin:1 trace:1 opposite:1 paid:1 algebraic:2 αr:1 automorphism:1 formulae:2 reducible:1 surprising:1 considered:4 average:1 phil:1 feynman:1 beables:1 precise:3 show:7 finkelstein:1 contemporary:1 spaces:3 deser:1 ensembles:3 written:2 only:23 explicitly:1 developed:2 normalizations:1 get:4 contracts:1 expectation:1 aα:3 aβ:1 nearly:1 symmetrically:2 yield:1 kernel:1 physically:2 lnp:1 namely:2 inequivalent:2 concern:1 einselection:1 detect:1 αt:5 ways:2 review:4 behind:1 between:10 reading:1 inﬁnite:3 2αr:2 august:1 vertical:2 ﬁgure:1 concentrate:2 comm:2 como:2 contractive:1 come:1 philosophically:1 σc:1 many:3 according:5 propagation:1 berry:1 σq:1 filtering:1 pole:1 iterations:1 moreover:5 considering:1 west:1 mart:1 workshop:1 engine:2 direction:6 occurs:1 photon:5 traversal:24 noncommutative:1 realities:1 those:2 paying:1 single:3 steinberg:2 situation:5 tunneling:13 wroclaw:3 coupled:4 characteristics:1 technology:1 everyday:1 fractals:3 same:5 archive:1 physical:2 events:15 status:1 singapore:2 arose:1 without:6 components:1 model:14 dimension:2 manifold:1 being:8 tip:1 aspect:1 polish:2 reality:1 lebesgue:2 photons:1 seems:1 except:1 lett:9 ruschhaupt:2 eigenstate:1 real:5 aspects:3 around:1 rules:1 sketched:1 early:1 vacuum:2 using:5 accepted:1 mod:2 particle:22 reduces:1 chamber:4 audience:1 either:1 stationary:3 reduced:1 twelve:1 duration:1 provided:1 dimensions:1 critical:1 provides:1 refer:1 measuring:1 power:1 potentialities:1 symp:1 sixty:1 haba:1 discussed:3 generated:2 practical:2 coquereaux:1 ot:8 sensitively:1 instruments:1 variable:4 references:1 determine:1 einstein:1 operator:8 theoretically:1 hep:3 log:2 sobotka:1 strictly:1 there:12 lot:1 hartman:5 complete:2 mics:2 irreversible:1 arranged:1 ωt:1 quantitatively:1 liouville:4 ωc:2 wants:1 ac:3 certain:1 aj:1 am:1 general:2 examine:1 invertibility:1 together:1 formulation:1 spends:2 sarkar:1 again:1 equivalently:1 remarks:3 leblond:1 deriving:1 important:4 bounded:1 peak:1 a6:1 readings:1 backward:1 calls:1 mass:1 decoherence:2 gαβ:5 gαα:1 consider:5 pointing:1 forbidden:1 commute:1 expressions:1 research:1 tt:4 tr:1 ﬁlled:1 justiﬁcation:1 ti:9 stochastic:3 case:18 returning:1 very:6 multi:1 hamiltonian:5 t2:2 prolonged:1 t0:6 t1:8 observables:8 unproblematic:1 small:2 largo:1 ten:1 rate:3 enhancement:2 haag:2 what:1 nonlinear:5 gβα:10 section:6 method:3 contrast:1 ranges:1 tracks:4 directions:7 equations:1 inspired:1 allows:2 action:5 family:5 vii:1 ﬁrst:5 ask:1 takes:2 probabilities:3 ψt:5 chaotic:5 taken:1 more:12 3ev:1 operators:7 studied:1 particular:4 foundations:1 producing:1 keeping:1 der:2 r3:7 spontaneous:6 deﬁne:1 compare:1 states:16 unbiased:1 numbers:1 sharp:3 information:10 needs:3 rather:5 acts:1 ghirardi:4 maps:5 acta:3 ensemble:2 simplicity:1 algebra:3 derived:2 orbits:1 olkiewicz:2 plane:7 faculty:1 fl:1 response:2 short:2 fundamental:6 helv:3 help:1 september:1 essence:1 soon:1 paper:5 through:2 existence:1 its:10 inquiries:1 energies:1 solving:1 actually:1 detected:6 microscopic:2 systems:17 framework:2 speculate:1 ift:2 easily:3 ifs:1 fully:1 level:4 2e:1 stopped:1 found:5 universit:1 uniwersytet:1 subsystem:3 generation:2 energy:4 reduce:1 idea:5 ﬂow:1 measurement:24 quantum:121 http:1 beyond:1 event:10 try:1 since:2 adhere:1 acting:1 print:1 conﬁrmed:1 benjamin:1 localization:6 reason:4 put:3 asi:4 phd:1 beginning:2 parametrized:2 computers:1 existential:1 probability:6 radical:1 number:4 done:3 least:1 passes:1 guess:1 introduction:2 twenty:1 smoothes:1 tata:1 construct:1 assumption:1 essays:2 uttiker:5 part:6 norms:1 believe:1 kind:2 recording:1 determined:1 doubly:1 toward:2 treated:1 electrodynamics:1 aﬃne:2 routledge:1 bohm:8 depending:1 self:3 recognizing:1 internal:1 measurability:1 towards:1 quote:2 reach:1 most:3 nothing:1 alpha:1 measured:1 branching:6 clear:1 sometimes:1 optical:1 electrons:1 exp:3 velocity:1 physics:12 emulsion:1 parameters:4 distributed:3 abelian:1 his:3 notation:1 dependent:3 zurek:1 continuum:1 arxiv:1 set:3 tree:3 unpublished:1 see:4 individual:10 chambers:1 constellation:1 visualize:1 currently:1 conditions:1 available:5 recently:2 attention:1 incident:2 distinguish:2 electrical:1 both:2 last:1 generator:1 pdp:6 sensitive:1 connection:1 whole:2 point:17 reasons:1 ga2:2 dimensional:7 simply:1 mathematically:4 pp:3 described:14 perspectives:1 due:2 kondrat:1 intricacies:1 describes:4 pd:2 ph:12 pi:2 pl:1 wheeler:2 understand:1 5ev:1 ǫa:2 p1:1 look:2 p4:1 solid:4 tetrahedron:2 while:6 optimization:2 replaced:3 behavior:11 couplings:2 engineers:1 landauer:1 merwe:1 unitary:3 vol:1 averaging:4 von:1 oﬀ:2 itself:4 vanish:1 emphasize:4 widely:1 higher:1 development:2 literature:1 levels:1 uses:1 chemistry:2 powering:2 λt:2 shape:1 questions:2 ldt:1 cut:1 kluwer:1 theorem:1 putnam:2 uniﬁcation:2 couple:1 quest:2 projects:1 formal:1 semi:5 follows:3 shapes:1 arthur:1 popular:1 mathematical:9 sketch:1 neumann:1 creation:1 some:6 back:6 examples:1 scale:2 describing:2 measurements:13 ψt1:11 prog:1 proc:2 run:1 jumps:12 infra:3 step:2 relating:1 hilbert:9 pα:1 simulation:7 kwiat:2 range:3 frigerio:2 diﬀerences:1 into:7 within:3 isomorphic:1 statistics:1 extremely:1 question:5 long:2 sections:2 rimini:4 elsewhere:1 lint:2 delta:1 line:9 active:1 characteristic:2 erice:1 up:5 us:19 continuously:1 similar:7 called:1 gisin:3 constant:5 chap:1 formalism:9 grw:6 dashed:5 coded:1 elements:4 calculating:1 problems:1 develops:1 structure:2 ago:2 implies:2 algorithm:4 required:1 cooked:1 having:1 once:2 partial:1 results:7 inﬁnitesimally:1 ga:16 centers:1 ﬁtted:1 deterministic:9 uniqueness:1 include:1 continues:1 wave:20 electron:4 crosses:1 mixing:1 transmission:1 deals:2 evy:1 eigenvalues:1 noted:3 eﬀective:2 smaller:4 jump:8 imply:1 traveling:1 dynamics:7 index:2 apparatus:1 giving:1 expressed:1 experiment:3 poles:1 exchange:2 respectively:1 ihα:1 growing:1 extreme:1 great:1 trans:1 involved:1 resulting:5 makes:1 honor:2 involves:2 integrations:1 decrease:1 reﬂected:1 apply:1 causal:2 cloud:5 use:4 deﬁnition:4 classically:1 doubt:1 formally:1 becomes:4 70th:1 popper:2 detects:3 ρa:2 account:2 araki:2 extension:1 freedom:6 control:3 process:21 high:2 sought:1 winfried:1 varied:1 destroying:1 located:1 sim:7 superluminal:1 philosophy:1 collection:1 physik:1 ﬁxed:1 realized:1 advocated:1 light:1 counter:1 bina:1 chapman:1 evolutionary:1 wigner:1 produces:1 interpreted:1 contractions:1 including:1 omnes:1 eﬀect:6 chosen:2 degrees:5 choose:2 derivative:1 weber:4 greater:1 orthodox:2 wolfgang:1 front:2 rotation:1 dirac:1 university:4 unpredictable:1 l2:2 mode:2 disregard:1 accompanied:4 beneath:1 traces:1 homogeneous:3 reﬂection:18 related:1 measure:4 our:18 special:3 out:6 category:1 res:1 rev:7 chaos:14 jadczyk:16 ref:4 red:3 interactions:1 diagonal:1 approaches:7 york:5 thrust:1 monographs:2 interaction:3 geometry:2 times:17 counterpart:1 length:4 errorbars:2 davis:5 rudolf:1 south:1 heuristically:1 third:1 iht:2 publication:1 adjoint:1 system:34 relations:2 their:5 perfectly:1 accompany:1 exactly:2 lublin:1 simulate:1 fuzzy:2 remember:1 automorphic:4 appealing:1 distinguished:1 julian:1 wroc:1 need:4 cosmology:1 clearly:1 viewed:1 angle:1 able:2 mechanism:3 instance:2 concerns:1 detector:23 gψ:1 heisenberg:5 lectures:1 gα:1 diﬀusion:2 device:1 class:5 tensor:1 url:1 proceedings:2 mechanical:3 fact:6 visualized:1 inﬁnitesimal:1 saturated:1 rough:2 trivial:2 ωct:1 based:1 insuﬃcient:1 should:4 muga:2 postulated:2 local:3 overall:1 words:3 applying:1 ωc0:1 evolution:18 precession:1 pulses:1 view:7 predictive:1 computed:1 exists:1 hβ:1 catastrophic:1 hα:7 packet:11 intensity:1 computer:1 enhanced:5 packed:1 interacting:1 state:27 invariant:2 quoting:1 reproduced:2 w01:2 w02:2 physicist:1 10ev:2 nimtz:5 problem:12 interpretations:1 instant:1 taking:3 etc:3 bristol:1 otherwise:2 comment:1 ch:1 cf:1 walk:1 modeling:2 respect:1 superselection:3 piecewise:8 trajectory:7 oﬀers:1 copies:1 electr:1 describe:5 corresponding:2 c2:2 present:4 noncommuting:2 subsets:1 value:3 rectangular:1 will:16 va:3 gorini:2 almost:1 vi:1 refs:1 squid:1 thus:12 dual:2 cini:1 perhaps:3 indistinguishable:1 strange:3 wavepacket:1 eds:3 iop:1 v0:8 infinite:1 identity:1 schr:3 center:5 modeled:3 well:2 thought:2 patterns:1 position:5 arising:1 usual:2 less:1 tcu:1 obtain:2 underlying:1 macroscopic:2 adv:1 density:2 bell:4 hall:1 simple:4 nato:6 semigroup:1 ought:1 increases:1 know:2 press:5 height:6 modiﬁes:1 necessary:1 like:7 martin:1 become:4 works:1 because:5 classical:47 phenomena:1 searching:1 alive:1 growth:1 aﬀects:1 ﬁnite:6 lead:1 instantaneous:1 does:4 transmitted:1 biology:1 journal:1 expansion:1 although:3 th:4 transformations:3 gained:1 pike:1 about:9 actual:1 world:10 universe:1 dependence:2 introduced:3 subset:1 own:1 h0:1 h1:1 primas:3 van:1 additional:3 transfer:4 noticed:1 appl:1 naturally:3 function:20 north:1 hq:1 but:15 repeated:2 convergence:1 lindblad:1 he:1 made:1 evident:1 whether:2 wish:1 limit:2 iterated:6 va2:1 distribution:2 mechanics:13 int:1 denote:2 periods:3 functions:2 compared:1 corporation:1 claiming:1 deﬁned:2 other:11 details:2 theor:1 conclusion:1 repeat:1 coupling:10 factors:1 rule:1 original:2 scientiﬁc:2 8th:2

quant-ph9911114.txt \|@word gs:9 consider:4 chinese:1 fabricated:1 leads:3 roy:4 grateful:1 a45:2 arik:1 squeezing:2 present:1 analogous:1 applied:1 zhang:1 fan:3 coon:1 condition:1 knight:2 tanh:6 convenience:1 optics:6 work:1 nbs:12 direct:1 literature:2 cosh:4 zero:3 further:2 odd:8 linear:4 even:10 index:1 what:2 nonlinear:10 appear:1 sun:1 section:2 fortschritte:1 above:13 a233:1 new:3 method:3 satisfy:3 condensed:1 lee:1 ggs:7 respectively:2 here:7 china:2 sinh:1 box:1 institute:1 involved:7 study:5 studied:3 usually:1 bp:4 makes:2 fbs:1 matos:2 via:2 apr:1 yuen:2 plenum:1 aphy:1 unit:1 use:1 commun:1 negative:4 next:2 a51:1 a50:2 a53:2 a52:1 a54:1 a59:1 torre:1 type:3 more:1 becomes:2 operators:11 brune:2 known:3 cases:1 iv:1 iii:1 deformed:4 science:2 equation:13 when:1 oscillator:4 fock:27 following:1 example:5 beijing:2 wang:4 give:3 haroche:1 states:53 want:1 every:1 verify:1 discussion:1 six:1 daskaloyannis:1 reducible:1 monroe:1 sfes:3 opt:11 instead:1 puri:3 parameter:5 css:1 fp:2 fu:11 algebra:21 may:2 max:1 ladder:30 applications:1 sss:1 representations:1 excited:1 engineering:1 fo:1 natural:1 iθm:1 ss:3 grant:1 sv:6 su:7 interpolates:1 lη:3 so:2 fundamental:1 hassan:3 representation:2 order:1 typical:1 s0:1 nlcs:5 help:1 over:1 professors:1 paper:3 ce2:2 nbss:1 mentioned:1 japan:1 its:1 derive:1 interesting:5 glogower:1 boson:2 systems:1 s1:1 them:1 combination:4 pegg:7 introduce:2 acta:1 now:3 hall:1 easily:3 february:1 finite:7 by8:1 kerr:2 orthonormal:1 mode:1 found:4 2n:5 as3:1 spinor:1 weyl:1 directly:2 as4:1 as9:1 hypergeometric:2 reduce:3 displacement:2 investigated:1 combining:1 quantum:30 laboratory:2 eq:31 special:3 shown:3 tombesi:1 space:17 since:4 rev:30 denotes:1 mη:1 ref:2 math:10 shows:3 foundation:1 theory:3 associate:2 davidovich:1 completely:1 ecs:6 york:1 definition:2 derivation:1 domokos:1 first:10 probability:2 number:9 set:1 another:6 given:5 rewritten:1 glauber:3 introduction:1 eqs:5 relations:2 their:1 1c:3 intermediate:4 1d:1 realization:1 man:2 structures:4 national:1 a31:1 academy:1 optical:1 pnm:2 α2n:2 iθn:1 coefficients:4 king:1 roles:1 loudon:1 annihilation:5 matter:1 solomon:1 classes:2 a43:1 were:1 a48:2 buzek:1 penson:1 generalization:3 frbs:1 seen:3 viewed:1 lie:6 sj:2 hgs:11 note:1 sciences:1 k0:4 generalized:1 do2:1 heisenberg:2 added:6 scripta:1 gallardo:1 bss:1 algebraic:14 satisfying:3 phase:9 lerner:1 considered:3 professor:1 ko:2 kn:1 physica:1 typeset:1 ks:7 yang:2 principle:1 exp:18 holstein:2 usual:2 physics:3 sum:1 fact:1 show:2 supported:1 joshi:3 substituting:2 find:5 d1:1 feng:2 proposed:1 parameters:1 state:56 should:1 only:1 generators:7 ocs:6 moussa:1 do:6 inθ:1 get:8 de:2 sf:3 bear:1 gen:7 liu:1 arxiv:1 acknowledgments:1 investigate:3 europhys:1 nγ:1 shapiro:2 multiplying:2 reference:2 fe:1 see:4 result:1 discussions:1 recently:2 detect:1 commutation:2 marmo:1 written:5 determined:1 various:2 between:1 barranco:2 geometric:2 email:1 αn:2 terms:6 a41:2 however:1 huang:1 both:4 last:1 limits:1 many:3 according:2 admit:3 raimond:2 filho:2 whole:2 detailed:1 co:2 cn:1 conclude:1 appeared:1 nˆ:3 dimensional:4 cs:16 ps:9 addition:1 three:2 been:3 expected:1 ph:1 choose:2 obtained:11 corresponding:4 θm:5 photon:25 2in:3 coherent:8 representative:1 those:1 case:3 reciprocal:1 pacs:3 expanded:2 rbs:7 examine:1 eigenstate:1 will:4 while:3 squeezed:5 procedure:1 stoler:2 real:3 cand:1 matsuo:1 saleh:1 vogel:2 vol:1 non:4 walmsley:1 equal:1 ii:1 claimed:1 bargmann:1 zaccaria:1 agarwal:4 different:3 walters:1 author:1 make:1 radiation:2 same:2 complex:3 quant:1 several:1 pan:2 development:1 used:3 sudarshan:1 nj:1 sivakumar:1 normalization:1 euro:2 primakoff:1 well:4 academic:1 without:2 left:2 teich:1 just:1 nd:2 wagner:1 obtain:14 transforms:1 using:5 previous:1 letting:1 integer:1 conclusions:1 olya:2 seems:1 other:1 lett:14 easy:2 transformation:1 identical:3 iθ:5 l83:1 lcs:4 eigenvalue:1 evaluate:1 decomposed:1 possible:1 ce:3 vacuum:2 world:1 accepted:1 decomposes:1 mod:10 semiclassical:1 shephard:2 follows:1 reduces:3 abdalla:3 either:1 arbitrary:2 szab:1 often:1 2iθ:1 people:1 creation:3 some:3 understood:1 gilmore:1 examples:4 b2:1 ccast:1 provided:1 phoenix:1 electromagnetic:1 welsch:1 expansion:3 binomial:5 revtex:1 bs:25 properties:3 raymer:1 discussed:4 o:9 posess:1 a2:9 act:2 introduced:6 ηf:1 soc:2 own:1 wineland:1 ηn:1 into:3 obtaining:1 nothing:1 hermitian:2 references:1 operator:51 jing:1 span:1 iphy:1 question:1 transform:1 was:2 naturally:2 function:12 barnett:11 elsewhere:1 form:6 oll:1 removes:1 but:2 formalisms:11 removed:1 partially:1 applying:1 2πm:1 us:2 below:2 limit:2 distribution:7 define:1 similar:2 called:3 eigenvector:2 aa:1 ac:1 constant:2 defined:19 certain:2 abstract:1 am:2 general:11 single:1 interchanged:1 our:1 formalism:21 sasaki:5 physical:1 functions:3 stumpf:1 susskind:1 nm:3 no:2 na:1 tara:2 generally:4 detail:1 field:6 setting:1 republic:1 es:3 eiθ:3 kinds:4 a13:1 sqs:2 subspace:3 deriving:2 ξk:1 sides:1 structure:17 assume:1 together:1 mancini:1 adam:1 time:1 n0:3 n1:4 svs:3 once:1

quant-ph9911115.txt \|@word concept:2 consider:1 skip:1 brownian:1 results:1 founded:1 eds:1 entropy:2 consists:1 expressions:1 adjustment:1 contributions:1 looking:1 certainly:1 inverse:1 superpositions:1 collisions:1 eˆ:13 tr:6 environment:2 tl:1 does:1 present:1 under:1 kλ:4 analogous:2 indicating:1 prigogine:1 p2:1 straightforward:1 very:8 collision:2 dell:2 choice:3 weighting:1 electron:1 ultraviolet:1 lecture:1 condition:1 leads:2 incoherent:1 level:2 notes:1 t0:4 leave:1 discrete:1 eigenvalues:1 inspection:1 equation:6 dilute:1 dealing:2 direct:1 approximation:2 second:2 uncomfortable:1 further:1 dynamics:8 implemented:1 linear:1 even:2 aim:1 plays:1 appear:1 giving:2 associate:1 reminiscent:1 ˆb:4 experiment:1 poles:1 ˆf:2 ˆh:1 new:4 ˆk:14 l1:6 ˆm:7 scenery:1 1997b:2 1997a:2 aˆk:6 respectively:3 fock:3 diagonal:1 objects:1 separation:1 equations:1 appears:2 z2:2 obtained:1 difficulty:1 involved:1 study:1 larger:1 typically:1 describing:1 subdynamics:2 usually:1 opinion:1 adopting:1 suitable:7 via:2 family:1 scales:2 qˆ:2 replace:1 apply:1 circumvent:1 linearly:1 derivatives:1 use:1 ht:2 takes:3 found:1 positive:3 charge:1 properties:1 few:1 ψh:2 doubt:1 memory:9 taken:2 means:5 stage:2 type:1 theoretical:3 more:7 separated:2 lowering:1 becomes:1 operators:3 odinger:3 berlin:2 carrying:1 basically:1 particular:1 known:1 foundations:3 must:5 kraus:2 account:2 valued:1 quantized:1 unbiased:1 recall:1 setup:2 created:1 mi:2 mv:4 values:2 following:4 example:2 numbers:1 control:1 grained:3 f2:7 renormalization:1 cosmological:1 process:1 relativistic:1 arise:1 stressing:1 states:6 indicates:2 his:1 taking:1 sense:1 looses:1 information:3 celoria:2 rather:1 describes:2 discussion:1 breaking:2 feature:1 located:1 pure:2 symposium:1 map:5 description:12 transforming:1 thermodynamic:2 philosophy:1 derived:1 mapping:6 reaction:1 representations:1 law:1 short:1 natural:3 dynamical:3 effective:2 yielding:1 introducing:1 element:2 provide:1 extrapolation:1 so:6 fundamental:1 enter:1 representation:3 make:1 typical:5 operations:1 holds:3 correlation:3 pauli:1 developed:1 pointed:1 microsystem:4 expects:2 interpreted:1 produced:1 london:1 looks:2 statistical:12 banach:1 numerable:1 existence:2 kinetic:3 still:1 its:4 before:2 derive:1 treat:1 till:1 fined:1 expectations:2 actually:1 zubarev:3 microscopic:1 systems:3 ahk:1 mail:2 hidden:1 h0:6 correspondence:1 non:6 gibbs:4 than:3 trh:2 press:1 universality:1 evolution:8 introduce:1 framework:2 effects:5 twoparticle:1 arriving:1 nov:1 now:4 smoothness:1 densities:1 represents:1 name:1 d3x:5 d3y:2 hamiltonian:7 d3p:1 orthonormal:1 realistic:1 l2:7 mode:1 fields:3 2m:4 universit:2 subset:2 macrophysics:3 eh:1 ek:1 independent:1 energy:2 ef:4 stronger:1 related:9 elementary:1 milan:2 interplay:1 measurement:1 quantum:14 our:4 avoided:1 extract:1 out:2 matrix:2 space:10 since:2 holevo:2 particles:2 may:2 istituto:2 formula:1 objectivity:2 after:1 theory:13 interactions:2 change:1 fisica:4 standard:1 extraordinary:1 completely:1 base:2 york:1 axioms:1 log:2 definition:3 interaction:2 derivation:1 r3:2 could:1 keep:1 motion:1 appearing:1 place:1 massive:1 assumed:1 corrections:1 first:4 initial:2 suffix:1 symmetry:1 hλ:5 variables:8 directly:1 open:2 f1:11 intermolecular:1 given:4 asymptotic:1 introduction:1 leading:3 dipartimento:2 system:12 least:1 indicate:1 assumption:1 brevity:1 too:1 master:2 molecular:1 challenge:1 recovered:1 gives:1 shifted:1 conˆ:2 relationship:1 exactly:1 part:6 review:1 attempt:1 eliminated:1 representing:1 peculiar:1 positively:1 superposed:1 unfortunately:1 isolation:1 approximations:1 ktr:2 final:1 preparation:10 matter:3 determined:2 contrary:1 supposed:1 fˆ:2 providing:1 treated:1 symmetries:1 outstanding:1 well:1 modern:2 generalization:1 say:1 need:1 seen:1 obviously:1 linked:1 irreversibility:2 heff:1 built:2 self:1 able:1 isolated:5 mechanism:2 k2:1 high:1 potential:3 take:2 objective:6 davies:3 detector:1 channel:1 heisenberg:2 formulas:2 trace:1 shall:1 price:2 measures:1 clearer:1 paid:1 most:3 boltzmann:1 connected:1 but:6 phase:1 probabilistic:1 class:1 eigenfunctions:1 interferometry:1 constructed:1 consequences:1 considered:5 performances:1 detectors:1 order:1 optical:1 principle:1 velocity:2 charged:2 physics:6 notion:1 incomplete:1 show:1 supported:1 anyway:2 rough:1 fine:1 based:2 parameters:2 situations:2 negligible:1 should:3 increasingly:1 only:9 coefficients:2 molecules:3 factor:1 bureau:1 local:3 equilibrium:5 do:2 mixture:2 viewpoint:1 di:8 express:1 expectation:2 truly:1 methods:1 joint:1 words:1 vacchini:4 dt:1 lahti:1 justified:1 holland:1 qp:4 processes:1 continuum:3 covering:2 conditions:3 arxiv:1 factorization:1 tuned:1 source:1 qm:5 view:1 body:1 set:4 mandatory:1 reference:2 uq:1 frame:2 correlations:1 differs:1 depends:1 descriptions:1 enhanced:1 dµ:1 best:1 satisfying:1 interacting:2 tackling:1 macroscopic:4 positivity:1 functionals:1 state:10 features:1 closed:1 between:3 boundary:2 approach:4 available:1 wf:5 terms:6 tricky:1 nature:1 initially:1 however:3 key:1 configuration:1 distribution:2 observable:2 essentially:3 piece:1 last:2 many:1 region:2 decay:1 according:1 attributed:1 context:2 cof:1 whole:2 experimental:1 comment:1 mechanics:6 relevant:10 point:3 pov:1 written:1 considers:1 considering:1 resorting:1 described:9 thermodynamics:2 locally:2 due:3 been:5 z1:2 reduction:1 much:2 coarse:5 basic:4 ph:1 hardly:1 abstract:1 arises:1 corresponding:1 qsf:6 both:1 coherence:1 gas:1 confinement:1 representative:2 systematic:3 demand:1 efficients:1 assigning:1 those:1 case:4 utmost:1 look:1 consultant:1 microphysical:2 will:7 invoking:1 slippery:1 behavior:2 applies:1 property:2 robin:2 procedure:9 maximal:1 detailed:1 unitary:2 von:1 thus:4 cone:1 beautifully:1 busch:1 different:1 italy:2 perform:1 microsystems:2 same:1 any:7 shifts:1 quant:1 schematic:1 avoids:1 finite:4 ludwig:3 transferring:1 meets:1 calculation:1 used:1 reinterpretation:1 singapore:1 trajectories:2 hydrodynamics:1 infinite:2 uˆ:1 schr:3 modes:1 nucleare:2 epr:1 analysis:1 bohr:1 academic:1 peculiarities:1 without:1 comes:3 components:1 position:1 model:2 arising:2 usual:1 isometry:1 just:1 being:5 obtain:1 rest:2 assigned:1 sources:1 underlying:1 immediately:1 scattering:7 yet:1 mittelstaedt:1 previous:2 density:6 nonrelativistic:1 k1:1 simple:5 other:5 treatment:2 δpq:1 relevance:1 ψˆc:1 structural:1 transformation:1 momentum:2 idealization:1 real:1 aspects:1 wˆ:4 replaced:2 sums:1 possible:3 spanned:1 confined:1 world:2 aiming:1 apart:1 loss:4 ˆbq:2 ˆbp:5 necessary:2 like:2 particle:9 persistence:1 sezione:2 reduced:1 mathematical:2 satisfactory:1 qed:3 classical:4 some:7 back:1 sight:1 absent:1 happens:1 scale:7 dense:1 electromagnetic:2 avoid:1 investigations:1 ak:1 dz1:1 dz2:1 assuming:1 either:1 measuring:1 scientific:1 indicated:2 slight:1 journal:2 electrically:1 how:2 shifting:1 nonseparability:1 hilbert:3 hiding:1 ρˆm:6 about:4 central:1 extension:1 aˆ:9 factors:1 o:1 compatible:1 range:1 eεt:1 introduced:1 considerations:1 h2:3 instruments:1 into:3 h1:3 recognize:1 appropriate:2 references:1 operator:13 amsterdam:1 physical:1 neumann:1 deal:1 elastic:1 ψk:6 removing:1 springer:2 there:1 question:2 transform:1 long:1 conservation:2 way:6 naturally:1 function:1 jones:1 north:1 complete:2 form:5 enough:3 lennard:1 preparations:1 idealized:1 hk:4 neutral:2 link:3 gain:1 basis:2 highest:1 irreversible:1 unmixing:2 volume:1 infn:2 2πi:2 inside:5 smooth:1 up:1 us:5 international:1 vˆ:1 limit:6 uh:2 uk:2 thermalization:1 ρm:4 problem:4 uf:7 called:2 expect:1 strongly:2 associated:5 choosing:1 separability:1 af:1 defined:1 milano:4 universal:1 contribute:1 general:4 conserved:1 formulation:1 nazionale:2 work:1 simplest:1 deeper:2 functions:4 paradox:1 no:6 eq:2 nf:2 reality:1 field:11 setting:2 role:5 spatial:1 nice:1 conclude:1 picture:3 briefly:1 elements:4 generates:1 problems:1 variation:1 prepared:3 generated:1 suited:1 generalized:4 sider:1 nuclei:2 structure:5 ago:1 implies:2 using:1 eff:2 requires:1 interval:1 graining:2 mass:4 fact:2 time:25 observables:4 decoherence:2 starting:2 lanz:6 once:1

quant-ph9911116.txt \|@word comparatively:1 desirable:1 consists:1 regularize:1 looking:1 const:2 under:1 solution:9 force:11 miller:1 estimates:1 approximation:1 second:8 rigorous:1 dedonder:1 implemented:1 even:5 sheeted:1 above:4 conduct:1 new:40 pioneering:2 κn:1 here:4 represented:3 path:7 obtained:4 study:7 maioli:1 fourier:1 changes:6 classification:1 replace:1 derivatives:2 would:3 negative:3 mediate:1 call:1 type:4 successful:1 solitons:1 odinger:6 berlin:1 former:10 must:4 me:2 springer:3 word:2 quartic:1 work:1 theories:1 itself:3 my:2 example:5 give:1 generically:1 attract:1 guarantee:1 end:2 beyer:1 sitting:1 feature:1 recovers:1 hor:1 ordinary:2 description:1 oscillators:4 after:4 inessential:1 summarize:1 law:2 arch:4 parallel:6 types:2 third:2 decreasing:1 order:3 interpretation:2 satisfied:1 london:3 innovative:1 before:1 fix:1 complex:12 olver:1 emphasize:1 maximal:1 them:4 repulsive:1 they:7 singularity:7 reasonable:1 each:1 went:1 mean:1 fairly:1 series:5 principles:1 rp:7 particles:1 re:11 daniel:1 rm:3 sinh3:1 sinh2:10 linear:2 abramowitz:1 standard:2 admits:1 estimate:3 incorporates:1 asymptotical:1 starts:2 hull:1 creates:1 generalizations:5 already:6 features:1 restrict:1 another:2 sturm:1 trost:1 similarly:1 top:2 needed:2 listed:1 john:1 whitham:1 peculiar:1 distance:1 approximations:1 zero:1 preparation:1 feeling:1 minus:3 perturbative:6 mind:2 spectrum:12 manner:1 seem:3 seminar:1 forced:1 strength:1 convenient:1 latter:7 responsible:1 isolated:1 thorough:3 forces:9 degenerated:1 4b2:1 shall:11 diminishing:1 wells:1 regular:2 letter:3 phase:1 observation:2 principle:2 section:2 distances:2 solutions:8 analogue:2 d2:4 just:5 paralleling:1 kukulin:1 hamiltonians:1 do:2 de:1 reversal:2 dr:2 normalizable:4 covering:1 nicely:2 phenomenologically:2 observed:3 result:4 best:3 techniques:1 exponent:1 symmetric:32 simplest:1 encounters:1 terms:3 parallels:2 extend:1 weak:3 wu:1 improve:1 cos:3 irregular:1 presumably:1 appeared:2 polynomial:4 three:7 been:19 quickly:1 much:4 expected:1 entered:1 families:2 deeper:3 gemma:1 applied:3 exception:1 tanh:2 near:4 leaves:1 phenomenological:6 ir:2 iu:2 im:2 ic:1 containing:1 make:1 periodic:3 quant:6 split:2 unfortunate:1 several:5 grows:1 hermiticity:3 independent:3 numerical:6 potentials:10 suitable:3 shortly:1 academic:2 kratzer:1 possesses:1 left:2 quoted:1 newton:1 solvability:6 facts:1 scattering:2 yet:2 previous:1 similarities:1 eckart:5 hille:1 innocent:1 l87:2 iλ:1 iβ:3 iε:10 possible:4 background:1 unique:1 specific:1 intertwines:1 right:1 old:3 czech:3 easy:3 indirect:2 ignore:1 cooper:1 subclass:2 core:2 illustration:2 constructive:1 powerlaw:1 super:1 properties:2 impenetrable:1 acquire:1 months:1 recollect:3 plus:2 slightly:2 considerations:4 presence:3 bound:10 fern:3 down:1 lies:4 hermitian:13 often:2 existed:1 nodal:1 initial:5 class:3 way:10 astrophysics:1 was:1 form:9 offer:3 differences:1 failure:1 removed:1 anew:1 proved:1 abstract:1 proves:4 exist:1 check:1 physical:7 locality:1 vanishes:1 guardiola:3 ny:1 setting:2 role:2 denotation:1 nr:1 shrink:1 intend:2 models:36 preceding:1 felt:1 uniformly:1 meisinger:2 variable:2 parities:1 jones:2 regime:1 coulomb:2 assume:1 proposed:3 interval:2 time:5 remarkable:1 skip:2 leads:1 comments:2 ros:2 depend:1 quasi:6 marks:1 anharmonic:1 methodical:4 seemingly:1 choice:7 normalizability:1 ective:1 stays:1 exact:4 bring:1 did:1 proposals:1 leave:1 solved:1 unexpected:2 oscillation:2 cosh:9 appear:3 axes:1 uniform:2 current:1 illustrations:2 appeal:2 satisfy:1 supporting:1 understanding:1 cos2:2 groups:1 appears:1 change:7 symetric:1 shift:7 studied:6 trial:1 simultaneous:1 graffi:1 domains:1 conveniently:2 studies:3 nmax:13 emerge:2 useful:4 subcategory:7 merely:2 prove:2 sake:1 positive:5 predictions:1 symbolizes:1 approach:4 bender:16 apparent:1 deformed:4 originally:1 oscillator:11 modified:2 values:2 growing:1 subcategories:2 figure:1 bessis:2 performed:1 unphysical:1 verlag:1 regularization:4 fortunately:1 discussion:1 means:5 write:2 dominance:1 economy:1 product:1 mar:1 paramount:1 may:36 dx2:1 applications:3 produce:1 drastic:2 natural:1 outline:1 whenever:1 sp:2 explicit:9 sh:3 so:10 representation:1 indeed:6 mainly:2 years:1 stability:1 course:3 experiments:1 still:8 derive:1 group:2 interesting:3 vicinity:1 coordinates:8 forms:3 attraction:1 offers:2 mail:1 main:4 correspondence:4 non:14 half:1 now:5 hall:2 teller:8 inversion:1 arrows:1 realistic:1 em:4 domain:3 en:19 ei:1 significantly:1 ef:3 conventions:1 eu:2 eq:15 space:2 increase:3 attracted:1 contained:1 formula:4 correct:1 unifying:1 theory:6 derived:2 possibility:1 quite:2 complicated:2 besides:1 e0:1 forbids:1 dunne:2 language:1 transition:6 thing:1 place:1 undesirable:1 first:13 origin:7 symmetry:11 variables:7 waves:4 directly:1 open:2 angular:1 size:1 given:1 caught:1 indicate:1 brevity:1 convention:1 speaking:1 gives:3 continuous:1 x2:8 x3:4 x1:1 than:3 x4:3 milton:2 unfortunately:1 accordance:1 coulombic:1 were:3 ann:1 generalization:2 say:5 recover:1 any:5 symmetrized:7 downwards:2 note:2 sciences:1 potential:18 resembling:2 opposite:4 4u2:1 paid:2 algebraic:2 formulae:6 pair:1 analytically:1 latex:1 especially:4 surprising:1 dordrecht:1 quantity:1 precise:1 show:2 merit:1 discovered:1 scarce:1 paradoxes:3 ground:4 analytic:3 only:22 znojil:17 get:2 cannot:3 symmetrically:2 gen:21 reveal:1 summary:1 mapped:1 reveals:1 encouraged:1 subsequent:1 review:5 enough:2 between:11 reading:1 notice:5 vertical:2 suppresses:1 jr:1 comm:1 analyzed:1 originates:1 dates:1 many:4 according:1 approximative:1 comes:2 among:3 continuation:2 dutt:3 innovations:1 ωx2:2 moreover:1 unusual:2 analogies:1 locally:1 mark:1 direction:2 enable:1 formed:1 careful:1 irrelevant:1 spirit:2 case:6 globally:1 might:4 chap:1 situation:1 tunneling:1 prevalence:1 regularity:3 sudden:1 return:4 different:6 contents:1 author:1 same:9 shifts:1 arguments:1 constructed:1 breakdown:2 invariance:3 cr:1 pures:1 no:3 roughly:1 without:1 solve:1 components:1 coordinate:1 termination:2 ujf:2 dimension:3 l107:1 unsolvable:2 stegun:1 infeld:1 ch:1 touch:1 seems:2 lett:12 versa:4 republic:2 momentum:1 real:28 complemented:1 easily:5 rules:1 harmonic:11 mol:1 confined:2 using:3 accepted:1 mod:4 particle:1 either:1 fully:1 downward:2 2x:2 respect:3 provided:5 dimensions:2 confirm:1 critical:1 bessel:1 refer:1 power:2 equivalent:1 broken:1 comparison:1 central:1 theorems:1 discussed:1 practical:2 mutually:1 aˇcek:1 mixed:1 luck:1 perturbed:1 cambridge:1 communication:1 numerically:1 references:1 strip:1 elementary:5 harrell:1 there:8 start:2 strict:1 emergence:1 complete:6 curiously:2 improved:2 liouville:3 strongly:5 ab:3 certain:3 describe:1 general:5 file:1 av:1 fill:1 again:2 deserve:1 rosen:2 field:3 terminating:1 parameterizations:1 complutense:1 separate:4 a2:1 bounded:3 suited:1 l61:1 perturbatively:1 curve:2 mimic:1 appl:1 original:3 forget:2 ceases:1 trigonometric:1 zinn:1 equivalence:1 misses:1 removal:2 alvarez:3 preserved:1 th:2 homepage:1 straightforward:1 puzzled:1 very:5 induce:1 sons:1 surprise:1 difference:3 condition:6 hamiltonian:2 list:2 large:2 small:6 biological:1 employing:1 ten:1 nbs:1 tex:1 integrability:1 further:2 canonical:1 what:3 nonlinear:1 sum:1 version:2 method:1 contrast:4 zaragoza:1 component:1 ranges:1 spector:1 concluding:1 strong:4 equations:2 antisymmetric:1 inspired:2 extremes:1 pick:1 narrow:1 jackiw:1 oschl:8 via:2 family:7 viz:2 readily:2 proceed:1 distinct:1 contains:3 more:16 initiated:1 ugge:1 tested:1 particular:5 known:10 keeping:2 recall:2 equation:8 centrifugal:1 remain:2 levai:1 history:1 f1:5 compare:1 impossibility:1 states:10 junker:1 numbers:4 sense:2 axis:9 respective:4 rather:1 breaking:1 intended:1 wiley:1 singularities:1 mapping:1 biophysics:1 plane:2 fd:1 cannata:4 horizontal:1 fl:1 short:5 spectra:4 negligible:1 sect:3 fundamental:1 help:1 essence:2 soon:1 paper:3 existence:2 its:53 energies:13 conjugation:1 late:1 absence:1 systems:4 jacobi:11 debrecen:1 deformation:4 supersymmetry:1 tentatively:1 motivated:1 framework:2 cosh2:6 smoothness:1 2u:2 2v:1 2r:3 always:1 loosely:1 2z:1 2d:2 inequality:1 2a:3 2b:3 found:1 2n:7 characterized:4 formulate:1 energy:7 idea:4 expect:1 quantum:21 infinity:5 really:1 discrete:5 since:4 acting:1 denoted:1 occurs:1 voros:1 reason:3 members:1 put:1 definition:2 omit:1 exponentially:1 universidad:1 consequence:1 laguerre:5 feel:2 number:4 preservation:1 maple:2 differ:1 perturbation:2 introduction:3 least:2 obtainable:1 assumption:1 scheme:2 smoothed:1 recovered:1 observations:1 shifted:1 option:1 relationship:1 immediate:2 part:2 authors:1 schr:6 sign:4 molecular:1 determined:1 motivation:1 holzwarth:1 paths:1 generalizes:1 constructions:1 majority:1 generalized:3 analogy:2 towards:1 most:8 significant:1 extremely:2 model:19 clear:1 sometimes:1 coincides:2 traditional:1 exp:3 physics:1 lying:1 ambiguities:1 particularly:2 phenomenon:3 relation:1 find:1 believe:1 parameters:4 factor:2 integrable:1 dominant:1 notation:1 dependent:1 remedy:1 closely:2 during:1 coth:1 arxiv:4 factorization:1 spiked:1 set:4 achieved:1 unpublished:3 see:3 arc:1 descriptions:1 close:1 contour:2 positivity:1 various:3 conditions:4 available:3 recently:5 missing:1 attention:5 analogues:1 vanishing:4 distinguish:2 both:14 enables:2 last:5 quantization:1 connection:3 context:3 vault:1 whole:10 arbitrarily:1 point:3 simple:1 asymptotically:7 corresponds:1 dimensional:9 simply:3 described:1 pt:52 due:6 asymptotics:4 ph:6 pn:2 empty:2 addison:1 gap:1 lives:2 demand:2 replaces:2 classifications:1 exponential:1 pacs:1 straight:3 while:1 replaced:1 error:1 couplings:9 binding:1 encountered:3 obstacle:1 hyperbola:1 grant:2 virtually:2 higher:2 literature:1 lie:2 assignment:1 usually:1 levels:4 moving:1 predecessors:1 recent:4 lower:2 analysis:6 obviously:2 wedges:1 chemistry:2 lowers:2 mimicked:2 shape:10 atomic:1 questions:3 alternative:3 cut:1 kluwer:1 guaranteed:2 source:2 theorem:1 relevance:3 violations:1 solvable:30 transformation:1 surprised:1 loss:1 integer:3 bit:1 complexification:2 formal:4 rotate:1 imposed:1 semi:3 shaped:3 systematically:2 follows:3 shapes:1 communications:1 2nmax:2 popular:3 mathematical:1 methods:1 2iε:1 some:6 back:2 examples:2 curious:1 savage:2 resonances:2 novelty:1 integration:7 eliminate:1 saad:1 minimal:1 patient:1 bb:1 step:4 bs:3 dictated:1 integers:2 anything:3 constraint:4 simulation:1 range:2 repulsion:6 rho:1 unnoticed:1 into:2 within:13 appropriate:3 proportional:2 question:2 long:3 handbook:1 madrid:1 analyze:1 complexified:1 gauss:3 ioffe:1 line:11 exhaustive:1 intuitive:1 characteristic:1 up:3 us:14 par:1 approaches:1 similar:9 called:9 constant:2 defined:2 char:1 single:1 warning:1 formalism:1 defines:1 paradox:4 tentative:1 elements:2 conventionally:1 excitation:1 problems:1 polynomials:7 generated:1 evai:5 papp:1 structure:1 land:1 implies:3 vice:4 lanl:2 turbiner:2 requires:1 once:3 aguilera:1 partial:2 results:2 illustrated:1 ge:1 broader:1 reˇ:1 compact:1 simon:1 contours:1 wave:18 continued:1 categories:2 notes:1 try:2 cas:2 manifestly:2 inspection:2 compensated:1 sukhatme:3 seventies:1 sin2:3 insertion:2 odd:2 invertible:2 morse:8 degree:1 respectively:2 following:3 sinh:12 abbreviating:1 extreme:2 remark:2 roychoudhury:1 larger:1 implementation:1 resulting:3 makes:1 involves:2 composed:1 varshni:2 private:1 jaff:1 decrease:1 imaginary:14 use:2 asymptotic:2 commun:1 remains:8 few:5 themselves:2 l195:1 formally:1 becomes:6 occurred:1 hints:1 tunnel:1 obvious:2 publications:2 proof:1 weaker:2 bent:2 purposes:1 high:2 bend:1 sought:1 tan:1 sin:5 singular:13 physik:2 fits:1 introduced:1 computations:2 light:2 counter:1 chapman:1 subsequently:1 insight:1 facilitated:1 decay:1 ln:2 lr:3 lx:4 symmetrization:3 practice:1 landau:1 rotation:1 february:1 university:2 unpredictable:1 l1:1 enigmatic:1 related:9 operator:3 decays:1 our:51 special:2 out:2 category:4 rep:1 rev:14 mediated:2 lecture:1 ref:6 math:29 interactions:3 frank:1 eck:4 completely:2 khare:3 york:5 interaction:4 could:1 keep:1 counterpart:2 length:1 hence:3 scarf:3 andrianov:2 scene:1 precisely:2 publication:2 hyperbolic:1 behaves:1 their:17 intermediate:1 final:4 boettcher:7 commutativity:1 academy:1 exactly:16 too:7 richer:1 submitted:2 limiting:1 appealing:2 kepler:1 constrained:1 apparently:1 clearly:2 agency:1 able:2 mechanism:1 lectures:1 who:1 mimics:1 connected:1 preliminary:1 why:3 consequences:1 stronger:1 mechanical:1 fact:2 violation:3 text:4 bagchi:1 supported:2 terminate:1 purely:6 trivial:1 agrees:1 o:5 based:2 should:1 employed:3 he:1 local:3 move:1 exceptional:3 overall:2 lucky:1 ones:1 numerous:1 differential:4 fixes:2 navarro:1 aef:1 fixed:1 qo:3 strengthened:1 requirement:1 temporarily:1 exists:1 frame:1 acquires:1 buslaev:1 state:11 difficulties:1 closed:6 invariant:6 boundary:5 ends:2 ability:1 importance:1 reproduces:1 key:3 interpretations:1 limits:1 attributed:2 etc:2 admit:1 safely:1 ck:3 detailed:4 relevant:1 cf:3 cz:2 table:1 addition:1 restrain:1 copied:1 define:2 controlled:1 c2:6 c1:6 present:15 quotation:1 multi:1 subsets:1 value:3 choices:1 will:13 revisited:1 vi:1 refs:2 wkb:1 thus:2 encouragement:1 liouvillean:2 partner:2 parts:1 finite:4 privileged:1 difficult:1 http:1 cubic:4 upon:1 effect:4 infinite:2 frequently:1 expand:1 numbered:1 off:1 reflection:2 acknowledgement:1 nevertheless:1 well:11 pham:1 sets:1 firstly:1 usual:4 spherical:2 less:4 klauder:2 preprint:7 bell:2 sky:1 reasons:3 developments:1 term:2 know:2 press:1 immediately:2 insert:1 necessary:2 like:2 become:4 page:1 accessible:2 parity:5 because:1 classical:3 regularized:2 growth:2 sufficiently:3 avoid:1 does:7 obey:2 wesley:1 although:2 analyses:2 about:4 justin:1 introduces:1 dependence:4 compatible:2 important:1 andez:3 rendered:1 pergamon:1 washington:1 guard:1 square:2 mere:2 van:2 additional:3 transfer:1 noticed:1 quadratic:1 terminates:1 notices:1 naturally:1 function:8 hypergeometric:3 hs:2 brand:1 but:3 repeated:1 construction:2 ho:2 insertions:1 highest:1 partially:3 made:1 instructive:1 smooth:2 below:4 limit:2 problem:1 mechanics:17 int:2 interchanged:1 atomki:1 supersymmetric:2 functions:13 detail:1 arctan:1 other:6 details:5 branch:1 concerning:3 conclusion:2 repeat:1 expressible:1 chem:2 stay:1 hulth:6 lifschitz:1 upwards:2 coupling:5 prevalent:1 4v:1 rule:2 understand:1

quant-ph9911117.txt \|@word partial:7 consider:5 separates:1 results:1 illustrated:2 proposition:3 grateful:1 devoted:1 whose:1 depend:1 tr:9 γj:1 finally:1 monotonically:1 swap:1 γm:1 under:7 xxiv:1 analogous:1 applied:2 orthogonal:2 mixing:6 matrices:10 condition:4 entire:1 trb:1 vector:2 eigenvalues:3 barbara:1 smaller:2 says:1 lewenstein:2 deutscher:1 linear:10 what:1 stands:1 witnessed:1 giving:1 assisted:1 pawel:2 new:2 increasing:1 hb1:2 method:1 hb2:1 compact:2 full:1 equals:2 desired:1 plenio:1 box:1 great:1 canadian:1 technical:2 study:2 larger:4 contradiction:2 amount:2 resulting:1 procedure:1 action:1 bob:3 studies:1 involves:1 deﬁne:3 useful:1 family:4 private:1 ﬁrst:2 unitary:2 apply:2 use:5 additive:1 asymptotic:2 would:6 prove:3 remains:1 positive:42 γi:1 deﬁnition:4 hilbert:1 ψk:7 ψi:14 call:1 therefore:3 jonathan:1 theoretical:1 γn:2 bennett:1 share:1 particular:2 known:2 must:2 ibm:2 ρf:19 mm:1 recall:2 equation:2 mn:6 remain:1 values:1 concepts:1 following:5 example:4 stimulating:1 proof:7 point:2 figure:1 give:3 preserving:3 distillation:3 states:32 minimum:1 numbers:1 hyperplane:1 david:1 conversely:1 information:3 end:1 majorization:1 s1:4 holds:3 feature:2 write:1 how:1 criterion:5 pure:26 map:14 product:5 mar:1 algebra:2 may:1 max:1 after:1 applications:1 faculty:1 cambridge:1 summarize:1 unentangled:1 times:1 hannover:2 natural:1 explicit:2 sk:12 complexity:1 so:2 expression:1 operate:1 bipartite:12 operations:8 ρred:1 developed:1 over:1 held:1 paper:2 through:1 committee:1 still:1 its:5 before:2 ﬁnd:4 thank:1 maps:22 lo:14 conjugation:1 systems:2 schmidt:86 combination:2 propose:1 distilled:1 introduce:1 they:6 half:1 aka:1 rotation:1 now:2 easily:1 february:1 always:1 university:2 hermitian:2 unextendible:2 each:4 found:7 repeating:1 characterized:2 mean:1 subset:1 domain:3 hard:2 idea:1 related:2 quantum:6 relates:1 operation:3 beyond:1 eq:8 witness:2 out:3 divincenzo:4 shown:5 matrix:25 space:2 since:6 rev:1 research:2 increase:8 denoted:2 akademischer:1 ref:5 math:1 theory:4 associate:1 nonadditivity:3 completely:6 ask:2 definition:2 derivation:1 geometry:1 could:3 nonnegative:3 terhal:4 onto:2 assign:1 first:1 separable:4 initial:3 probability:2 number:55 rank:31 exact:1 construct:2 another:1 carry:1 impossible:1 open:1 illustrate:1 given:1 necessarily:2 rewritten:1 similarly:1 concentrating:1 behaves:1 system:2 least:8 heights:1 needed:2 assumption:1 too:1 scheme:1 1n:1 proving:1 part:3 superoperator:3 review:6 july:1 x1:1 uhlmann:3 separability:6 coefficients:1 karol:1 require:1 namely:2 submitted:2 classes:1 were:2 gives:1 poland:1 exhibit:1 fashion:1 thapliyal:1 rewrite:1 borrowing:2 argument:1 zyczkowski:1 say:2 seen:1 any:12 conversion:1 depending:1 lim:1 latter:1 able:1 mif:1 note:3 take:2 computation:1 play:1 most:4 germany:1 nothing:1 suﬃcient:2 class:4 classiﬁcation:1 acknowledges:2 special:1 satisﬁed:1 kn:3 physics:5 notion:3 quantity:1 shor:3 show:11 violation:1 manipulation:1 bring:1 relation:2 stepwise:1 copy:4 written:1 than:7 tomiyama:1 lemma:8 only:10 going:1 local:7 do:2 mixture:1 quantph:1 get:1 watson:2 cannot:5 words:1 du:1 transposition:6 arxiv:1 maciej:1 acknowledgments:1 mapped:1 conversions:1 set:8 their:1 exists:5 observed:1 see:5 result:3 discussions:2 alternative:2 best:1 aro:1 said:1 tensor:5 positivity:6 yet:1 µm:2 state:51 µn:4 between:2 invariant:1 conditions:3 email:1 publishers:1 terms:3 extend:3 nature:1 importance:1 choi:1 transpose:1 however:1 inseparable:1 comm:1 convertible:1 both:1 limits:1 many:2 taking:2 equal:2 contract:1 connection:1 straint:1 interesting:2 hσ:3 qubit:2 hρ:2 com:1 supply:2 simple:2 corresponds:1 dimensional:1 simply:1 maximize:1 lagrange:1 respect:1 transformations:1 basis:4 equivalent:1 px:1 locally:1 copies:7 been:12 defined:1 reduction:2 much:2 pg:1 ph:12 pi:3 pl:1 fig:1 sufficient:1 convert:2 bmt:2 maximally:8 spin:1 protocols:1 case:3 developing:1 value:1 will:13 institute:2 while:1 suppose:1 behavior:1 property:3 characterizing:1 vectors:11 formulation:1 thus:2 symmetrize:1 ii:5 characterize:1 itself:3 conn:1 develop:1 grant:1 perform:2 make:4 same:4 complex:2 quant:11 mixtures:1 higher:1 hermiticity:3 used:1 numerical:1 hand:1 entanglement:15 invariance:1 implement:1 lower:5 center:1 scenario:1 makes:1 underlies:1 well:5 academic:1 sets:3 dimension:1 usual:1 ny:1 λp:5 protocol:2 popescu:1 less:3 newton:1 obtain:1 actions:1 gda:2 transforms:1 immediately:1 λk:10 polish:1 λi:3 λn:5 λm:3 kluwer:1 density:30 characterization:1 seems:1 cc:13 armin:1 theorem:9 guarantees:1 transformation:1 noting:1 identical:1 aspects:1 nielsen:1 mor:2 showing:1 possible:6 additivity:1 possibly:1 entangled:15 mathematics:3 using:3 bit:1 necessary:4 like:2 follows:5 alice:3 either:1 arbitrary:1 ha1:2 ha2:1 reduced:1 sketch:1 because:1 methods:1 classical:4 some:10 understood:2 examples:1 b2:2 convex:4 undistillable:1 extensively:1 esf:1 does:3 decomposition:4 power:1 performed:1 bm:5 bn:6 pose:1 bi:1 expansion:1 properties:2 about:1 ol:1 carried:1 extension:1 tracing:1 o:1 range:1 a2:2 ensure:1 greatly:1 mixed:16 introduced:1 restrict:1 nsk:1 letters:7 h2:2 communication:5 into:2 bound:13 bruss:2 negative:1 coeﬃcients:1 distillability:1 parties:1 operator:3 algebras:2 log:3 support:3 there:9 question:3 workshop:1 low:1 way:1 convertibility:1 was:2 function:4 tight:3 form:4 smolin:3 but:6 construction:1 hn:15 he:1 made:3 horodecki:9 whether:4 characteristic:1 yorktown:1 us:6 converted:3 problem:1 b1:1 cirac:1 proved:4 diﬀerently:1 ai:2 certain:2 aj:1 am:4 evidence:3 peres:4 single:2 exist:1 our:2 journal:1 work:2 check:1 physical:6 again:1 no:4 when:10 deﬁned:1 multipliers:1 application:1 other:3 role:1 details:1 nonincreasing:1 austauschdienst:1 conclusion:1 denote:2 completes:1 a1:1 important:2 bases:3 implies:2 assume:3 equivalently:1 scientiﬁc:1 time:2 n1:2 n2:1 having:1

quant-ph9911118.txt \|@word aguilera:13 limited:1 partial:1 caused:1 truncated:1 results:14 integration:3 leads:1 ge:1 montr:1 expressions:3 adjustment:1 contributions:1 simon:1 bx2:6 those:1 under:1 very:2 wave:2 entries:1 exact:6 condition:2 hamiltonian:17 solution:2 integrated:1 discrete:1 eigenvalues:13 anal:1 upper:6 torres:1 estimates:1 direct:3 approximation:2 second:1 castro:1 further:4 chem:3 odd:1 substitute:1 even:1 will:2 errors:4 richard:1 selected:1 diaz:2 subspaces:1 nine:1 increasing:1 method:7 confluent:2 degree:1 here:4 reported:1 flannery:1 focused:1 directions:1 slater:1 xα:3 fifteen:2 appears:2 obtained:12 study:1 allows:2 trial:1 suitable:1 makes:1 hermite:2 integrations:1 replace:1 select:1 readily:1 use:3 x44:1 eψ:4 positive:2 contains:1 suppl:1 next:1 ψn:2 therefore:2 scope:2 h1d:1 von:1 ψd:1 more:3 separated:1 becomes:4 factor:1 corrected:2 odinger:11 appendix:4 normalized:4 particular:2 known:2 iii:4 must:1 h11:1 equation:11 work:8 oscillator:18 values:6 znojil:5 example:2 f1:2 figure:1 organized:1 indicates:1 minimum:2 performed:1 council:1 occur:1 rather:1 enl:3 eigenenergies:1 chemical:1 instead:1 parameter:7 singular:17 may:2 notre:1 after:1 derived:1 dx2:6 applications:1 natural:1 outline:1 effective:2 spectra:1 explicit:3 yielding:1 element:3 representation:1 order:1 δmn:5 rounded:1 words:1 indeed:2 over:4 pascal:1 paper:2 london:1 mentioned:1 kinetic:1 its:1 supplemented:1 rapidly:1 2λb:1 chosen:1 interesting:5 better:1 according:1 systems:1 jacobi:1 main:1 h0:9 non:2 good:1 fig:1 introduce:1 mention:1 they:1 acta:1 nov:1 now:3 hall:7 easily:1 term:5 tonian:1 always:1 university:4 presented:5 sufficiently:1 2b:1 each:1 x10:1 found:3 2n:4 side:1 carlos:1 schemes:1 financial:1 energy:8 hypergeometric:2 reduce:2 related:1 used:4 substantially:4 our:5 eq:14 special:2 canada:2 gol:4 shown:3 matrix:21 space:2 rounding:1 restricted:1 since:3 rev:1 research:3 encourage:1 formula:2 ref:8 correct:2 math:10 shows:1 occurs:1 dman:4 diagonal:1 free:4 put:1 estimate:2 e1:1 e0:4 dirichlet:1 recipes:1 support:1 first:7 origin:1 features:1 omitted:1 number:5 bhattacharyya:1 another:1 angular:3 given:12 boulevard:1 their:3 introduction:1 eqs:1 needed:3 1d:1 variational:37 x2:10 schr:11 x1:2 than:1 intrinsically:1 e21:6 wide:1 sections:1 zero:1 determined:3 were:4 perturbative:1 lowest:1 acknowledged:1 ann:1 turned:1 generalization:1 concordia:1 seen:1 recover:2 clearly:1 eal:1 built:1 depending:1 studying:1 able:1 sciences:1 potential:10 generalized:5 finding:1 unperturbed:1 begin:1 most:1 but:2 analytically:1 class:2 exponent:2 reduces:4 calculated:1 later:1 coincides:2 bret:2 physics:2 fact:1 phenomenon:1 show:1 soluble:2 minimizing:3 solutions:3 substituting:1 rough:1 d2:7 find:1 ground:8 parameters:2 written:1 should:1 only:1 coefficients:2 maisonneuve:1 integrate:1 employed:3 hamiltonians:1 hope:1 above:1 means:1 secular:1 de:1 cannot:1 dx:5 report:1 gen:4 qu:1 arxiv:1 eves:1 navarro:13 europhys:1 spiked:12 view:1 set:10 art:1 fascinating:1 depends:1 sec:4 terms:2 hammer:1 eigenfunctions:3 nuclear:1 away:1 state:8 difficulties:1 closed:1 x24:1 boundary:1 approach:2 x22:1 notice:1 recently:1 extend:1 however:1 pathak:1 gratefully:1 vanishing:1 improve:2 both:1 refinement:2 equal:1 hψ:2 enℓ:1 expression:2 teukolsky:1 labelled:1 point:2 harmonic:18 16b:1 dimensional:5 bγ:1 polynomial:1 respect:2 forms:1 described:1 basis:15 simplification:1 been:4 int:2 treat:1 interest:1 kronecker:1 ph:1 austriaca:1 dame:1 corresponding:3 eduardo:1 subspace:4 hmn:3 observe:1 equations:1 present:5 case:8 pacs:1 expanded:1 engineering:1 value:2 employ:1 near:2 optimization:1 suppose:1 procedure:1 h3g:1 vol:1 characteristics:1 refs:1 thus:4 iv:4 ii:5 itself:1 conf:1 grown:1 different:2 grant:1 eigenvalue:2 quant:1 harmony:1 finite:1 higher:3 literature:1 numerical:7 hand:2 levels:1 purpose:2 potentials:2 off:1 minimize:1 adapted:1 no:1 analysis:21 solve:3 comparisons:1 dimension:11 restore:1 λv:2 quoted:2 λx:1 obtain:4 λb:2 klauder:4 character:1 except:1 other:1 lett:4 diagonalization:6 momentum:3 real:1 increased:1 ebec:1 read:2 evaluate:2 spanned:1 press:3 using:2 necessary:1 particle:1 follows:3 nasser:1 e00:2 integrals:1 arbitrary:1 accuracy:2 page:14 mathematical:1 because:4 methods:1 smoothly:1 czech:1 lebanon:1 csfr:1 b4:3 francisco:1 table:11 curious:1 diagonalizing:1 provided:3 est:4 dimensions:6 confirm:1 avoid:1 l11:1 does:1 provides:2 saad:5 proc:2 scientific:1 equivalent:1 wavefunctions:2 step:1 although:1 bx:2 properties:1 hadron:1 comparison:1 cn2:1 extension:1 algebraic:1 discussed:1 west:1 andez:2 22n:1 cambridge:3 letters:1 presence:1 previously:1 pergamon:1 into:3 numerically:1 functional:1 fern:2 right:1 references:1 operator:2 harrell:2 statistics:2 additional:1 h01:1 h00:4 was:1 flynn:1 naturally:1 function:3 complete:1 form:1 some:8 extended:1 volume:1 delta:1 convergence:1 level:1 hd:5 treats:1 compute:4 type:1 bounds:7 us:2 minor:1 problem:9 similar:1 clear:1 h0d:1 mechanics:1 required:1 associated:1 computing:1 defined:1 cover:1 abstract:1 general:5 quantum:2 single:1 formulation:1 formalism:1 identities:1 constructed:1 again:2 functions:10 nm:1 variety:1 when:3 guardiola:3 field:1 valid:1 spatial:5 department:2 mathematics:2 conclusion:1 elements:15 solano:1 setting:1 problems:5 variation:1 generated:3 important:2 papp:1 structure:1 acknowledgment:1 vetterling:1 interval:2 4n:1 n2:1 starting:1 4a:10

quant-ph9911119.txt \|@word concept:1 partial:2 virmani:1 pointing:1 entropy:6 computation:1 edu:1 reasoning:5 issues:1 consider:1 calculate:2 minσ:1 tr:1 finally:1 those:1 under:4 ingredient:1 very:5 rise:1 induce:1 choice:1 presented:1 tra:2 knight:3 notes:1 proposals:1 large:1 eigenvalues:1 optics:1 programme:1 upper:2 smaller:2 past:1 fold:1 zero:1 what:2 section:2 satisfy:4 led:2 respectively:1 never:1 here:2 explore:1 plenio:7 others:1 strong:1 deduced:1 great:1 institute:1 popescu:3 approaches:1 commonly:1 example:1 amount:1 products:1 pick:1 bob:2 narrow:1 tasks:1 useful:2 characterises:1 patience:1 formulates:1 achievable:1 apply:1 orderings:1 total:4 manipulate:1 additive:1 asymptotic:3 would:9 prove:1 positive:1 give:1 ψi:4 therefore:2 jonathan:2 more:6 acceptable:1 constructs:1 particular:1 known:4 cases:2 ρa:3 originally:1 work:3 faced:1 values:3 caveat:1 following:2 could:1 proof:2 compare:1 stated:1 bennett:3 organized:1 states:26 effectively:1 minimum:1 information:2 conversation:1 discussion:1 acts:1 rippin:1 how:2 pure:13 acta:1 brassard:1 product:1 may:2 earlier:1 epsrc:1 consequence:1 demonstrating:1 natural:1 purification:1 allow:1 order:3 operations:2 interpretation:1 indeed:3 over:1 satisfied:1 years:2 paper:3 london:1 its:1 perfect:1 jacobs:1 thank:2 interesting:2 forms:1 choose:1 main:2 might:1 them:3 good:4 greater:1 repercussions:2 they:6 inception:1 now:1 discuss:1 possess:1 term:1 vidal:2 reasonable:2 each:1 found:1 european:1 subset:1 ed:14 ef:20 reduce:3 equivalence:2 used:3 measure:15 quantum:4 our:11 happen:1 eq:2 special:1 out:6 divincenzo:1 shown:1 quantify:1 since:2 rev:12 denotes:1 increase:2 daniel:1 lecture:1 correct:1 theory:1 standard:1 completely:1 formation:10 ask:1 e1:3 generate:7 e2:3 just:2 ordering:9 place:3 hence:3 first:2 separable:1 already:1 manuscript:1 vedral:5 number:6 infinite:1 given:5 introduction:1 least:1 assumption:1 listed:1 wootters:4 continuous:2 attempt:1 july:1 copy:2 than:4 john:1 determines:1 require:4 submitted:1 result:4 epr:1 argument:2 tregenna:1 elsevier:1 any:5 lie:1 leverhulme:1 forces:1 coincide:1 towards:1 trace:1 investigations:1 measures:28 singlet:4 most:2 eisert:1 acknowledgements:1 inequalities:1 consequences:1 considered:1 implications:1 inaccuracies:1 physics:1 fact:2 precise:1 show:2 supported:1 fifty:1 bring:1 attempts:1 find:1 postulates:2 slov:1 2bz:1 state:5 should:3 only:3 candidates:1 bernstein:1 local:2 continuity:1 do:1 means:1 joint:1 cannot:2 during:1 procedures:1 regarding:1 resource:1 approach:3 arxiv:1 analytical:1 through:1 requirement:2 set:12 questions:2 correlations:1 relative:2 see:2 college:1 tackles:1 discussions:1 said:1 tensor:2 ways:1 review:1 diluted:1 behind:1 various:2 between:1 reading:1 conditions:3 recently:2 ability:2 transpose:1 efficiency:1 key:1 rohrlich:1 come:1 concentrated:1 both:2 essentially:1 tractable:1 many:3 taking:1 conclusions:1 equal:1 against:1 conclude:1 simple:1 asymptotically:3 trust:1 singlets:1 described:1 transformations:1 addition:1 locally:1 ben:1 copies:1 been:6 much:2 basic:1 ph:4 pi:2 define:1 suggested:1 corresponding:1 demand:1 present:2 case:1 value:1 will:2 contemp:1 while:2 applies:4 property:1 sw7:1 supply:1 opt:2 almost:1 von:1 non:2 itself:1 different:4 perform:1 same:7 quant:4 orientated:1 distilled:1 modification:1 finite:1 difficult:2 development:1 investigated:1 http:1 schumacher:2 possible:3 entanglement:60 recent:2 lower:1 no:1 well:1 entanglements:1 proposed:4 being:1 newton:1 obtain:1 sources:1 aspect:1 regardless:1 unique:3 preprint:2 density:3 regarded:1 bell:1 add:1 caltech:1 lett:8 theorem:1 input:1 mod:2 identical:5 nielsen:1 february:1 distillable:8 using:3 accepted:1 helpful:1 necessary:1 like:4 follows:2 alice:2 either:4 output:1 preskill:2 www:1 because:1 methods:1 classical:2 people:1 some:9 examples:1 peter:1 dense:1 axiomatic:1 per:1 esf:1 does:2 connecting:1 assuming:1 demonstrated:1 benefitted:1 calsamiglia:1 slight:1 equivalent:2 processing:1 notable:1 agreement:1 although:1 feb:1 properties:2 year:1 practical:1 union:1 range:1 mixed:3 introduced:1 cambridge:1 previously:1 communication:3 into:1 numerically:1 bound:3 due:1 down:1 appropriate:1 references:1 ppt:1 neumann:1 deal:1 limn:1 strictly:1 there:6 question:2 long:1 imperial:1 start:3 workshop:1 was:6 function:3 form:2 smolin:2 but:1 hoped:1 true:1 surprising:1 horodecki:10 whether:2 characteristic:1 maximum:1 us:1 below:1 uk:1 demonstrate:1 blackett:1 gisin:1 proved:1 defined:5 abstract:2 describe:1 covers:1 general:4 single:1 laboratory:1 qit:1 physical:1 paradox:1 variety:1 rains:2 whereas:1 application:1 other:3 formalize:1 er:3 operators:3 conclusion:2 briefly:2 calculating:1 important:2 ago:1 implies:1 practically:1 required:3 starting:1

quant-ph9911120.txt \|@word code:19 consider:3 pointing:1 thomas:1 pta:1 entropy:13 computation:1 edu:2 segments:1 tr:2 young:1 send:9 finally:1 tb:8 sent:1 ta:10 random:4 string:4 zhang:1 valued:1 every:2 bounding:1 convexity:3 school:1 achievability:2 presented:1 transmission:3 ref:4 notes:1 trb:2 solution:1 noiseless:1 solved:1 dealt:1 small:1 eigenvalues:1 noted:2 averaged:2 direct:1 rate:11 further:1 peredachi:1 index:2 subadditivity:3 appear:1 section:5 http:1 decoding:4 access:6 above:3 new:4 westmoreland:2 satisfy:1 edited:2 measurements:2 respectively:2 here:6 china:6 strong:2 box:1 vectors:1 allows:2 amount:2 schumacher:2 λr2:1 bob:38 λr1:1 control:1 useful:4 projection:1 highly:1 addressed:1 achievable:8 total:1 senders:4 select:1 use:4 spoke:1 prove:8 positive:1 properties:2 calculation:1 live:1 therefore:2 encode:1 theoretical:1 more:2 sharing:1 share:2 particular:3 cases:1 must:3 ρa:13 springer:1 ρb:3 science:3 mn:4 ρr:1 ρt:1 following:1 example:4 proof:6 distribute:1 beijing:1 want:2 process:1 permutations:1 organized:1 allahverdyan:2 states:9 uak:4 typicality:1 allowed:2 tak:7 information:21 winter:6 orthogonal:1 orthogonality:1 how:2 hou:1 xxxi:1 sij:1 ensemble:3 product:8 our:5 sacrifice:1 wiley:1 applications:3 coming:1 efficiently:1 natural:1 third:1 light:1 correspond:1 element:4 so:11 alphabet:2 2nr2:1 2nr1:1 order:2 interpretation:1 over:7 symbols:2 course:1 paper:5 including:1 thesis:1 still:2 its:1 before:1 thank:1 ρ2a:1 chosen:1 choose:7 main:1 non:1 good:1 combination:1 noticing:1 enrico:1 they:6 hands:1 nov:1 discuss:2 easily:1 term:1 university:2 orthonormal:1 sufficiently:1 inequality:6 reasonable:1 each:4 2l:2 schemes:1 desirability:1 idea:1 measurement:8 quantum:16 laboratory:1 eq:7 special:1 out:1 large:2 shown:1 matrix:2 space:4 since:3 rev:4 holevo:5 bennet:1 increase:1 attracted:1 lecture:1 electronics:1 issue:1 qd:1 foundation:1 log2:9 theory:3 hull:3 guess:1 free:2 approaches:1 york:2 jozsa:1 pairs:1 ρrs:2 ρrt:3 r1:25 r2:25 messages:1 enforce:1 length:3 gordon:1 wehrl:1 onto:1 first:9 initial:2 probability:11 coding:3 channels:1 done:1 another:1 message:2 precisely:1 given:2 πa:6 similarly:2 introduction:1 eqs:2 system:2 construct:1 their:3 rates:3 scheme:8 bits:2 part:2 alphabets:1 bennett:1 than:2 john:1 wiesner:2 was:3 second:3 project:1 qtb:2 saa:30 ψac:3 measure:2 locations:1 need:2 seen:1 any:1 viewed:2 angle:1 zero:1 note:4 subjects:1 generalized:2 analogy:1 transmit:1 analogs:1 caltech:1 channel:17 converse:5 multiple:6 established:1 who:2 what:1 satisfying:6 letter:10 pair:1 class:1 considered:1 clear:1 adopt:1 cover:1 vertices:1 tech:1 physics:4 sum:2 quantity:1 probl:1 show:1 supported:1 purely:1 find:2 ensembles:1 enough:1 should:2 lemma:3 only:2 pretty:1 rectangle:1 do:1 his:2 means:1 dd:1 overall:1 words:5 drawn:1 closure:3 arxiv:1 qc:1 miles:1 common:1 fixed:2 set:3 exists:1 achieved:1 national:1 maximum:2 relative:1 see:6 sec:1 result:4 close:2 phases:1 said:1 capacity:11 tensor:1 review:1 please:1 eigenstates:2 state:7 between:3 progress:1 conditions:1 email:1 available:1 notice:1 latin:1 recently:1 initially:1 attention:1 however:1 hefei:2 cut:1 huang:1 distinguish:2 distribution:6 essentially:1 many:1 region:4 according:8 receiver:2 tra:2 supply:1 asymptotically:2 cd:2 dimensional:2 sequences:4 pp:2 described:1 transformations:1 basis:1 due:1 been:1 povm:6 pa:3 combined:2 basic:1 pk:8 ph:6 pi:1 ak:9 define:2 modern:1 corresponding:1 subspace:1 interpretations:1 m1n:1 coherent:1 denote:14 case:4 intriguing:1 schmidt:1 transformation:3 will:7 while:2 suppose:14 shall:1 error:9 property:1 unitary:1 von:12 thus:4 site:1 systems:4 equal:1 technology:2 different:3 perform:1 things:1 make:1 same:2 unity:2 concavity:1 quant:5 used:2 infinity:1 imply:1 lochak:1 average:2 codes:4 uses:2 outmost:1 entanglement:5 expand:2 recent:1 off:1 acknowledgement:1 charlie:16 without:1 s22:1 academic:1 s21:1 sets:2 position:1 guang:1 proposed:1 less:1 compound:2 distant:1 using:3 λn:1 previous:2 rapid:1 density:2 bell:1 character:1 signals:1 other:1 lett:1 theorem:15 remaining:1 gave:1 iα:5 possible:3 ψbc:1 increases:1 predetermined:1 know:1 world:1 mod:1 necessary:1 follows:2 signal:5 alice:35 wooters:1 schwarz:2 reduced:1 preskill:1 www:2 because:5 often:1 classical:10 sequence:3 conditional:7 some:8 convey:1 convex:3 ccast:1 proceeding:1 normal:1 per:2 does:2 provides:2 tends:1 pea:8 refer:1 s12:1 s11:1 although:1 hilbert:3 noisy:1 about:2 pα:16 discussed:3 o:1 mixed:1 shared:1 raised:1 letters:2 ηa:4 levitin:1 communication:3 rotations:1 bound:2 jβ:5 three:2 right:1 references:2 determine:2 operator:1 ρta:4 next:2 neumann:12 deal:2 her:2 there:2 question:2 partite:3 long:1 decode:4 sections:1 vienna:1 himself:1 complete:3 form:3 pe:7 but:3 properly:1 decoder:3 hb:37 attainable:1 ha:29 considerable:1 he:10 waste:1 consist:1 up:1 us:2 international:1 fermi:1 cit:1 problem:1 called:1 entropies:3 aa:15 ab:2 proved:3 defined:1 abstract:2 describe:1 doesn:1 general:1 examine:2 referee:1 formulation:1 inf:1 mutual:2 qβ:15 when:4 application:1 book:2 shannon:2 papers:1 department:1 superdense:3 elements:2 may:2 users:3 ustc:1 includes:1 bounded:1 independently:2 implies:1 assume:1 rs:1 together:2 time:1 n1:1 n2:1 strings:7

quant-ph9911121.txt \|@word represent:2 measurements:2 consider:4 magnetic:10 global:1 splitting:12 gy:1 leads:1 roy:1 scalar:1 ψcl:4 whose:1 calculate:4 concerned:1 th:2 under:1 te:6 orthogonal:1 far:6 wave:17 electron:2 rotational:2 mixing:3 matrices:2 special:2 four:3 vibrational:4 level:2 turns:2 notes:1 solution:5 large:5 vector:3 math:3 science:1 small:4 eigenvalues:1 challenge:1 degeneracy:3 velo:1 upper:1 smaller:1 says:1 ρm:5 estimates:1 sign:2 approximation:2 fold:1 second:1 rigorous:1 further:1 chem:4 odd:2 theory:9 aim:1 what:3 plays:1 stands:1 celebrated:1 while:4 expressed:1 henceforth:1 eckel:1 experiment:1 fractional:3 momentum:1 acknowledgments:1 contrast:2 coefficient:5 full:1 notions:1 component:3 here:2 atoms:2 highly:1 directions:1 strong:2 equations:2 appears:1 obtained:4 hbo:3 wesley:1 shift:8 study:2 amount:1 decouple:1 jackiw:1 uniquely:1 useful:3 family:1 scales:1 requiring:2 namely:2 natural:1 baskets:1 replace:1 scaled:1 weaker:1 apply:1 total:1 linearly:2 conventional:1 asymptotic:3 would:1 distinct:2 positive:2 negative:3 classically:1 therefore:2 m3:1 m2:1 meyer:1 type:1 tell:2 more:1 israel:2 transcendental:1 becomes:1 operators:1 equipped:1 odinger:3 basically:1 particular:1 must:1 parameterize:1 springer:1 valued:1 recall:2 equation:6 work:1 det:1 dev:1 boyce:1 obvious:1 kendrick:1 following:1 decoupled:1 numbers:5 f1:2 f2:2 f3:6 wang:2 give:1 calculation:1 suggestions:1 generically:2 states:2 something:1 degenerate:4 soc:1 travel:1 holds:1 fourth:1 parameter:2 gordon:2 oscillatory:1 may:1 wiley:1 plane:1 inst:1 choice:1 meaningful:1 attempt:1 spectra:3 parameterized:1 interpolates:1 precise:1 so:4 encyclopedic:1 taking:1 representation:2 order:16 restriction:1 wigner:3 nucleon:1 over:2 move:1 expects:1 approximants:1 london:1 satisfies:1 still:2 its:3 diagonalized:1 group:1 probability:1 fit:1 energies:4 interesting:1 solving:2 vicinity:2 coordinates:2 degrees:4 systems:1 dyson:1 puts:1 non:2 good:1 combination:2 surrounds:1 fig:1 introduce:1 encouraging:1 break:1 exponentially:1 half:4 front:1 singularity:1 now:2 eigenvalue:4 term:2 equality:1 higgins:1 always:1 hamiltonian:3 approximant:1 powell:1 conic:2 vibrations:3 l3:1 2b:1 radial:3 crossing:56 2m:2 identifies:1 higher:1 characterized:1 mean:1 homogeneous:1 spinor:1 harm:1 arxiv:1 formulate:1 ej:1 ed:3 energy:13 hypergeometric:4 reduce:1 related:3 each:1 elementary:1 expect:1 ez:1 quantum:10 our:4 approximated:1 avoided:4 eq:9 neighbourhood:1 out:3 singularly:1 matrix:3 space:1 since:6 rev:3 research:2 rd:1 include:1 mediated:1 hill:1 lecture:1 correct:1 interchanging:1 foundation:1 turning:3 linear:5 dictionary:1 8m:1 divergence:1 diagonal:2 standard:2 reason:3 e1:4 combes:1 e2:1 derivation:1 created:1 times:2 turn:1 avron:2 isotropic:6 hence:2 promotion:1 kawada:1 neglect:1 first:2 origin:11 xi:1 features:1 symmetry:2 variables:1 number:2 sack:1 lond:1 intuitively:1 directly:1 carry:1 precisely:1 electronic:13 angular:1 wilczek:1 given:3 perturbation:1 sheet:1 introduction:1 leading:6 crossings:3 system:1 approximately:1 their:2 calculations:1 airy:2 dfg:1 molecular:8 gives:4 tool:1 part:5 x2:3 schr:3 x1:1 than:2 intrinsically:1 kind:1 double:1 require:2 see:6 preparation:1 hagedorn:1 determined:2 enables:1 powers:1 motivation:1 sees:1 ann:2 measure:1 interpretation:1 say:1 seen:1 minimally:1 zero:5 convenient:2 potential:5 generalized:4 forces:1 mit:1 towards:1 shall:9 duclos:1 phases:1 mead:6 regular:2 sheets:1 formulae:1 adds:1 why:1 technion:2 characterizes:1 typeset:1 points:1 electrons:2 clean:1 mechanical:2 ρm2:1 physics:3 bateman:1 fact:1 sector:1 show:1 supported:1 purely:1 solutions:5 subtle:1 d2:1 find:1 slow:1 ratio:2 proportion:1 should:2 only:8 bσ2:1 molecules:1 factor:6 thompson:2 employed:1 hope:1 do:1 klein:1 means:4 dependent:1 lifshitz:1 overall:1 fc:9 ones:1 reversal:2 ϕj:1 dr:1 geometric:1 differential:5 wightman:1 remove:1 oppenheimer:4 rotationally:2 twice:1 common:1 farther:2 magneton:1 set:3 ser:1 imposing:1 j3:2 opposite:1 depends:1 close:11 analog:1 surfaces:2 fails:2 said:1 eigenfunctions:1 nuclear:8 away:1 irt:1 symmetric:2 favor:1 enough:1 identification:1 closed:1 between:6 invariant:3 boundary:3 conditions:3 across:1 notice:1 terms:3 importance:1 however:2 sadun:1 distinguish:1 understanding:1 come:2 thank:2 cos:3 region:3 density:2 equal:1 zeeman:18 figures:1 berry:2 comm:2 kasahara:1 expression:1 unitarily:1 point:6 simple:1 asymptotically:2 dimensional:4 associated:1 decoupling:2 create:1 oder:1 due:3 reduction:4 describes:1 treat:1 azimuthal:2 ph:1 anomalously:2 anomaly:2 abstract:1 lett:1 addison:1 aj:1 antiperiodic:1 subspace:2 precision:1 gap:3 fund:1 external:1 general:2 spin:4 case:8 look:1 pacs:1 value:2 iξ1:1 will:9 near:25 match:1 situation:1 property:1 ir2:2 eimθ:1 unitary:1 von:3 wkb:3 thus:1 surface:1 itself:1 ia:1 busch:1 conical:4 orbital:1 different:2 poincar:1 quant:1 pauli:2 units:4 dimensionless:1 gets:1 couple:1 interpolation:1 status:1 independent:5 infinity:4 singapore:1 numerical:1 effect:2 counterparts:1 levels:5 infinite:1 invariance:1 landau:1 normalization:1 lower:1 off:2 modes:2 scenario:1 analysis:1 bohr:1 academic:1 components:5 studying:1 model:3 moments:1 obtain:2 rest:1 atomic:5 using:1 pryce:1 eigenstates:1 adding:1 cut:1 application:2 ϕ2c:1 a392:1 elgart:1 extends:1 treatment:1 mod:2 transformation:1 iξ2:1 real:3 iθ:1 leipzig:1 breaks:2 results:1 spanned:1 plenum:1 press:3 integer:2 bit:1 intersection:4 helpful:1 semiclassical:2 like:1 particle:1 follows:1 qualitative:1 manifest:1 δj:2 either:1 arbitrary:1 leaves:1 reduced:1 sketch:1 neumann:2 classical:2 seiler:3 some:1 born:4 provided:2 scale:3 dimensions:1 nonempty:1 eiθ:1 normal:1 integration:1 comments:1 trimers:4 everything:1 does:5 unit:1 proc:2 refer:2 bornemann:1 power:3 equivalent:1 bo:8 broken:1 revtex:1 mcgraw:1 imaginary:1 takes:2 about:2 central:1 carried:1 world:1 column:1 freedom:4 anomalous:3 dependence:1 o:2 opik:1 bounded:4 longuet:1 truhlar:1 perturbed:1 homogenization:1 into:1 integral:5 three:1 martinez:1 lies:1 references:1 operator:2 proportional:7 a3:1 weight:1 area:1 strictly:2 there:5 transform:1 fast:2 low:1 way:1 vas:1 analyze:1 was:2 function:20 elsewhere:1 form:5 shapere:1 quaternionic:1 removes:1 berg:1 magnitude:1 gain:1 haifa:1 true:3 he:20 prevents:1 smooth:1 up:1 us:6 below:2 limit:2 problem:3 mechanics:2 constant:2 int:1 certain:1 universal:2 describe:4 linearity:1 denote:2 separating:1 single:2 defines:1 functions:7 compared:1 nm:1 no:1 commutes:1 when:4 field:9 other:1 role:1 details:1 department:1 mathematics:2 conclude:1 polar:1 a1:1 ξi:1 meaning:1 a2:1 nucleus:1 variable:1 lang:1 land:1 coupling:1 assume:3 normally:1 rule:1 dρ:3 4m:1 mass:4 lying:1 time:5 nuclei:1 requires:1

quant-ph9911123.txt \|@word ibid:4 externally:1 epeau:1 sci:1 consider:7 switched:1 rev:18 magnetic:2 global:1 bandgap:1 focus:1 leads:5 computation:12 shimony:1 wǫ:1 expressions:2 denotes:3 sch:3 looking:1 c0:1 depend:2 calculate:1 iii:3 pth:1 should:1 γk:2 charge:2 investigation:2 indicate:2 protocols:1 under:3 vrijen:2 include:1 case:13 probe:1 straightforward:1 orthogonal:1 very:2 results:13 electron:7 every:1 figs:2 resonant:1 1ps:1 condition:5 rotating:4 presented:3 opt:1 issue:1 proposals:2 large:1 readout:3 donovan:1 differential:1 indices:1 eigenvalues:1 refer:2 programme:1 application:1 mn:1 deutsch:3 edu:1 direct:3 pulse:13 sign:1 approximation:1 zero:4 design:1 dordrecht:1 chen:1 greenberger:4 dynamics:1 reina:3 linear:2 index:1 errors:1 adjustable:1 section:11 3w:12 near:2 expressed:3 ak4:1 current:2 waiting:1 experiment:2 above:6 new:4 net:1 increasing:1 method:1 exercise:1 pose:1 simultaneously:1 kamada:1 degree:1 exchange:1 awschalom:1 respectively:4 doing:1 promising:3 modify:1 teleportation:3 here:16 atoms:3 ranges:1 condmat:1 ei:1 selective:5 departamento:1 separation:1 address:1 active:1 luis:2 coupling:7 equations:1 arena:1 antisymmetric:1 environment:2 involved:1 study:2 studied:2 wn:1 akj:4 uk:2 action:2 resonance:5 implement:1 suitable:2 changes:1 king:1 via:2 followed:4 figure:4 scales:1 semiconductors:2 while:2 logical:1 highly:3 addressed:2 total:4 manipulate:1 wang:1 gaas:1 intensive:2 use:3 takes:4 would:2 dalibard:1 jozsa:3 laflamme:1 predictions:1 hilbert:6 anticommutation:1 explicitly:2 m1:4 m3:2 memory:1 iem:1 type:2 theoretical:1 today:1 more:3 introducing:1 comparison:1 successful:2 initial:13 operators:4 odinger:2 leonard:1 carrying:1 qds:30 particular:5 foundations:1 hole:2 producing:1 adequate:2 must:2 states:41 account:2 excellent:1 defines:1 science:3 equation:4 work:4 mk:4 mj:5 values:7 following:4 hansen:1 example:3 proof:1 control:9 ions:1 iek:5 challenging:1 links:1 give:4 calculation:1 bennett:4 implementations:1 high:1 indicates:1 performed:5 rodr:2 junctions:1 information:11 ǫt:1 requirements:1 processors:1 mutually:1 provide:3 discussion:5 get:3 range:1 regions:1 how:2 amazing:1 pure:3 manipulating:1 gate:10 ignore:1 parameter:7 ensemble:2 brassard:3 lindberg:1 product:2 mar:1 description:3 may:2 earlier:1 derived:1 different:8 applications:1 produce:1 fe:1 date:1 wave:8 data:1 fm:4 constants:1 varied:1 bogot:1 realized:1 jiang:1 outline:1 effective:1 computations:1 light:8 explicit:2 correspond:2 ghz:18 algorithms:1 fundamental:5 decreasing:3 american:1 order:3 operations:12 horne:3 gershenfeld:1 acts:2 exploited:3 developed:1 over:8 despite:1 vary:1 burkard:2 years:1 report:1 paper:5 pulses:11 experimentally:1 mentioned:1 still:1 ieee:1 its:1 before:6 lf:1 write:2 teleporting:1 acknowledge:1 chosen:2 theorem:1 solving:1 τb:7 decreases:2 li:1 wineland:1 window:3 offers:1 itano:1 systems:3 initializing:1 rabi:3 main:4 into:2 rwa:1 non:3 mechanisms:2 gibbs:1 combination:1 entire:2 obtaining:1 evolution:5 introduce:3 band:3 steane:1 equidistant:1 effects:2 commun:1 symposium:1 oxford:2 feature:1 now:3 realize:1 expresion:1 eigenvalue:1 term:1 2w:4 cory:1 fixed:6 corners:1 university:1 hamiltonian:7 imamoglu:2 orthonormal:2 sufficiently:1 mode:1 reasonable:3 each:5 found:2 2n:1 giving:1 side:2 2j:4 em:9 schemes:2 neil:1 another:2 ek:7 generation:21 series:1 energy:5 kane:2 principles:1 frames:2 ando:1 frequency:2 knill:1 proportional:1 quantum:65 laboratory:5 operation:1 transitions:1 eq:17 special:1 out:2 divincenzo:5 shown:3 opened:1 space:7 restricted:1 furthermore:1 since:6 crucial:2 research:1 semiconductor:7 rf:1 mediated:1 pendent:1 induced:1 ref:5 occurs:1 shows:4 reporting:1 turning:1 theory:3 interactions:1 ısica:1 m4:1 possibility:6 contrast:2 inputting:1 formation:1 facilitating:1 e1:8 generate:4 e3:8 e2:13 interaction:7 katzer:2 could:2 computers:2 so:3 gotoh:1 times:2 silicon:2 length:7 levels:3 place:4 universidad:1 hence:15 epr:1 onto:1 βj:2 βk:2 excitonic:10 probability:4 kafatos:1 number:4 explored:1 employing:1 fast:2 colombia:1 changing:2 electronic:2 angular:2 hood:1 given:16 rewritten:1 their:7 introduction:1 eqs:1 achieved:1 system:14 relations:1 compulsory:1 needed:1 brevity:1 normalization:2 realization:5 scheme:7 unpublished:1 gives:4 e0:14 preserved:2 relationship:1 trapped:2 johnson:4 park:2 stress:2 task:1 ak3:2 optical:9 too:1 manipulation:3 schr:2 believe:1 than:2 coefficients:6 dynamical:2 steel:2 wide:2 nanostructures:1 hundred:2 target:1 require:1 summary:1 depends:1 project:2 individual:8 amplitude:2 were:2 tion:1 adopts:2 result:4 seminal:1 raman:1 fig:8 symmetries:2 generality:1 electrodynamics:1 measure:1 spectrum:1 curves:2 7w:6 colciencias:1 su:6 further:1 need:4 seen:1 unaffected:2 demonstration:2 any:7 strength:8 mermin:2 able:3 mechanism:3 note:3 articles:1 potential:1 square:1 finding:5 donor:1 averin:1 towards:1 electric:2 centre:1 diminishing:1 wells:1 most:2 involving:1 eight:1 preliminary:1 phase:6 analytically:3 intrinsic:1 mabuchi:1 achievement:1 inequalities:1 subspaces:3 observation:2 considered:3 kj:1 later:2 stronger:1 feynman:2 proceedings:1 part:1 mechanical:3 nanostructure:3 physics:6 ak1:3 dot:8 precise:1 shor:3 tron:1 show:3 violation:1 doped:1 discovered:1 chuang:2 solutions:5 trivial:1 find:2 ground:1 based:7 ıguez:2 parameters:6 implementation:4 iωt:1 ox1:1 operational:1 analytic:1 only:7 going:1 candidates:1 factor:3 irrelevant:1 constant:2 havel:1 local:1 achieve:1 do:1 dm:6 dj:5 radiated:1 cryptography:2 means:1 fahmy:1 zurek:2 de:4 2jz:1 ones:4 ϕi:4 preparing:1 dx:1 ϕj:3 combinations:2 compute:1 represented:1 3a:4 processes:1 experi:1 podolsky:1 fields:2 goldwasser:1 arxiv:1 motion:1 comprising:1 consisting:1 roger:1 qd:9 gammon:2 analytical:4 through:1 transistors:1 view:2 set:7 modulo:1 computed:1 our:5 frame:3 ωt:7 see:3 computer:6 sec:1 us:11 discussions:2 recently:2 news:1 nonlocality:1 techniques:1 preparation:1 interdot:5 capacity:1 commutation:1 nuclear:2 review:2 currently:1 artificial:1 label:1 qubits:12 state:38 determined:1 john:1 between:5 balandin:1 subscript:1 diagonalized:1 conditions:6 available:1 barenco:2 terms:3 ability:1 jz:7 nature:5 importance:2 lange:1 attention:1 however:3 scalability:1 incident:3 ji:1 jk:1 subspace:5 dependance:1 dimensional:2 cirac:1 problem:8 both:8 enables:3 zoller:1 numerically:1 many:1 taking:2 density:3 biexcitonic:1 explore:1 figures:3 femtoseconds:1 microcavity:1 qubit:9 whole:1 experimental:12 ck:10 relevant:1 co:1 bell:26 simple:1 annual:1 ca:1 relaxation:1 corresponds:1 alamitos:1 factorize:1 distinguish:1 exploit:1 written:1 away:1 ae:1 cp:8 sherwin:1 considering:1 pp:1 described:7 transformations:2 capable:1 addition:2 create:2 due:1 been:5 int:1 detuning:1 much:4 flopping:1 interest:1 basic:1 ph:2 meeting:1 define:1 dots:12 obtained:4 generating:1 describe:1 controlled:4 commutes:1 coherence:1 excite:1 requires:2 gap:4 zeilinger:3 relevance:1 coherent:4 external:1 c3:1 c2:1 c1:1 maximally:13 spin:2 those:1 applied:3 compatible:1 laser:6 josephson:1 pacs:1 solid:7 tetrahedron:1 kimble:1 value:6 iτ:2 will:3 dephasing:1 error:1 situation:1 ultra:1 35th:1 yablonovitch:1 procedure:5 london:1 real:1 unitary:5 coupled:13 vi:1 iv:3 ii:2 bias:1 cond:1 qit:1 march:1 technology:1 monroe:1 increased:1 acknowledgments:1 containing:1 thereby:1 perform:5 suggest:1 realizing:1 demands:1 radiation:2 same:1 quant:2 diagonalize:1 units:2 dimensionless:1 several:6 four:2 development:1 independent:1 used:5 solved:1 numerical:5 effect:1 possible:4 driven:6 znse:2 compared:1 arrived:1 hospitality:1 entanglement:4 eigenenergies:3 fabrication:1 off:2 recent:3 eigenvectors:1 elec:1 finesse:1 whose:1 obstacles:1 well:4 kept:1 analysis:1 without:1 directly:1 equispaced:1 solve:1 dashed:1 model:4 usual:2 gates:5 proposed:9 eigenenergy:1 rosen:1 aǫ:1 obtain:2 4th:1 germanium:1 shape:2 tasks:3 distant:1 thanks:1 aspect:1 world:1 heterostructures:1 rapid:2 kluwer:1 conclusions:2 5w:1 point:4 discuss:1 signals:1 valid:1 lett:13 δpp:1 diagonalization:2 input:1 mod:1 transformation:6 momentum:2 identical:1 aspects:1 eigenfunction:1 easily:2 rules:1 providing:1 absence:2 3pu:1 spanned:3 luminescence:1 increases:1 netherlands:1 entangled:28 vacuum:8 confined:2 using:9 bit:4 makhlin:1 correcting:1 disadvantage:1 loss:5 like:1 follows:5 qualitative:1 performing:4 exploiting:1 separately:1 wooters:2 δm:3 yields:1 arbitrary:3 inter:1 reduced:2 spins:5 because:1 qed:2 classical:4 creation:1 some:1 searching:1 chavez:1 acad:1 cr:1 duration:1 small:1 process:3 nanometer:1 diagonalizing:1 specific:1 throughout:1 lead:1 cavity:3 broad:1 per:1 esf:1 does:1 provides:1 steps:1 proc:2 demonstrated:3 2a:6 eigenfunctions:3 varying:1 eiϕ:12 obey:2 indicated:2 processing:7 agreement:1 expansion:2 commencing:1 clarendon:2 binder:1 santa:1 eiφ:1 hadamard:7 exciting:2 notation:1 properties:1 cnot:9 stage:1 integers:1 about:1 khitrova:1 usa:1 universe:1 basis:9 discussed:4 practical:3 excitons:12 andes:1 ox:2 mixed:1 considerations:1 soc:1 cambridge:1 previously:1 communication:1 h0:3 within:2 rotations:7 ηi:1 three:4 pair:1 appropriate:1 right:1 einstein:1 operator:1 england:1 next:4 mental:1 span:2 prepare:1 ψk:7 transfer:1 support:1 there:1 long:3 los:2 appl:1 way:1 ed:2 2m:4 scientific:1 was:2 function:9 jones:1 complete:1 form:6 femtosecond:1 hp:7 m2:2 shnirman:2 encodes:1 idea:1 construction:1 detect:1 hl:3 he:1 few:1 applying:1 society:1 multiplicity:2 mat:1 up:4 devices:3 until:1 excitement:1 placed:1 represents:2 spectroscopy:3 distribution:1 similar:1 jz2:1 distance:1 detailed:1 ac:2 interval:1 associated:7 computing:2 defined:1 universal:2 aj:1 am:1 covers:1 general:5 peres:1 oscillations:2 single:20 enable:1 exist:1 wavelength:1 corresponding:1 physical:3 mosca:1 codes:1 no:1 exciton:9 ekert:4 wavefunction:1 when:1 meekhof:1 field:8 conceptions:1 other:2 ψghz:2 details:1 becomes:1 department:1 quiroga:2 theor:1 ev:1 optically:6 picture:2 briefly:1 elements:9 denote:2 excitation:2 photon:2 preceding:2 searched:1 problems:1 variation:1 helpful:1 generated:1 important:1 vectors:1 n2:7 biexciton:3 matrix:4 building:1 bulk:1 tailored:1 longer:2 4w:1 required:5 rule:2 phonon:1 fact:5 time:13 far:1 decoherence:10 starting:4 having:1

quant-ph9911124.txt \|@word logarithms:1 consider:9 remarkable:1 particular:1 results:2 existing:3 four:1 computation:1 stochastically:1 consists:2 query:41 primes:4 revealed:3 causes:1 relationships:1 whose:1 simon:2 depend:2 chain:43 gcd:1 deterministic:5 finally:1 preserved:1 under:2 alberta:1 include:2 updated:4 confirmation:1 returned:2 straightforward:1 very:5 continues:1 splitting:1 worst:1 entries:1 24th:1 difference:1 continued:1 illustrated:2 solves:2 proc:3 list:7 large:4 item:5 convenience:1 indices:1 noted:1 matematik:1 upper:2 consistent:5 α2n:1 zero:1 follow:1 even:1 what:2 richard:2 t2n:1 section:1 selected:1 access:3 version:3 3n:1 above:7 new:14 method:3 shallit:1 deduces:1 understanding:1 modular:2 address:2 represented:1 consideration:2 along:2 implicit:1 referring:1 box:1 search:1 accomplishes:1 specialized:1 larger:3 accomplished:1 resulting:3 permutation:7 fourier:1 uniquely:1 via:1 followed:1 divide:1 outcomes:2 analyzing:1 select:1 use:1 subsumes:2 would:4 prove:3 distinct:2 positive:2 coins:1 next:3 few:1 call:3 therefore:1 calgary:3 until:6 more:5 zeroes:1 formally:2 far:1 sharply:1 informally:2 known:2 foundations:1 must:2 fly:1 keeping:1 contradicts:1 science:2 focs:3 grover:2 values:9 following:7 root:3 example:7 proof:5 figure:11 stated:2 process:3 permutations:4 collision:4 indicates:1 minimum:4 performed:4 allowed:1 occur:2 information:13 end:1 goal:3 algorithms:1 how:1 map:1 may:1 after:7 containing:1 reflect:1 choice:3 data:1 response:4 efficiently:1 short:1 branches:1 imply:2 whenever:5 separations:2 element:5 complexity:6 so:8 asserts:1 every:3 transitivity:1 order:20 operations:1 restriction:1 unfolds:1 xi:2 including:1 y1:10 y0:30 y3:3 y2:4 ieee:1 its:2 before:1 chosen:1 interesting:1 solving:1 actually:2 estimating:1 choose:2 main:2 might:3 yi:8 yk:5 yj:4 return:1 collide:1 accumulate:1 nov:1 now:6 2t:1 represents:1 intuitively:1 always:2 university:2 possibilities:1 sufficiently:2 each:8 2m:8 2n:55 2h:2 2k:1 weighted:3 weight:3 generation:1 t2:2 idea:2 constitute:1 yield:1 quantum:13 our:2 eq:1 event:3 out:1 canada:2 discrete:1 restricted:1 since:6 contained:1 denoted:1 postpone:1 suffices:2 occurs:6 math:1 1n4:1 earlier:3 theory:4 contain:2 little:1 possibility:1 vazirani:3 small:1 completely:1 complicated:1 ord:12 responding:1 beginning:1 additional:1 cycles:1 created:1 could:2 length:7 place:2 exponentially:1 onto:1 assign:2 first:12 xj:2 xk:1 major:1 already:2 probability:15 number:13 ordπ:1 randomized:3 construct:3 reached:1 array:3 size:9 given:4 introduction:1 unknown:2 least:9 returns:3 too:1 siam:3 john:1 bits:1 final:2 exactly:1 eliminates:1 simulate:1 x2:1 natural:1 eliminated:1 x1:1 than:5 updating:1 distance:2 determines:2 divisible:1 tree:10 second:3 accesses:1 negligibly:1 determined:11 were:1 accessed:3 tion:1 outcome:1 w2:3 exhibit:1 comput:1 acknowledged:1 ann:2 randomly:3 say:2 need:1 linked:3 viewed:1 latter:1 montgomery:1 note:5 instance:1 potential:2 finding:13 negligible:1 mit:1 begin:1 added:1 unless:1 shall:1 track:1 most:5 significant:1 termination:1 contrasts:1 measured:1 advantageous:1 failure:3 average:1 sometimes:1 request:2 mechanical:1 responded:1 fact:2 nω:1 shor:4 show:3 supported:1 subtle:1 trivial:1 find:1 principal:11 based:3 guidance:1 inserted:6 state:1 should:1 lemma:13 only:7 explicitly:2 black:1 factor:1 constant:2 bernstein:3 do:2 watrous:1 means:1 dependent:1 trees:5 cannot:3 iwaniec:1 items:1 procedures:1 stoc:2 prime:4 reveal:1 evolution:1 resource:2 settings:2 arxiv:1 factorization:2 requesting:9 investigate:1 processed:1 queries:36 london:1 fixed:2 set:6 exists:1 bounds:5 see:1 computer:4 w3:2 result:3 w1:5 fail:1 contains:3 theoretic:2 fails:3 harman:1 ways:1 subsequent:1 definite:1 behind:1 correctly:1 between:2 consecutive:1 approach:1 email:1 available:1 terms:1 responses:3 extend:1 initially:1 wk:3 wj:7 wi:10 however:3 gratefully:1 problem:14 received:1 last:1 many:3 according:1 nserc:1 context:1 exceeds:1 qubit:1 otherwise:4 reside:1 among:1 adjusted:3 relevant:1 point:2 simple:1 ca:1 period:1 whatever:1 simply:1 path:15 polynomial:3 table:2 technicalities:1 considering:1 pp:8 computing:3 three:1 been:6 ai:5 yao:2 much:2 basic:1 inventiones:1 ph:1 empty:1 define:6 obtained:1 direction:2 aj:4 corresponding:2 both:1 sufficient:1 arkiv:1 external:7 systematic:1 child:1 present:1 case:6 exponential:2 value:22 will:4 suppose:4 behavior:1 error:5 associating:2 property:1 procedure:11 changed:1 vol:7 thus:2 non:1 vs:4 properties:1 binary:1 different:1 perform:2 things:1 make:1 same:1 any:13 quant:1 arguments:1 k2m:1 several:4 independent:4 literature:1 i1:1 i0:5 v0:4 v1:2 requests:1 a2n:1 cycle:11 lower:10 task:1 database:1 random:7 well:1 severe:1 solve:1 jutila:1 i2n:1 position:2 model:5 gates:1 obtain:1 assigned:4 recap:1 intervals:1 using:1 yet:5 previous:2 unspecified:1 k2:1 regarded:1 alternate:2 appeared:4 other:4 location:4 theorem:9 input:3 formal:1 remaining:1 branch:8 possible:11 corresponds:6 game:1 press:1 integer:3 bit:1 execution:5 moreover:1 mod:4 insert:1 necessary:3 helpful:1 success:1 sizes:2 follows:10 separately:1 steps:1 either:1 arbitrary:2 output:3 reduced:1 specifies:1 exceed:1 because:3 methods:1 classical:12 sequence:5 mathematicae:1 some:2 bach:1 28th:1 respect:2 proofs:2 leaf:4 decision:15 recorded:1 overlap:1 v2n:1 does:2 assuming:4 ucalgary:1 chains:3 algorithmic:1 power:1 uniformly:1 equivalent:2 step:2 symp:2 entirely:1 stage:1 comparison:2 about:7 carried:1 simplify:1 completing:1 theorems:1 o:13 remains:1 22n:6 soc:1 computational:1 acm:1 into:4 bound:8 due:1 pair:1 appropriate:1 references:2 determine:4 fast:1 log:1 probabilistic:4 there:7 transform:1 specifically:1 way:5 head:9 arise:1 form:3 removes:2 but:5 taken:4 link:2 divisors:3 partially:1 breakthrough:1 made:3 consist:2 proceeds:1 flip:1 us:1 below:3 distribution:4 later:1 associated:5 up:3 defined:2 certain:1 abstract:1 describe:2 general:2 single:2 ar:1 exist:2 ay:1 internal:9 functions:1 no:7 when:3 acknowledgments:1 setting:2 evasive:4 department:1 node:8 elements:11 problems:1 update:1 a1:1 a0:1 bounded:10 structure:1 auxiliary:1 algorithm:7 assume:1 starting:1 baker:1 depth:2 weights:1 time:1 cleve:2 n2:1 requires:2 once:2

quant-ph9912001.txt \|@word limited:1 consider:3 cussed:1 results:4 computation:3 consists:1 follow:1 denotes:8 localized:1 row:1 inverse:1 calculate:1 advantage:1 tt:1 technique:1 ts:24 presents:1 finally:1 vec:1 th:4 under:1 include:1 norm:1 case:14 charles:1 string:1 preserved:2 far:3 implicitly:1 23rd:1 springer:1 choice:1 stays:1 difference:1 dimen:1 obvious:1 presented:4 dif:2 solution:12 fewer:1 kannan:1 leave:4 solved:1 vector:11 small:3 enhance:1 dis:2 smaller:1 tem:1 speci:1 sical:1 second:5 plex:1 even:2 specification:1 nand:1 uniform:1 rithm:3 abs:4 above:3 new:3 consisting:2 margolus:1 simultaneously:1 respectively:1 here:3 diagonal:6 desired:3 selective:5 invented:1 equations:3 logarithmic:1 obtained:4 vazirani:1 search:25 leaves:1 vectors:2 commonly:1 accomplished:2 helps:1 composed:1 appropriately:2 followed:1 pling:1 scaled:1 boolean:1 1st:1 apply:2 use:3 feb:1 would:2 army:1 probabilities:2 next:3 few:1 sample:5 therefore:4 exhaustive:1 simpler:1 type:3 until:1 reflects:1 more:4 started:1 outputs:1 factor:1 hein:1 carrying:2 everywhere:1 basically:1 known:4 uation:1 hold:1 iii:2 states:22 account:1 valued:1 science:2 equation:2 work:4 london:1 remain:1 grover:6 values:2 following:12 making:2 repre:2 root:2 example:2 attain:1 computers:2 high:3 priate:1 walsh:1 performed:1 tions:2 counting:2 absolute:1 information:3 needs:5 goal:1 sit:1 buhrman:2 premultiplying:1 feature:1 how:5 pure:3 answer:1 gate:3 verlag:1 sin:1 brassard:2 inputs:3 de:1 blocks:1 replacing:1 ancilla:2 after:5 applications:8 evaluations:1 engineering:1 clearly:1 third:4 ss:1 su:1 element:3 perhaps:1 annealing:1 so:6 fundamental:1 xxx:4 order:4 operations:9 restriction:1 holds:1 help:1 office:1 developed:1 over:4 entries:2 murray:1 course:1 paper:8 through:4 mentioned:1 converting:1 still:2 avenue:1 its:3 before:1 rapidly:1 chosen:1 interesting:1 systems:5 communication:1 main:2 non:1 good:1 primary:1 framework:4 reaches:1 they:2 half:2 rotation:2 now:1 nor:1 easily:3 inversion:9 several:1 dirac:2 opera:1 concave:2 orthonormal:1 each:10 found:1 transferring:1 notes:1 referred:1 domain:3 square:4 statis:1 another:2 due:1 constitute:1 society:1 used:5 sion:1 quantum:49 our:1 operation:8 beyond:1 out:9 shown:8 funding:1 matrix:18 space:5 zalka:1 rep:1 since:5 rev:1 chaos:1 research:2 may:6 hill:1 maximized:1 denoted:5 lecture:1 get:1 gov:4 shows:5 sented:2 theory:6 normalized:1 ory:1 given:5 standard:2 labs:2 completely:3 complicated:2 eigenvalues:2 initialize:1 jozsa:1 generate:3 additional:1 advance:1 starts:1 could:6 transition:3 40th:1 times:2 inverts:1 tor:1 exponentially:1 assumed:1 hence:1 think:1 first:19 major:1 initial:3 probability:20 powerful:1 number:11 ond:1 synthesize:2 simplified:1 least:1 directly:1 carry:1 reached:1 precisely:1 open:1 size:2 1s:2 similarly:3 introduction:1 structured:1 system:10 approximately:4 needed:1 1d:1 realization:1 applegate:1 bits:1 final:1 gives:1 distribu:1 hoyer:2 collapse:1 exactly:4 took:1 immediate:2 quan:1 too:1 ference:1 representing:1 than:3 kind:1 ben:1 target:6 showed:1 sections:2 tree:1 zero:4 normalizing:1 amplitude:14 were:1 tion:7 gathering:1 generality:1 unchanged:3 runtimes:2 say:2 conjugate:1 need:6 seen:1 seem:1 linked:1 solitons:1 mountain:1 complexity:1 note:4 nota:1 take:2 finding:1 algorithms:16 analogs:1 needle:1 multiple:6 object:1 reach:2 falls:1 most:2 significant:1 organization:1 phase:10 acknowledgements:1 probabilistic:2 class:4 observation:1 considered:2 average:1 later:1 paragraphs:1 drive:1 part:1 mechanical:15 25th:1 fied:1 section:18 fact:1 quantity:1 particularly:1 inspire:1 show:2 supported:1 discovered:1 solutions:4 carefully:1 effi:1 find:3 tapp:2 based:1 enough:1 only:6 going:1 indeed:1 bernstein:1 tude:1 columns:1 notation:4 means:1 simplest:1 cannot:1 valuable:1 words:2 international:1 unaltered:1 gen:1 becomes:2 stoc:5 reveal:1 evolution:1 qu:3 arxiv:1 nayak:1 including:1 thanks:1 composite:2 computed:1 achieved:1 testing:1 bounds:1 observed:3 depends:1 computer:4 sec:2 result:5 corre:1 primality:1 mea:1 points:4 a400:1 nett:1 surement:1 state:65 various:1 between:1 available:1 terms:2 missing:1 qubits:10 transpose:1 however:2 wi:1 answers:1 solu:1 deutsch:1 distribution:12 both:1 cos:1 grassl:1 many:1 annual:2 equal:10 contract:1 iv:1 qubit:13 estimation:2 com:3 boyer:1 tum:1 arbitrarily:6 30th:2 relevant:2 bell:2 simple:1 sampling:8 dimensional:5 written:4 ashwin:1 iterations:1 constant:1 considers:1 conference:1 wigderson:1 described:2 ciently:1 basis:13 addition:1 create:2 three:4 been:4 quickly:1 describes:1 basic:5 expected:1 transformed:3 ph:5 pro:1 choose:2 digits:1 generating:1 controlled:1 easy:1 0s:1 2iu:1 subspace:1 else:2 worked:1 applied:1 multi:5 unlike:2 examine:1 value:6 remaining:1 will:9 suppose:1 error:2 situation:4 procedure:1 unitary:10 almost:2 eral:2 thus:4 according:6 ii:4 vs:1 conserve:1 binary:2 different:3 develop:2 perform:1 make:1 same:9 any:9 complex:5 quant:5 gets:1 ampli:1 difficult:1 development:1 extended:2 http:4 lowing:1 effect:1 sys:1 v2:1 uses:1 contribution:1 identity:1 recent:1 eigenvectors:3 database:1 whole:1 analysis:5 observations:1 without:1 solve:1 simulated:1 very:2 position:3 consisted:1 gates:4 just:5 less:1 being:2 obtain:1 rest:1 ideas:1 transforms:1 sam:1 immediately:2 rotates:1 previous:6 rapid:2 application:5 point:4 royal:1 except:4 source:3 valid:1 extends:4 samples:2 input:11 haystack:1 transformation:16 generalized:4 real:2 tics:1 2u:9 breaks:1 repetitions:2 measurement:2 possible:6 lanl:4 game:1 using:3 bit:1 fractals:1 loss:1 rotate:1 like:5 follows:1 performing:1 communications:1 steps:16 either:2 arbitrary:12 output:9 inter:1 clas:1 exceed:1 classical:12 sequence:5 successfully:1 some:4 searching:2 28th:1 specified:10 sen:1 provided:1 vol:2 scale:1 describing:1 integration:1 comments:1 does:2 assuming:1 fol:1 yields:2 proc:8 step:1 become:1 hadamard:1 approximating:1 super:3 hilbert:1 transformations:3 about:1 carried:1 constraint:1 column:1 certainty:1 discussed:3 o:10 carries:1 wolf:1 algo:3 act:1 mean:1 invert:2 functions:1 equally:1 computational:2 letters:1 presence:1 previously:2 acm:5 into:12 getting:1 down:1 multiply:1 extending:1 references:1 operator:2 proportional:1 cho:1 log:2 prepare:1 synthesized:2 measured:1 there:6 transform:4 fast:2 lidar:1 synthesizes:1 start:1 lov:1 way:1 analyze:1 was:12 function:5 tight:1 conditional:2 form:1 effects:1 fundamentals:1 denoting:1 but:4 volume:1 repeated:3 larger:1 trying:1 amplify:1 made:2 applying:3 versions:1 maximum:4 uts:12 sum:1 problem:5 define:2 similar:5 called:3 mechanics:2 instead:1 4u:3 proved:1 computing:10 defined:7 certain:3 abstract:1 describe:2 general:5 single:14 transi:1 resented:1 corresponding:1 ing:1 distributions:1 constructed:2 nj:1 rederive:1 no:5 when:8 nal:1 field:1 other:6 sponding:1 digital:1 ferent:2 conclusion:1 symposium:5 elements:4 superposition:17 problems:5 biham:2 includes:1 generated:2 tribution:1 focs:1 structure:2 building:1 independently:1 longer:1 algorithm:33 assume:1 required:6 nasa:1 time:1 cleve:2 starting:6 strings:1 once:2

quant-ph9912002.txt \|@word consider:5 illustrates:2 inadequacy:1 results:1 illustrated:1 counterfactual:4 follow:1 expressions:1 whose:1 depend:1 tr:1 investigation:1 overlaps:1 case:4 straightforward:1 orthogonal:3 mixing:1 experimentally:1 difference:1 matrices:5 leads:1 school:1 level:1 large:3 ascribed:1 small:1 noted:1 consistent:1 direct:2 second:2 further:1 odd:2 even:4 what:1 unavailable:1 giving:1 ˆb:6 experiment:4 attitudes:1 above:3 new:1 acknowledgments:1 supporting:1 degree:1 respectively:1 concepts:1 here:1 represented:1 along:4 obtained:1 rigorously:1 institute:1 products:2 stressed:2 opinion:1 composed:1 regardless:1 outcomes:1 total:1 linearly:1 confidence:1 probabilities:3 give:1 predictions:1 scenarios:1 noting:1 type:15 more:1 israel:2 becomes:1 operators:1 constructs:1 validity:1 tested:3 particular:1 known:2 cases:1 account:1 ma:1 err:2 work:1 reproduce:1 fock:1 tracing:1 dec:1 example:7 numbers:1 claim:2 compare:1 stated:2 calculation:1 arise:3 originates:1 states:31 his:3 refine:1 allowed:1 distinguishable:7 axis:5 end:1 discussion:1 get:1 criterion:1 pure:5 answer:1 weaken:1 product:2 description:6 may:5 ancilla:3 symmetrisation:1 wrong:1 summarize:1 register:1 acknowledged:1 allow:1 definitions:2 interpretation:12 terno:2 paper:1 statistical:1 existence:1 its:3 manuscript:1 personal:1 exact:3 boson:1 degrees:1 systems:2 inconsistencies:2 mail:1 undermines:1 non:2 they:4 half:1 now:2 several:2 demonstrably:1 asher:1 each:1 found:1 2n:9 individually:2 weighted:1 ed:1 used:1 quantum:4 our:1 operation:1 eq:2 out:2 deals:2 shown:3 matrix:7 space:1 since:2 rev:2 particles:13 daniel:1 correct:3 realisation:1 theory:1 possibility:1 clarify:1 york:1 definition:1 consequence:1 first:4 separable:4 probability:6 number:2 philosophical:2 another:1 impossible:2 quality:1 illustrate:1 given:9 their:4 πn:1 system:1 needed:1 statement:1 diego:1 gives:1 spindown:1 grant:1 ryzhik:1 exactly:6 immediate:1 appearence:2 copy:1 than:1 clarifying:1 polarized:1 see:4 preparation:12 matter:1 individual:2 result:3 san:1 cohen:12 argument:1 say:1 cumbersome:1 any:3 unsuitable:1 note:1 ideal:2 take:1 formulas:1 begin:1 opposite:2 singlet:1 but:8 gradshteyn:1 exercises:1 appear:2 technion:3 observation:1 considered:1 detectors:2 points:1 physics:2 fact:1 supported:1 recipe:1 chapters:1 inconsistent:3 subtle:1 find:1 help:2 distributed:1 operational:1 only:5 local:4 meant:2 mixture:1 means:1 between:9 cannot:2 despite:1 procedures:2 arxiv:1 set:4 binomially:1 observer:2 correlations:2 distinguishability:3 detection:1 depends:3 computer:1 projections:1 discussions:1 techniques:2 ways:1 label:1 symmetric:1 state:15 identification:2 simplest:2 reading:1 available:3 triplet:1 terms:1 reproduced:1 nature:1 qubits:1 ignorance:7 however:4 gratefully:1 distinguish:3 article:1 improve:1 both:3 taking:1 according:1 against:5 σz:2 σx:2 estimation:1 experimental:2 comment:1 bell:1 reasons:1 directions:1 simply:1 moreover:3 oliver:1 described:4 acceptance:1 pe:7 ph:1 pi:4 addison:1 direction:2 deeper:1 maximally:3 spin:6 those:3 p2:1 p1:1 pacs:1 eigenstate:2 will:1 while:6 suppose:1 error:2 procedure:3 unsatisfactory:1 almost:1 vj:1 thus:3 them:3 itself:1 il:1 technology:1 different:4 author:1 perform:1 indistinguishable:1 same:9 quant:1 arguments:6 mixtures:2 finite:2 independent:1 jeffrey:1 literature:1 ni:4 hand:3 entanglement:5 identity:1 recent:1 modes:1 nevertheless:1 no:3 epr:3 analysis:1 obviously:1 academic:2 sets:1 claims:1 identify:1 immediately:1 reality:1 eigenstates:2 polarization:1 kluwer:1 density:13 photons:2 book:2 questioned:1 easy:2 theorem:1 relevance:1 espagnat:2 ought:1 identical:1 sums:1 possible:4 department:1 vacuum:1 press:2 using:1 replace:1 like:1 particle:3 should:6 reduces:1 either:3 integrals:1 because:2 methods:1 namely:1 exposed:1 creation:1 some:4 examples:4 table:1 indistinguishability:1 happens:1 lead:2 measurements:1 thank:1 overlap:3 unit:1 analyzed:2 dropped:1 equivalent:2 perpendicular:1 wesley:1 binomial:1 explicitely:1 bz:1 comparison:1 actual:1 freedom:2 discussed:1 dependence:1 o:1 nonvanishing:1 extensions:1 mixed:14 22n:2 into:1 down:2 pair:1 appropriate:1 operator:2 unambiguous:1 statistics:3 there:2 question:1 abovementioned:1 series:1 analyze:1 was:1 complete:1 differences:1 preparations:6 haifa:1 especially:1 2πe:1 veiled:1 whether:1 up:3 us:4 dordrecht:1 below:3 ui:6 highlight:1 distribution:1 similar:1 agree:1 mechanics:1 ac:1 defined:1 implications:1 general:1 peres:2 multiparticle:2 examine:1 physical:3 again:2 locality:1 when:3 graduate:1 other:5 role:1 details:2 test:1 conclusion:1 separate:1 ascribe:2 problems:1 representable:2 prepared:3 meaning:1 important:1 implies:1 assume:1 together:1 original:1

quant-ph9912003.txt \|@word represent:1 externally:3 consider:1 nonlocal:1 limited:1 caused:1 magnetic:2 ψ1s:2 unique:1 fabricated:1 four:1 facilities:2 selection:3 comments:1 computation:16 foundations:1 consists:1 gn:3 contributions:1 issues:1 row:1 gyromagnetic:1 aligned:1 depend:1 rf:3 factoring:1 environment:1 charge:9 depending:1 under:1 cm3:1 forbidden:1 applied:4 conjecture:1 adiabatic:2 very:2 alternatives:1 impart:1 emphasizes:1 induce:2 results:5 electron:35 manipulated:1 figs:1 1s:2 exact:1 condition:1 common:2 splitter:1 presented:4 irreducible:4 viable:2 large:4 addressable:3 phase:6 small:1 relation:1 optics:1 configurations:1 logistics:1 illustrating:1 deutsch:4 miller:1 consistent:1 10a:1 direct:1 pulse:16 approximation:1 second:4 design:4 traveling:1 further:2 even:1 enticing:1 what:2 defence:1 adds:1 appear:1 richard:1 3s:1 section:11 expressed:1 uniform:2 current:4 version:1 currently:4 above:3 mosca:1 international:2 ever:2 consisting:1 temperatures:1 satisfy:3 explosion:1 respectively:3 component:4 here:12 atoms:8 reported:1 selective:10 operating:1 isotope:3 meet:1 represented:3 coupling:12 change:1 notably:1 search:2 stark:3 institute:1 shift:8 yablonovitch:2 step:1 sx:2 simultaneous:10 unpaired:4 microcavities:1 usually:2 resonance:9 fourier:1 makes:1 zubairy:1 involves:2 king:1 composed:3 tasks:1 spatially:1 figure:5 ions:1 requiring:1 readout:2 vii:2 a2s:2 brought:1 visible:1 specifics:1 iz:4 aimed:1 org:5 total:1 manipulate:1 use:2 takes:1 working:1 army:2 distinct:6 positive:1 predictions:1 nobel:1 few:2 depicted:3 noting:1 therefore:2 ψl:1 memory:1 combines:1 type:3 theoretical:1 more:6 schematic:1 brings:1 operators:1 pairs:1 missile:1 correspondingly:1 far:1 particular:4 known:1 ψ2s:2 mounted:1 iii:4 must:12 hardware:1 mf:2 hour:2 science:2 challenge:2 work:2 mi:6 london:3 worth:1 impasse:1 remain:1 grover:4 splittings:2 ms:7 cal:1 believed:1 fulfill:1 dec:1 root:1 example:2 fulfillment:1 control:9 nearest:2 sub:1 transition:6 reasonably:1 indicated:2 stated:1 process:1 introduces:1 ak:7 suggestions:1 generically:1 states:6 numbers:3 allowed:1 analysis:2 times:1 unordered:1 guarantee:1 information:8 requirements:11 rather:1 ideas:1 discussion:1 breaking:1 algorithms:3 species:1 machine:1 located:1 100mhz:1 criterion:2 low:1 pure:1 significance:1 gate:8 microwave:16 roy:2 20nm:1 exponentially:1 simplicity:2 alternative:3 may:3 earlier:1 scalable:1 diagram:2 applications:1 produce:4 concern:1 jozsa:3 wave:10 data:1 efficiently:1 storing:2 sz:3 diagonal:4 ot:1 natural:1 liquid:2 computations:1 register:2 correspond:1 ghz:1 st:1 rendered:1 generic:4 si:6 so:4 microseconds:1 representation:7 subsequently:1 order:5 operations:10 integrated:1 gershenfeld:4 eigen:1 constituents:1 over:3 displayed:1 flips:10 years:1 computational:4 pulses:2 japan:1 cold:1 suffer:1 ieee:1 its:6 chemical:1 group:1 termed:1 energies:1 interesting:2 temporal:1 scully:1 edge:1 offers:1 systems:3 constitutes:1 annual:2 isaac:1 might:1 h0:4 tsp:1 split:1 them:1 greater:1 combination:1 adiabatically:1 universality:4 adjacent:1 arsenal:1 scaling:2 mitigated:1 slichter:1 focus:1 substrate:1 rotation:1 now:5 discuss:4 nor:1 execute:1 double:1 2s:2 always:1 university:1 hamiltonian:3 loosely:2 identified:3 establishing:1 capability:4 sufficiently:2 harness:1 arrow:4 each:1 inherent:1 2n:1 polynomially:1 macchiavello:1 individually:3 schemes:4 neil:1 energy:6 kane:7 principles:1 constitute:2 interferometer:2 isotropic:3 measurement:1 quantum:63 laboratory:4 operation:10 beyond:3 salesman:1 special:1 out:9 divincenzo:3 shown:7 accomplish:1 network:2 factors:1 since:1 interference:5 research:3 rd:1 method:3 acting:2 mediated:6 10khz:1 conjectured:2 induced:11 cause:2 occurs:1 announced:1 shows:1 provide:2 theory:2 interactions:3 hirai:1 given:10 free:1 drives:1 labs:1 manifestly:1 approaches:1 california:1 elsewhere:1 element:1 e5:1 e4:2 e6:1 e1:1 e3:2 e2:3 revolutionary:1 enormous:1 interaction:19 marshall:1 could:3 computers:1 david:3 counterpart:1 isi:2 place:1 massive:1 approach:1 transfer:3 βn:5 diminishes:1 facilitate:1 gif:10 first:5 major:1 initial:8 features:1 symmetry:3 widely:1 feel:2 omitted:1 number:3 echo:1 utilized:2 least:1 another:4 calculational:4 array:1 electronic:21 angular:3 hood:1 size:2 properties:1 necessarily:1 publication:2 likely:1 los:1 introduction:1 fl:1 top:1 system:14 construct:2 their:1 intermediate:1 realization:7 scheme:21 bits:4 gives:1 shell:3 isomorphic:1 collapse:1 exactly:2 esoteric:1 sy:2 transverse:1 optical:5 favorable:1 shifter:1 than:7 center:1 wide:2 colleagues:1 third:2 isolation:1 require:1 measured:1 transferred:12 limiting:1 preparation:8 linkable:1 individual:2 kth:1 nanostructured:1 were:1 toward:3 treated:1 distinguished:1 seminal:2 turned:1 manner:1 ans:1 seen:1 bohr:1 demonstration:2 any:6 option:2 mik:5 strength:1 genuine:1 mil:1 output:2 harper:1 pursued:1 orland:1 aside:1 contact:3 chiba:1 sciences:1 emphasis:1 potential:1 square:1 best:1 command:1 techniques:5 rate:2 hyperfine:14 criteria:4 unless:1 gβ:1 though:2 serve:1 molecule:1 zender:1 impurities:1 severe:1 involving:2 connected:1 significant:2 device:3 turchette:1 future:2 extremely:2 class:2 magnitude:1 mach:1 found:1 observation:1 mediation:1 feynman:2 part:1 tech:1 principle:2 subsequent:3 usual:1 physics:1 notion:1 choice:1 shor:3 directorate:1 text:1 detection:2 labels:1 discovered:1 registers:2 chuang:4 especially:1 determined:1 find:1 ground:4 o:1 satisfies:1 slow:1 layout:1 implementation:1 distributed:6 operational:2 only:4 explicitly:1 screening:1 developed:1 satisfied:1 identification:4 local:2 achieve:1 characterization:1 intractable:1 his:2 template:1 quantph:1 means:1 dependent:1 βh0:1 simplest:1 kind:1 imparted:2 facilitated:1 beam:1 new:1 combinations:1 procedures:1 target:4 prime:1 following:3 evolution:1 resource:1 waveguide:3 arxiv:6 yield:1 summary:1 qc:4 stored:1 eiϕ:2 processed:1 shf:2 contain:1 including:1 anticipate:1 nist:1 atomic:2 magneton:2 requirement:2 set:6 art:5 ser:1 reference:1 achieved:1 flip:1 observed:1 namely:1 computer:17 migration:3 enhanced:2 terms:5 displacement:1 nonlocality:2 prototypical:1 subject:2 tensor:2 bowden:4 nuclear:58 mabuchi:1 laureate:1 bias:2 materials:3 initially:1 state:30 difficulties:1 various:1 routing:1 between:3 progress:1 reading:1 conditions:7 email:1 discovery:1 available:5 31p:1 recently:3 ability:1 constituted:2 qubits:10 lange:1 attention:1 weak:1 however:6 scalability:3 rapid:1 ws:2 orbitals:2 distinguish:1 outer:2 configuration:2 suppressed:2 suggested:1 both:3 last:1 limits:1 met:1 qft:3 similar:2 conclusions:1 according:2 zeeman:7 flipped:1 enabling:1 sensitive:2 involve:1 logic:6 selectively:2 qubit:8 experimental:1 otherwise:2 ch:2 study:1 jeff:1 simple:3 ca:1 relaxation:2 specification:1 corresponds:2 advancement:1 concluding:1 cirac:1 regulated:2 applicability:1 governed:1 polynomial:1 associated:2 cw:1 ps:5 enunciated:1 implanted:1 described:2 submanifold:1 decoupling:2 basis:6 equivalent:2 due:2 been:1 int:1 much:1 combined:1 expected:1 ph:6 meeting:1 universal:12 fig:22 controlled:10 sufficient:4 photon:2 meekhof:1 coherent:3 external:2 spie:1 aviation:1 spin:71 present:3 case:2 multi:1 novel:3 laser:14 exponential:3 auxiliary:1 solid:3 engineering:1 evaluated:1 transformation:6 will:4 near:1 optimization:1 suppose:1 gnk:2 35th:1 guide:3 procedure:1 unitary:6 coupled:5 vi:2 simulations:1 thus:9 iv:6 ii:5 ik:2 obstacle:1 auxilliary:1 triple:1 ia:1 ic:1 technology:5 monroe:1 orbital:2 binary:1 different:1 develop:1 april:1 perform:2 references:1 silicone:1 format:5 lett:6 same:4 clearly:2 member:1 shifts:3 stimulated:1 quant:6 virtually:1 coworkers:1 several:1 development:3 independent:1 calculation:1 used:4 http:5 see:1 again:1 defy:1 trajectories:2 upon:4 effect:1 hand:4 driven:1 ion:1 running:2 levels:1 purpose:2 entanglement:7 robust:2 dielectric:1 fabrication:4 built:1 task:2 off:2 traps:1 scenario:2 database:1 rules:1 weapon:1 variety:1 well:5 advantages:1 obviously:1 exceedingly:1 without:1 solve:1 position:1 model:1 sensing:1 ekert:2 left:3 gates:8 manifold:2 aerospace:1 proposed:10 less:2 nanoseconds:1 necessitate:1 deexcitation:3 feher:1 via:9 identify:1 transforms:1 useful:3 momenta:1 speed:4 previous:1 impetus:1 loading:1 zoller:2 application:1 ψks:1 bell:1 royal:1 except:1 transformed:1 treatment:1 technological:1 input:2 extensive:1 mod:1 excited:5 momentum:2 generalized:2 pair:1 optimizations:1 aspects:1 definitive:1 rev:10 exploiting:1 read:12 narrower:1 couple:1 term:3 early:1 entangled:6 background:1 performance:1 press:1 using:7 bit:9 execution:8 apart:1 theor:1 necessary:2 particle:1 follows:1 signal:3 performing:1 isotropy:1 nanoscience:1 specific:5 private:1 yields:1 either:2 integrals:1 arbitrary:2 expresses:1 essential:1 spins:9 right:3 methods:5 classical:8 sequence:2 conditional:4 some:2 searching:1 nanostructures:1 selectivity:1 respect:4 proper:1 peter:2 kimble:2 nonzero:1 provided:3 scale:2 esr:4 lead:1 realistic:1 avoid:1 measurements:2 overlap:8 does:2 proc:4 demonstrated:6 core:1 cgk:1 nmr:6 contingent:1 power:1 journal:1 processing:1 executable:2 machzehnder:1 host:1 symp:1 ratios:1 2m:1 hadamard:2 sandwiches:1 refers:2 intense:1 cnot:2 comparison:1 would:1 most:1 universe:1 capable:2 discussed:6 location:1 recognized:1 constituting:1 practical:4 addition:1 range:4 alleviated:1 preskill:3 neighbor:2 stuart:1 mixed:1 introduced:2 consequently:1 homogeneous:1 soc:4 cambridge:2 followed:2 wineland:2 communication:1 into:3 within:6 splitting:1 bound:2 negative:1 accommodate:1 remarks:1 engendered:1 promise:1 elementary:1 next:3 rely:1 intrinsic:2 there:4 relegated:1 transform:2 long:1 width:1 cultivation:1 lov:1 inner:2 strong:2 forward:1 instead:1 was:3 1khz:1 function:6 complete:1 form:2 offer:1 forming:1 regard:3 but:5 sophisticated:1 construction:1 atom:33 line:1 level:6 proposal:1 he:1 fluorescence:5 embedded:2 ψf:2 up:2 frequency:4 fermi:2 spectroscopy:3 problem:3 addressability:2 called:1 nature:2 mechanics:1 fulfills:2 later:1 constant:3 a1s:1 computing:5 defined:1 certain:1 abstract:1 general:1 globally:1 single:16 exist:1 rule:2 our:12 corresponding:6 high:1 functions:3 transitions:4 entirely:1 no:7 amounts:1 whereas:4 wavefunction:1 dowling:1 elemental:4 field:8 other:4 digital:3 np:1 electrons:2 developers:1 symposium:1 draw:1 elements:3 conveys:1 superposition:4 excitation:14 felt:1 problems:6 ultimately:2 oracle:1 important:2 nucleus:2 included:1 nuclei:1 structure:1 phosphorus:1 independently:1 suffers:1 faster:1 algorithm:14 u1:3 assume:1 established:1 required:5 necessitates:1 together:5 compete:1 parallelism:2 time:9 cleve:2 decoherence:4 requires:2

quant-ph9912004.txt \|@word monte:1 concept:1 gs:1 consider:1 switched:1 varying:2 results:4 projected:1 four:4 eds:1 ge:1 cnx:3 ga:1 stochastically:1 consists:2 follow:1 research:1 gi:3 depend:2 esf:2 c0a:9 tr:1 factoring:2 environment:7 finally:1 cne:3 stable:2 kλ:14 nodes:1 c0s:5 reconsider:1 norm:2 applied:8 amplitudes:3 advantage:2 orthogonal:1 very:13 frequencies:6 rise:1 springer:3 wave:3 manipulated:2 additional:2 chuang:2 lecture:1 resonant:2 laser:35 condition:17 leads:6 gkλ:3 vibrational:1 level:12 positions:3 notes:1 proposals:1 solution:1 large:1 solved:3 vector:3 science:2 small:6 eigenvalues:1 optics:5 der:1 viola:1 excite:1 smaller:5 compensated:1 organised:1 foundation:1 0x1:2 a34:2 sin2:1 prediction:1 pulse:20 jump:5 surrounding:1 rate:18 dissipation:1 value:1 dynamics:1 implemented:1 odd:2 leakage:3 theory:1 even:10 index:1 what:1 errors:1 g23:1 section:16 remain:4 nϕ:2 waiting:1 experiment:6 subspaces:1 international:1 principal:1 method:3 cnot:1 edited:1 ibid:1 exchange:2 respectively:3 error:3 lange:1 equals:4 here:16 atoms:77 behaviour:5 plenio:8 possibility:1 separation:2 address:2 strong:1 equations:4 change:7 differential:3 obtained:5 eij:1 antisymmetric:3 parameters:2 institute:1 involved:1 larger:4 allows:5 completely:1 council:1 suggests:1 resulting:1 deutsch:2 resonance:2 suitable:1 changes:1 inhibited:1 via:5 projection:1 scales:1 namely:1 explained:2 logical:1 highly:1 addressed:1 a23:1 decrease:2 odinger:2 a24:1 total:4 establish:1 manipulate:5 standing:1 derivatives:2 use:6 hegerfeldt:4 superpositions:1 jessen:1 remains:5 abbreviations:1 give:4 physics:1 next:4 leaks:3 therefore:9 vi:1 taken:2 kaler:1 leaky:1 resonator:10 theoretical:3 more:4 separated:1 lowering:1 fly:1 initial:1 under:8 emission:16 berlin:3 observing:1 normalized:1 particular:1 known:3 foundations:1 iii:3 must:2 entangle:2 states:76 account:1 decouples:2 equation:4 work:4 london:4 mt:2 macroscopically:1 grover:1 values:5 following:10 fulfill:2 roos:1 spontaneous:11 example:8 performed:3 control:1 ions:2 challenging:1 eg:1 mirrors:11 process:4 neglected:3 haroche:2 high:4 effectively:2 nogues:1 numbers:6 want:2 arise:2 domokos:1 yang:1 information:2 six:1 end:1 straightforward:2 briegel:1 provide:1 interacts:2 discussion:2 acts:1 haake:1 algorithms:2 how:9 große:1 criterion:4 pure:2 simplifies:2 sij:1 parameter:3 sin:5 belongs:3 simplicity:1 description:4 may:1 demonstrates:1 after:3 cambridge:3 computation:2 constants:2 rauschenbeutel:1 short:4 physical:4 third:1 ghs:1 ss:1 light:2 approximation:6 explicit:1 correspond:1 st:8 ones:1 so:5 sørensen:2 g14:1 g13:1 order:7 terms:4 proposal:1 operations:10 unnormalised:1 interpretation:1 help:8 ith:1 indeed:1 over:8 move:5 g34:2 held:1 paper:2 pulses:8 r2493:1 statistical:1 fidelity:3 still:4 agrees:2 its:6 humboldt:1 sciences:1 derive:2 rapidly:4 symmetry:1 decay:9 chosen:5 actually:1 better:1 according:1 itano:1 fig:10 annual:1 rabi:9 decreased:1 main:4 setting:1 theo:1 measurement:6 them:5 good:5 pauli:2 press:3 propose:3 material:1 heinzen:1 cover:1 couples:1 they:8 optimal:1 own:2 rotation:3 now:5 discuss:8 overlap:1 easily:5 february:1 several:1 2s:4 always:3 university:1 hamiltonian:15 huelga:2 hermitian:1 orthonormal:4 sufficiently:1 iff:1 magnitude:2 mode:29 realise:1 knight:10 found:3 universit:1 european:1 2i:1 neglects:1 individually:3 schemes:1 england:1 directly:1 populated:8 cote:1 there:1 energy:1 idea:2 society:1 frequency:5 proportional:3 quantum:38 laboratory:1 operation:1 transitions:2 eq:31 out:15 leave:1 shown:8 reducing:1 literature:1 matrix:2 driving:2 space:8 profit:1 rev:30 nκ:5 denotes:1 increase:1 re:1 daniel:1 wolf:1 performs:1 denoted:3 formula:1 shortly:2 ref:7 math:1 shows:2 gate:1 numerical:1 linear:1 discrete:1 gardiner:2 mechanisms:1 1s:3 free:23 weakly:1 bertet:1 reason:1 perturbation:1 generate:2 milburn:1 care:1 definition:1 pairs:2 interaction:21 could:3 transition:5 times:2 arccot:1 initiate:1 length:5 levels:3 place:5 assumed:2 consequence:1 y34:1 onto:2 neglect:2 first:10 ieee:1 major:1 already:3 bσi:3 probability:15 stevens:1 zeroth:1 number:5 xy:1 inhibits:1 dfs:44 another:3 lidar:5 open:1 ser:2 akλ:4 given:23 long:7 checked:1 needed:1 introduction:2 interact:2 behaves:1 πn:1 system:61 least:3 their:6 rates:3 too:1 1g:2 postulate:1 scheme:9 bits:1 gives:4 trapped:12 bacon:3 acquire:1 leaking:1 braun:2 optical:3 manipulation:6 x2:1 off:2 july:1 x1:1 uders:2 than:9 coefficients:6 population:2 distance:2 effective:5 fold:1 was:6 second:3 submitted:1 limiting:1 annihilation:3 determined:2 measure:1 achieved:1 schneider:1 zanardi:2 calculation:1 correction:2 turned:1 tregenna:2 unlikely:1 seen:2 misra:1 any:3 heff:5 strength:2 zero:5 efficient:1 carlo:1 responsible:3 able:1 ideas:1 mechanism:5 note:2 instance:4 ideal:2 potential:1 steane:2 take:6 simplified:2 destroy:1 detector:1 degenerated:1 exactly:1 c2s:1 serve:1 measures:1 g24:1 most:1 germany:1 kempe:2 phase:3 laflamme:2 mundt:1 why:1 observation:2 considered:6 sg:1 clear:1 later:1 detectors:2 drive:1 g12:3 proceedings:2 construction:1 principle:5 exp:1 mechanical:1 thank:1 velocity:1 ueff:1 usual:1 normally:1 sum:1 fact:2 joining:1 precise:2 shor:4 show:6 supported:2 rotating:1 2g:11 relation:1 lloyd:1 wigner:1 longer:1 find:8 ground:9 o:1 based:1 2bz:1 spite:1 dp0:1 implementation:1 explain:1 entangling:2 outside:8 negligible:3 should:4 dalibard:1 only:14 going:1 candidates:1 subsection:2 factor:3 thompson:1 employed:1 partially:1 thousands:1 interested:1 do:6 predict:1 mixture:1 carmichael:1 above:2 notation:4 wide:2 df:24 beams:1 zurek:2 overall:1 cannot:3 meyer:1 during:6 dt:2 interpreted:3 a14:1 cos:4 evolution:15 caves:1 transfered:1 fields:2 goldwasser:1 arxiv:1 summary:1 lukin:1 investigate:1 stored:2 c2a:1 occurance:1 through:9 fixed:6 view:1 hκ:1 available:1 requirement:1 set:2 lasers:1 our:3 hγ:1 0s:4 generalisation:4 maximum:1 detection:2 see:9 computer:4 college:1 result:3 discussions:1 close:6 analog:1 preparation:7 x12:1 doebner:1 subsequent:2 review:2 complementary:1 dipole:2 eigenstates:2 initially:2 state:61 a45:1 c2g:3 closed:1 between:19 wellens:1 approach:11 brune:2 guo:2 multiplied:1 attention:1 recently:1 ability:1 nature:1 qubits:10 emitted:10 weak:9 however:3 efficiency:2 bose:1 hundreds:1 suppressed:1 monitor:1 suggested:1 received:1 σi:11 outcome:2 last:3 2n:5 limits:1 many:3 gantmacher:1 conclusions:1 equal:4 fulfilled:1 assure:1 0a:10 und:1 0g:11 cog:3 0e:4 qubit:5 argue:1 whole:3 finds:2 experimental:1 otherwise:1 arbitrarily:6 detailed:2 cn:4 bell:1 simple:2 ca:1 each:9 corresponds:1 alamitos:1 dimensional:3 cirac:5 losses:2 dependent:1 respect:1 writing:1 factors:1 hω0:1 forms:2 raimond:2 aij:1 described:3 ag:1 symposium:2 basis:6 addition:3 simplification:1 create:2 due:14 been:9 quickly:1 much:7 slowly:2 damping:1 expected:1 combine:1 ph:9 ann:1 empty:4 define:3 controlled:1 both:1 suppress:1 sufficient:2 coherence:3 subspace:12 precision:1 coherent:1 observe:1 maximally:5 spin:1 present:1 case:13 k2:13 p0:13 schmidt:1 uncertain:1 excites:1 developing:1 quantenmechanik:1 engineering:1 evaluated:1 spontaneously:3 will:13 while:5 promising:1 grundlagen:1 hωk:1 35th:1 sw7:1 k1:13 opt:3 aa:1 unitary:3 costly:1 osnaghi:1 coupled:2 almost:1 vanishes:2 refs:3 formulation:1 thus:2 non:10 systems:2 iv:2 ii:3 duan:2 vanish:1 technology:1 coa:3 different:5 bollinger:1 intact:1 projector:1 degenerate:1 james:1 perform:4 make:1 belong:2 radiation:10 same:8 shorter:1 shifts:2 unity:5 complex:1 quant:9 schematic:1 mølmer:3 regime:3 couple:1 higher:6 development:2 independent:1 emphasise:1 used:9 singapore:1 trajectories:1 sudarshan:1 effect:18 possible:4 driven:2 compared:3 necessity:1 intended:1 entanglement:2 changing:1 confines:1 ωk:2 eigenvectors:1 task:1 finesse:1 modes:3 pellizzari:1 acknowledgement:1 expression:3 no:19 well:2 roughly:1 know:2 concrete:1 mathematische:1 without:4 solve:1 components:1 quantitative:1 castin:1 arising:1 dimension:4 realised:2 construct:1 calderbank:1 proposed:3 less:1 observed:1 newton:1 obtain:5 ne:6 ekert:1 accumulate:1 underlying:1 distant:1 atomic:14 predicts:2 immediately:1 yes:1 brennen:1 yet:1 down:1 previous:4 poyatos:1 like:2 zoller:5 density:2 photons:11 point:1 dicke:7 iω:26 source:2 internal:1 transformed:1 lett:16 exempt:1 mod:3 suominen:1 excited:2 realisations:2 real:2 pair:1 entangles:1 vii:2 depends:1 demands:1 showing:1 sums:1 term:5 successful:3 increases:2 outcoming:1 entangled:7 vacuum:2 confined:1 using:12 part:1 emptied:2 correcting:1 apart:1 loss:2 rasetti:1 necessary:4 success:6 lost:1 follows:1 qualitative:1 adiabatic:1 c1g:4 c1e:1 loses:2 specific:1 steps:1 either:1 arbitrary:5 c1s:5 become:4 works:1 reduced:1 making:1 because:4 2iκ:1 neumann:2 classical:2 sequence:1 conditional:8 paragraph:1 identified:1 understood:2 elements:1 examples:1 choosing:1 duration:1 kinds:1 peter:1 provided:1 scale:5 describing:1 a13:2 lead:1 cavity:57 electromagnetic:3 avoid:1 measurements:4 recorded:1 schr:2 stops:1 dfss:2 cng:3 does:9 provides:1 cna:3 prog:1 proc:4 demonstrated:1 trap:1 conference:1 obey:1 uniformly:1 equivalent:1 processing:1 evolve:2 blatt:1 prepared:8 hilbert:3 von:2 takes:1 about:1 carried:1 world:1 simplify:1 og:1 discussed:9 dependence:1 oa:1 summarise:2 practical:2 union:1 range:1 ensure:2 beige:6 done:2 connected:1 introduced:1 subset:2 soc:4 contains:2 presence:4 wineland:1 into:8 within:1 auxiliary:1 stop:1 device:1 appropriate:1 scherer:1 determine:1 operator:9 ei:2 essen:2 rossi:1 behind:1 whaley:4 deal:1 prepare:4 transfer:1 placing:1 vedral:1 fast:4 imperial:1 los:1 describes:10 mandel:1 way:3 scientific:1 sections:1 gij:1 combined:1 function:1 complete:1 form:8 enough:2 metastable:3 registered:3 jun:1 but:8 sonderforschungsbereich:1 repeated:3 hi:1 atom:11 elimination:1 dissipative:1 hg:2 rolston:1 never:1 normalising:1 jonathan:1 applying:1 c1a:1 whether:5 inside:20 up:2 us:5 ωi:6 below:1 ui:1 emissions:1 uk:1 continuously:2 distribution:1 semiclass:1 similar:1 blackett:1 strongly:2 storing:2 interval:3 constant:2 zeno:8 computing:6 defined:2 certain:4 describe:6 proven:1 general:10 substantially:1 single:9 exist:1 periods:1 wavelength:1 corresponding:2 jaksch:2 constructed:2 again:3 functions:1 codes:1 gg:1 polarisation:1 na:5 fruitful:1 wavefunction:1 when:2 detail:5 ng:3 nx:3 field:29 other:10 becomes:5 test:1 finite:1 ns:6 picture:3 formed:1 denote:1 superposition:2 excitation:7 a12:3 photon:29 time:40 problems:2 includes:1 generated:1 important:1 palma:1 log:1 prepares:1 meystre:1 cns:3 coupling:12 algorithm:1 assume:8 requires:1 required:1 together:2 broadband:1 leibfried:1 teleported:1 leak:3 far:2 decoherence:14 roy:2 others:1 once:3

quant-ph9912005.txt \|@word limited:1 concept:6 managed:1 consider:1 both:3 alternatives:1 results:1 existing:1 illustrated:2 intricate:1 remarkably:1 issues:1 whose:2 certainly:1 amplification:1 paris:1 producing:1 subjected:2 presents:1 present:3 marks:1 stochastic:1 include:1 summarizes:1 division:5 finkelstein:1 far:3 could:2 implicitly:1 account:1 iii:1 wave:20 worst:1 decide:2 exact:1 condition:3 splits:1 themes:1 quantitatively:1 presented:2 positions:1 notes:1 list:3 solution:1 try:1 vector:1 dealt:1 equation:1 says:2 pragmatic:1 dealing:3 design:1 concludes:1 further:2 goes:1 even:2 trick:1 what:5 stood:1 apparatus:15 deeply:1 macroscopically:1 expressed:1 access:1 version:3 establishes:1 new:4 appeal:2 justification:1 notions:1 convergences:1 human:1 here:3 atoms:1 refinement:2 shouldn:1 objects:1 free:1 separation:1 active:1 dissipated:2 strong:1 interpret:1 ensembles:1 instituto:2 ref:2 hamiltonian:4 accepts:1 rests:1 elaborate:2 completely:1 experience:1 leaving:1 atom:1 permit:1 honor:1 criticism:2 emerge:1 useful:1 although:1 danger:1 suddenly:1 problematic:1 wataghin:1 hindsight:1 forefront:1 rarely:1 causal:5 select:1 standing:1 environment:14 use:1 superpositions:7 would:5 probabilities:1 circumstances:1 therefore:4 usp:1 taken:4 material:1 stage:1 theoretical:1 today:1 more:3 introducing:2 molecules:1 successful:1 becomes:3 constructs:1 odinger:3 aware:1 realized:1 reversible:1 ignorant:1 known:1 foundations:1 encountered:1 effort:1 must:4 high:1 keeping:1 thanks:1 indicates:1 avoiding:1 challenge:1 theories:1 remain:1 obstacle:2 obvious:1 concepts:3 following:3 dec:1 example:1 control:1 claim:1 council:1 indicated:1 brown:1 process:8 relativistic:1 states:10 collision:1 slit:1 recognized:1 want:1 information:17 provide:1 divided:1 six:1 how:10 criterion:2 frontiers:1 answer:1 ordinary:1 preferable:1 ensemble:1 intended:1 overall:1 advice:1 after:1 derived:1 santos:1 demanding:1 cambridge:8 choice:1 data:2 types:1 diagonal:1 short:1 branches:1 remember:1 whenever:1 emphasize:1 lines:1 element:1 rather:2 so:5 ultimate:2 fundamental:1 correlation:1 operate:1 order:1 talk:3 passages:2 interpretation:15 help:1 developed:1 over:4 altogether:1 soon:1 produced:1 course:1 paper:5 through:1 argued:1 existence:2 institute:1 still:5 pointer:1 its:11 before:2 thank:1 located:1 matrices:1 solving:1 gleb:1 actually:2 better:1 permanent:1 microscopic:1 systems:2 epistemological:2 main:1 might:1 overcome:1 split:1 them:3 good:1 thereby:1 descendants:1 practice:2 processes:1 introduce:2 anticipated:2 obeyed:1 mention:1 effects:3 they:3 cep:2 arriving:1 now:6 day:2 wiley:1 duality:1 always:2 university:6 traced:3 intricacy:1 someone:1 inherent:1 entirely:1 ifi:1 disappearing:1 formulate:1 challenged:1 doing:2 ed:2 energy:1 related:1 society:1 measurement:23 quantum:33 our:3 avoided:2 witness:1 description:5 deals:2 ultimately:1 matrix:3 space:1 tried:1 crucial:1 research:1 particles:3 investigation:1 cause:1 common:2 perception:1 theory:7 interactions:1 recommendations:1 ısica:3 attempt:2 departamento:2 quite:1 approaches:1 york:1 besides:1 put:2 inevitable:1 interaction:3 language:3 determining:1 recipes:1 motion:2 undesirable:2 consequence:2 uses:2 think:2 first:1 already:1 probability:1 radical:1 number:1 philosophical:3 done:1 specifically:1 another:1 force:1 open:4 fair:1 introduction:1 leading:1 top:1 system:23 unspecified:1 tradition:1 their:2 intermediate:1 dissipate:1 influence:1 postulate:2 perfectly:1 shifted:1 commutativity:1 collapse:2 pittsburgh:1 exactly:1 eliminates:1 speakable:2 part:3 somewhat:1 authors:1 kept:1 imposing:1 microphysics:1 essays:2 dynamical:1 parts:1 holland:2 princeton:2 double:1 require:1 instruction:1 royal:1 recording:2 matter:1 individual:2 contrary:2 historical:1 were:2 treated:1 distinguished:1 motivation:1 acknowledged:1 modern:4 mind:1 say:3 delineated:1 need:2 seen:1 apparently:2 any:7 routledge:1 realm:1 agency:1 able:1 ideas:1 potential:1 algorithms:1 wonder:1 urge:1 play:1 broglie:6 trace:2 though:4 price:1 who:4 reach:1 philosophy:1 involving:2 connected:1 claims:1 nothing:1 plays:1 measured:5 philosophers:1 don:2 observation:2 clear:2 devastating:1 inferred:1 julian:1 points:2 electrons:1 principle:2 mechanical:2 left:2 physics:7 notion:2 quantity:1 science:1 emerging:1 show:3 text:1 escobar:2 random:1 contemporary:1 bring:3 attempts:3 carefully:2 longer:1 deser:1 based:1 knowledge:3 irreversible:4 explain:2 state:2 should:5 identifies:1 surroundings:1 only:6 explicitly:1 ambiguity:1 employed:1 adequate:1 misidentified:1 do:5 his:6 above:2 invoke:1 undivided:1 zurek:8 de:12 stop:1 da:1 joint:7 ones:1 despite:2 during:1 procedures:2 him:1 elaborated:1 stability:2 evolution:5 ended:1 nicely:1 conditions:1 arxiv:1 remove:1 summary:1 experiments:2 she:2 activity:2 proponents:1 london:2 obscure:2 discussing:1 view:2 apparatuses:4 ignored:1 declared:1 set:2 constructing:1 observer:10 subatomic:2 lifetimes:1 correlations:2 packet:3 observed:1 see:2 decided:1 result:2 discussions:1 progress:1 best:1 subject:2 brazil:2 interview:1 mechanically:1 nuclear:1 away:2 definite:1 importance:1 outside:1 difficulties:1 various:1 cooperation:1 between:11 probably:1 boundary:3 reading:1 approach:11 notice:2 terms:1 nature:2 originated:2 physicist:3 jr:1 however:2 disturbance:1 jointly:1 extent:1 interface:1 faced:1 observable:6 collaborators:1 last:1 experimentalist:1 many:5 pertain:2 hint:1 according:2 against:1 distinction:1 argue:3 whole:1 experimental:3 suggest:1 co:2 bell:9 simple:2 reconstructs:1 tracing:1 corresponds:2 represented:1 maintained:1 moreover:2 destroyed:1 pp:13 sieve:1 described:4 basis:1 addition:1 been:2 trigger:1 change:1 recognize:1 degrees:3 ph:1 extreme:1 formalized:1 empty:8 define:2 corresponding:2 commutes:1 beforehand:1 concerning:1 coherence:1 protect:1 observers:1 coherent:1 deep:1 vagueness:1 those:4 quotation:1 applied:2 look:1 decades:1 davies:1 appearance:1 will:9 invoking:1 while:1 frustrating:1 region:1 procedure:2 postulating:1 unitary:2 ve:1 vi:1 von:24 formulation:2 thus:3 iv:1 ii:2 examined:1 attributed:1 claimed:1 acquires:1 different:6 perhaps:2 large:1 make:2 demands:1 same:2 clearly:2 paulo:4 complex:2 quant:1 arguments:2 physical:3 events:2 used:2 estadual:1 declaring:1 trajectories:3 effect:2 campinas:2 experimenter:2 purpose:1 necessity:1 frequently:1 circumvented:1 infamous:1 recent:2 transaction:1 schr:3 acknowledge:1 well:3 analysis:2 bohr:28 bohm:11 severe:1 without:1 solve:2 very:2 position:7 bodies:1 stressed:1 unified:1 excessive:1 proposed:1 less:1 being:3 guided:1 inactive:2 atomic:4 questions:1 using:1 schwinger:1 macroscopic:4 move:2 cut:6 monitored:2 density:4 point:2 had:1 passive:1 instrument:1 priori:1 treatment:1 resolved:1 aspects:1 around:1 disappearance:2 evaluate:1 spatial:1 possible:2 hiley:4 know:3 press:6 world:11 vague:2 formal:1 loss:1 imposed:1 like:3 particle:7 manual:1 loses:1 specific:1 remind:1 imposes:1 arbitrary:3 works:1 essential:3 mathematical:2 pertaining:1 right:2 neumann:24 deal:2 exposed:1 sends:1 obliged:2 subjectivity:1 some:5 somehow:2 born:1 scales:1 total:1 describing:2 avoid:1 unavoidable:2 overlap:2 instantaneous:1 does:2 discretion:1 whitaker:2 refer:2 measuring:6 destroys:1 object:1 scientific:1 vertex:1 undergone:1 experiment:1 step:1 interpretative:1 br:2 universe:3 refers:1 predictability:1 takes:1 exposition:1 about:5 central:1 carried:1 demarcation:1 freedom:3 introduces:1 o:2 remains:1 carries:2 unaccessible:1 act:3 introduced:3 consequently:2 own:1 dilemma:1 presence:1 instruments:1 into:4 device:1 appropriate:1 because:1 references:1 einstein:1 unambiguous:1 criticisms:3 classical:19 her:3 removing:1 support:1 there:4 question:2 long:1 review:2 describes:1 physicists:2 way:3 brazilian:1 forward:1 maze:1 analyze:1 was:10 function:7 irreversibility:2 form:1 enough:1 memory:2 but:14 back:3 subjective:3 pessoa:1 convergence:1 remote:1 cnpq:1 removed:1 true:1 he:5 made:3 up:2 us:2 international:2 below:2 problem:11 similar:1 mechanics:15 later:1 taste:1 certain:2 abstract:1 combining:1 moved:1 ao:4 single:2 exist:1 governed:1 laboratory:4 formalism:5 universidade:2 constructed:1 again:1 functions:3 weakened:1 no:8 when:5 detail:1 reality:2 field:1 other:3 role:2 special:1 branch:2 brings:2 test:1 mathematics:1 out:1 interpretations:2 conclusion:1 happens:3 elements:1 superposition:3 models:4 unicamp:1 felt:1 problems:6 much:1 meaning:1 scale:1 serious:1 included:1 arguably:1 fundamentally:1 ghost:1 implies:2 auxiliary:1 inevitability:1 resolution:1 required:1 daily:2 calculates:1 time:3 observables:2 decoherence:16 requires:1 unspeakable:2

quant-ph9912006.txt \|@word represent:2 footing:1 consider:3 remarkable:1 interference:1 lack:2 desirable:1 none:2 leads:4 bringing:1 selection:1 broader:1 consists:2 perturbations:1 gm:1 contributions:3 reasoning:2 causes:2 seemed:1 whose:4 certainly:4 depend:3 violate:2 2hi:1 concerned:3 seriously:1 former:1 vef:3 list:1 charge:3 ﬁnds:2 excluded:3 under:5 must:1 kξ:1 overlaps:1 case:16 attempts:1 reality:1 amplitudes:1 8m:1 straightforward:1 outside:1 very:11 tends:1 keeping:1 wave:31 suﬃciently:2 manifolds:1 summarized:1 2rv:2 matrices:1 play:1 condition:11 room:1 treating:2 entire:3 retaining:2 presented:4 altering:1 turns:3 t2:5 solution:15 aﬀects:1 viable:1 large:7 discrete:1 couched:1 detected:1 minimal:4 science:1 small:3 provided:1 hcm:2 speciﬁed:1 equation:67 proof:1 possibility:2 prevent:1 employing:2 grateful:1 periodicity:1 description:1 consistent:1 among:3 inconsequential:1 approximation:6 second:4 progress:2 nonhomogeneous:3 incidentally:1 further:2 implemented:1 canonical:1 even:16 oﬀer:4 what:7 nonlinear:27 const:1 stands:2 ambiguities:1 frameworks:1 section:11 celebrated:1 brief:1 d3:10 current:6 pawel:1 version:2 suspect:1 localized:1 above:4 selecting:1 new:6 mazur:3 worked:3 consisting:1 contrast:1 satisfy:2 christian:1 degree:1 exchange:1 respectively:2 ﬁelds:1 here:13 understanding:2 objects:1 galilean:9 separate:2 address:3 represented:1 consideration:2 along:2 strong:2 equations:19 change:1 ordinary:3 obtained:1 admits:1 almost:1 arrive:1 reconciling:1 suitably:3 slow:1 study:4 larger:1 experience:2 leaving:1 suggests:2 accomplished:1 periodic:1 resulting:1 negative:2 professor:3 stressed:1 action:5 t20:5 dismiss:1 suitable:1 makes:2 pathological:1 involves:3 appropriately:1 formulated:2 useful:3 addresses:1 mensky:1 nonseparability:2 prefer:1 private:1 modifying:2 ﬁrst:7 aimed:1 apply:2 total:3 planck:1 standing:1 derivatives:2 use:1 handled:1 would:9 remains:3 positive:2 until:2 contains:4 chooses:1 deﬁnition:9 next:4 comparing:2 linear:33 bialynicki:5 call:1 therefore:10 endowed:1 taken:1 associated:3 historically:2 more:17 introducing:3 treated:3 formally:2 γm:2 andrzej:1 becomes:2 acceptable:4 factor:1 line:1 odinger:39 correspondingly:1 everywhere:1 normalized:2 varying:1 known:1 actual:2 cases:2 had:2 states:12 γn:1 disguised:2 recall:1 originally:1 work:2 oscillator:2 modified:1 reproduce:1 mt:2 remain:1 vs:1 values:1 learn:1 following:1 2x2:1 dec:1 averages:1 example:3 decoupled:1 performed:1 f1:2 f2:3 ﬁnding:1 identiﬁes:1 indicated:1 process:2 december:1 choice:2 allowed:4 naturally:1 ann:1 ratios:1 indicates:2 identiﬁed:5 something:1 want:1 sense:5 sought:1 rescaling:1 occur:1 4em:1 crucial:1 information:2 needs:2 uxxx:1 end:3 p4:1 rather:10 s2:1 discussion:6 s0:2 feature:1 write:1 how:6 nontrivial:3 modiﬁcation:80 reducible:1 pure:1 collapse:1 instead:2 ﬁeld:4 constraints:1 parameter:3 sin:3 belongs:1 simplicity:4 product:3 diﬀers:1 incorporated:1 stable:1 may:11 earlier:1 derived:4 long:3 reﬂect:1 corrections:2 plane:3 demonstrating:1 coming:2 summarize:1 law:1 unacceptable:1 referring:1 constants:6 ambiguous:1 shortcomings:1 sx:4 natural:8 dynamical:4 four:2 light:2 many:1 lines:1 correspond:1 diﬀer:1 provide:2 maintain:2 so:10 sn:1 fundamental:3 sc:1 representation:4 order:8 talk:1 typical:1 separable:1 least:1 interpretation:5 2md:1 indeed:2 pointed:2 insight:2 expects:1 meter:5 interpreted:1 stability:1 combinations:2 paper:5 including:4 stimulating:1 motions:1 mentioned:1 still:3 its:30 ﬁnd:6 ﬁne:2 supplemented:1 derive:1 rapidly:1 thank:1 vulnerable:1 chosen:4 interesting:3 presence:1 complex:7 exhibits:1 ds:1 forms:1 absence:2 according:2 systems:5 constitutes:1 unbounded:1 criterion:1 main:3 might:3 alter:1 s1:2 maximal:3 them:7 good:2 motivated:2 greater:1 than:8 plays:1 matches:1 practice:1 evolution:3 introduce:3 cosh4:2 units:12 they:13 acta:3 singularity:1 now:13 discuss:4 nor:2 easily:2 term:15 finite:1 name:2 respectable:1 fully:1 university:1 hamiltonian:8 statement:1 factorizable:1 transmission:1 ﬁndings:1 transmitted:1 reasonable:5 each:3 inﬁnitely:4 found:8 entirely:3 referred:1 homogeneous:3 diﬀerent:6 domain:8 square:3 series:1 energy:61 ef:18 reduce:3 gaussian:9 used:1 ﬂow:1 constitute:3 onr:1 arrives:3 obtains:3 measurement:1 quantum:37 our:5 beyond:9 nonlinearities:2 special:2 out:13 category:1 emerges:1 shown:2 introduces:2 space:12 gradient:2 since:14 lagrangian:6 veriﬁed:1 adhere:1 looking:1 contained:1 performs:1 smod:1 perturbed:1 issue:5 correct:2 common:2 counterpart:1 marek:1 after:2 conjecture:1 theory:22 reformulated:3 interactions:1 perfectly:1 contain:1 mω:2 unexplained:1 free:4 standard:12 recalling:1 reason:2 necessarily:4 complicated:1 besides:1 put:5 care:1 definition:1 derivation:3 r2:26 starts:2 could:8 impose:2 noted:6 motion:14 turn:1 relativistically:1 place:2 tempting:1 nodal:1 consequence:1 moving:1 generalizations:1 mt0:3 south:1 first:1 origin:2 major:1 already:1 features:2 probability:8 eﬀective:3 predictive:1 radical:1 variables:4 number:2 lond:1 exact:2 email:1 smaller:1 adopted:2 another:12 xr:1 impossible:1 electronic:1 between:1 aharonov:4 given:7 derives:1 publication:1 covariant:1 similarly:4 introduction:1 leading:3 system:24 relations:8 identiﬁcations:1 einstein:1 their:4 assumption:4 eqm:16 observations:2 diﬀerence:1 realization:1 compromise:1 majority:1 scheme:4 ehrenfest:10 too:1 exploring:1 sealed:1 explanation:1 continuous:2 deﬁnitions:1 realized:2 employ:1 part:7 extensions:1 modiﬁcations:6 x2:6 attempt:1 imposing:3 believe:2 representing:1 separability:8 quantummechanical:1 expanding:1 observed:1 variational:1 conﬁgurations:2 unfortunately:2 elected:1 encompassing:1 distinguishes:1 largely:1 zero:7 aims:1 utilizing:1 matter:1 determined:4 yang:1 supposed:3 amplitude:6 were:2 providing:1 powers:2 dxu:1 lowest:1 motivation:3 entail:2 close:1 look:1 unchanged:3 turned:1 spectrum:1 departure:2 conditions:1 say:2 variable:1 manner:2 disturbing:1 need:1 seen:4 subjects:1 obviously:2 seek:2 any:17 viewed:4 relatively:1 gives:1 subsystems:3 generic:1 realm:1 depending:3 check:1 latter:3 nonseparable:1 zibin:1 note:1 instance:6 potential:17 take:1 finding:1 perturbation:1 coincide:1 paraphrase:1 m2:1 8m3:2 spectral:2 begin:1 exactly:1 unless:5 electric:2 anandan:2 though:3 attractiveness:1 underpinnings:1 object:3 xψ:1 falls:1 most:5 madelung:3 encodes:1 rescaled:1 remarks:1 diametrically:1 suﬃcient:1 probabilistic:2 class:3 manifested:1 interacting:1 soliton:6 observation:2 nonlinearity:4 considered:5 satisﬁed:2 adopt:2 possesses:1 points:4 rev:4 principle:2 exp:3 mechanical:8 boils:1 pretty:1 vries:3 satisﬁes:3 fact:14 quantity:5 decidedly:1 called:1 fieldtheoretical:1 drastically:1 particularly:1 phenomenon:1 show:3 supported:1 discovered:1 purely:2 stems:3 spaces:1 gauge:1 solutions:42 spurious:1 subtle:2 orski:1 d2:1 mycielski:5 impact:1 my:1 finally:1 based:2 just:4 parameters:2 challenge:1 situations:4 x0:5 enough:1 universal:1 should:11 impenetrable:1 only:18 explicitly:1 corresponds:1 ambiguity:3 postulated:3 employed:1 local:1 over:3 hope:3 carolina:1 continuity:10 do:6 his:2 dk:1 quantph:1 means:5 dependent:2 de:3 expectation:4 ut:1 truly:1 barrier:3 communication:1 cannot:9 ϕi:6 legitimate:2 words:1 probably:2 report:1 dt:5 du:1 dr:1 boundary:6 ansatz:1 normalizable:7 runs:1 resolve:1 bar:1 die:1 course:1 encounters:1 arxiv:1 suggested:2 yield:2 method:3 hydrodynamic:2 t00:2 analytical:1 through:3 fortunately:1 describes:2 require:2 knowing:1 requirement:1 set:2 decides:1 exists:1 phenomenologically:1 physically:24 unpublished:1 packet:8 ωt:6 plausible:2 argued:2 see:8 merits:1 result:3 eﬀectively:2 recently:2 best:1 hilbert:1 appear:4 phases:1 invoked:1 capacity:1 tensor:3 doebner:3 diﬀraction:1 ways:3 apparently:1 review:1 currently:1 functionals:1 naturwissenschaften:1 favor:2 state:6 smallest:1 identification:1 simplest:2 invariant:6 neither:2 approach:15 x20:1 tantamount:1 preserve:3 eﬀect:2 ar2:1 inﬁnite:5 terms:5 extend:2 nature:6 importance:1 component:3 attention:1 weak:4 however:18 interfere:1 implementing:1 vanishing:3 correspondence:1 longitudinal:1 picking:1 come:2 overestimated:1 inﬁnity:3 faced:2 observable:2 cos:2 last:4 goldin:3 always:4 2k:1 freely:1 region:3 conclusions:1 equal:7 foreign:1 anomalous:2 ln:5 hψ:1 entertain:2 present:2 dissipative:1 contribution:2 argue:2 com:1 regarded:1 grounds:4 conﬁguration:4 mechanics:15 relevant:5 point:4 wall:8 seems:9 enforced:1 insist:1 semiclassical:2 alone:1 maintained:2 simply:2 coordinates:1 applicability:1 respect:2 lmod:1 considering:1 ensures:3 described:2 generality:1 basis:1 addition:1 observing:1 oﬀers:1 three:12 been:8 alters:1 much:1 treat:1 interest:1 basic:1 expected:2 ph:4 linearizable:3 pol:3 paraphrasing:1 life:1 describe:3 roy:1 both:7 quantities:4 wheeler:2 levels:1 argument:1 2in:1 coherent:9 observe:1 lives:1 tνµ:2 demand:1 c2:2 despite:3 altered:1 spirit:1 those:5 applied:2 k2:1 exception:2 novel:2 processes:1 unlike:4 single:1 value:5 will:13 cast:1 while:2 p2:1 leaves:1 applies:1 situation:2 nonstationary:2 property:4 elaborate:1 procedure:1 nonrelativistic:2 real:7 deals:1 hoping:1 coupled:1 phenomenological:1 vanishes:6 secondary:1 thus:4 non:3 oﬀ:1 characterize:1 reads:1 obstacle:1 owing:2 adjointness:1 pronounced:1 vanish:6 seem:1 ﬁxes:1 different:1 grant:2 perhaps:5 suggest:1 make:3 formulations:7 lett:3 same:13 clearly:1 parts:3 quant:4 arguments:2 widely:1 largest:1 modification:15 φi:1 dimensionless:7 regime:1 conflict:1 berry:1 status:1 independent:1 extended:2 columbia:1 hopes:1 cubic:1 i1:2 i2:3 hand:3 usually:3 compared:1 uses:2 purpose:1 potentials:3 4d2:1 invariance:4 totally:1 normalization:5 safe:1 supports:2 schr:39 framework:5 nevertheless:1 expression:7 adheres:1 well:7 analysis:6 justiﬁed:2 bohm:3 without:4 solve:2 consistency:3 position:4 model:3 otherwise:1 dimension:13 comment:3 stringent:1 cosh2:2 proposed:5 less:2 being:7 formula:2 guided:1 newton:1 obtain:2 rest:1 detail:2 atomic:1 aspect:1 world:2 followed:1 alternative:4 arctan:1 speed:3 yet:7 captured:2 previous:2 adding:1 accepted:1 soluble:1 candidate:1 density:8 absorption:1 escaped:1 conclude:1 2r2:3 except:1 simple:4 valid:1 attractive:2 easy:2 theorem:4 relevance:1 role:1 tell:2 solvable:1 transformation:1 momentum:4 identical:1 exotic:1 psi:1 aspects:1 amended:1 depends:1 represents:3 read:1 operators:1 iγ:2 possible:4 spanned:1 harmonic:2 possibly:1 destroy:1 disadvantageous:1 unique:7 moreover:6 formal:1 dimensional:16 modifications:1 necessary:3 like:4 particle:1 identifying:1 follows:2 collective:1 unphysical:1 δr:2 δs:2 riddle:1 amod:1 discarded:1 δl:3 imposes:1 korteweg:3 either:3 modiﬁed:9 arbitrary:5 evolutions:1 gm2:1 stationary:13 reduced:1 mathematical:2 right:1 classical:14 understand:1 some:19 back:1 self:2 certain:1 understood:1 choosing:3 asserted:1 curious:1 kdv:4 soc:1 reasons:1 nonzero:2 possibilities:1 uniqueness:3 describing:1 dimensions:10 lead:2 electromagnetic:8 unavoidable:2 integration:1 comments:2 whole:1 staruszkiewicz:50 does:19 t0:2 assuming:4 yields:1 moderate:4 proc:1 demonstrated:3 refer:1 inserting:1 reserving:1 particular:6 run:1 obey:1 power:1 problems:2 equivalent:1 notable:3 expansion:2 hsm:2 restrictive:2 although:4 2m:13 imaginary:5 properties:5 takes:2 gained:1 comparison:2 about:2 aﬀect:3 usa:1 extension:4 constraint:5 freedom:1 mediate:1 discussed:15 dependence:2 o:3 sake:1 involving:1 ensure:2 stand:2 shared:3 mean:1 consequently:2 considerations:1 integrable:1 own:3 strangeness:1 accompanied:2 bu2:2 noting:2 into:5 within:5 integral:5 functional:6 nsf:1 due:8 down:1 phase:33 because:5 references:2 laplacian:1 determine:1 diﬃcult:1 operator:1 proportional:2 soon:1 relativistic:3 astronomy:1 additional:3 assumed:2 support:1 there:7 question:19 transform:1 fast:1 u2:2 conservation:5 way:12 forward:1 conceivable:2 was:10 assumes:2 opposed:2 function:15 speculate:1 complete:2 form:14 hr:5 phenomena:9 sound:1 identiﬁcation:1 but:15 idea:2 hi:6 delta:1 convergence:1 encoded:1 optical:1 promote:1 irreversible:1 proposal:4 partially:2 absent:1 made:1 infinity:3 consequences:1 consist:1 instructive:1 whether:1 characteristic:3 gravitational:1 variations:1 maximum:1 us:14 theoretical:3 below:1 decays:1 limit:15 demonstrate:2 problem:12 similar:3 clear:3 expect:2 detailed:1 changes:1 sometimes:2 constant:18 reconcile:1 up:1 czachor:6 abstract:1 contribute:3 am:2 meaningless:1 proven:1 general:7 conserved:1 exist:4 rule:2 formulation:18 elusive:3 πx0:1 ﬁxed:2 ﬁnite:9 physical:12 again:1 functions:5 avoided:1 dx:1 no:7 allow:1 when:6 deﬁned:7 quantization:2 coeﬃcient:1 acknowledgments:1 b14:3 other:29 marks:1 spatial:3 department:1 deﬁnes:1 really:4 belong:1 conclusion:1 apparent:1 intend:1 energetic:2 xr2:1 models:1 surprise:1 preceding:1 become:1 convincing:1 variation:1 yahoo:1 evolves:1 meaning:1 important:5 allowing:1 tackle:1 ballentine:1 birula:5 gets:1 structure:2 ago:1 rejects:1 kx:1 implies:8 coupling:7 assume:3 physics:2 packets:13 together:4 having:2 implied:1 incomplete:1 time:17 far:2 observables:2 decoherence:2 once:3 requires:3 original:9 virtue:2

quant-ph9912007.txt \|@word concept:2 sci:1 similarity:1 fox:2 brownian:6 results:4 illustrated:1 roy:1 go:1 follow:1 contributions:1 extra:1 depend:1 clarification:1 deterministic:2 nonlocal:2 presents:1 finally:1 investigation:1 those:1 th:1 stochastic:13 analogous:1 tc:2 ta:4 case:2 straightforward:1 zhang:2 differently:1 wave:10 difference:1 fractal:1 leads:4 presented:1 developing:1 solution:3 occurs:1 large:2 discrete:3 unrelated:1 small:2 inertial:3 intermittency:8 percival:1 smaller:2 force:7 sign:1 approximation:6 zero:2 displays:1 horv:1 further:2 bacterial:1 even:2 what:1 nonlinear:3 section:6 celebrated:1 version:1 establishes:1 fractional:1 new:2 order:5 ever:1 acknowledgments:1 movement:1 pioneering:1 deemed:1 full:1 realizations:1 here:2 tnm:2 free:3 dissipated:2 equations:3 appears:1 obtained:14 instituto:2 arrive:1 colored:2 root:1 study:2 larger:2 allows:4 p2:2 studies:1 pearle:4 although:2 scales:6 discontinuous:1 replace:1 scaled:1 wataghin:1 planck:2 unit:2 use:3 superpositions:1 would:1 chooses:1 next:2 comparing:1 squires:1 therefore:1 usp:1 gauthier:1 theoretical:1 more:2 introducing:2 started:2 becomes:1 company:1 line:3 odinger:11 tested:1 berlin:1 jmn:11 particular:2 known:1 cases:1 iii:3 account:2 ma:2 evolution:11 salvador:1 originally:1 des:1 modified:6 london:1 values:3 shlesinger:6 following:4 modifies:1 dec:1 spontaneous:3 example:1 initial:2 give:2 process:2 introduces:1 sample:3 indicates:2 council:1 allowed:1 simulation:1 reynolds:4 occur:1 verlag:1 fpe:4 csl:23 end:1 describes:2 di:1 ghirardi:3 feature:1 delay:1 df:2 axis:1 parameter:2 dominance:1 eatoires:1 description:1 undergoing:1 may:4 after:1 derived:2 different:3 olkiewicz:1 fb:1 coming:3 horizontal:1 choice:1 constants:1 gaussian:1 stress:1 short:1 attempt:2 dynamical:1 ss:1 lines:3 correspond:2 so:5 correlation:3 equation:46 interpretation:6 help:1 tales:1 developed:2 over:2 move:1 choose:1 wiener:1 paper:3 through:2 statistical:1 satisfies:4 cole:2 its:3 jnm:1 before:2 ld:2 osi:1 decay:1 chosen:2 interesting:2 lateral:1 affine:1 gleb:1 exhibits:1 actually:1 window:1 microscopic:9 systems:3 stephen:1 weber:2 freeman:1 non:3 return:1 views:1 integral:1 amenable:1 regarding:1 introduce:4 scaling:2 framework:1 tails:1 cep:2 now:3 yu:1 developments:1 above:5 easily:2 term:13 finite:1 characterizes:1 kpz:7 hamiltonian:1 k41:1 sufficiently:1 magnitude:1 2a:1 2m:3 2n:2 ifi:1 mean:7 homogeneous:1 domain:1 differential:3 energy:13 displacement:5 related:1 t3:2 frequency:1 ey:1 connect:1 measurement:1 quantum:6 our:6 beyond:2 eq:13 thick:1 out:1 dominates:1 matrix:2 space:4 gradient:1 jump:1 since:2 rev:16 research:1 re:3 equate:1 issue:1 correct:1 math:1 shows:1 klafter:1 linear:3 dictionary:2 localization:6 ısica:3 departamento:2 standard:1 counterparts:1 dynamics:1 put:2 estimate:1 bouchaud:1 starts:1 could:1 transition:1 ath:1 degrees:1 turn:2 length:3 corrections:6 frequent:1 first:3 already:1 features:1 probability:3 striking:1 variables:1 number:5 vicsek:1 done:2 another:1 ring:1 open:1 illustrate:1 given:7 derives:1 publication:1 introduction:2 eqs:1 system:11 approximately:1 master:1 calculations:1 white:4 wilkinson:1 gives:4 exploring:1 collapse:12 continuous:2 took:1 authors:2 injected:8 believe:1 than:2 diffusion:16 wide:1 kind:1 accordance:1 transferred:1 contrary:1 were:2 visited:1 stricter:1 enables:1 minus:1 function:12 fig:4 san:1 curves:1 apparently:1 any:1 paths:3 studying:2 latter:2 responsible:2 contact:1 potential:3 square:5 analogy:9 added:1 though:1 viscosity:1 simplify:1 involving:1 plan:1 phase:1 observation:1 considered:1 neighboring:1 average:1 coincides:2 physica:1 typeset:1 procaccia:1 points:1 exp:9 velocity:7 physics:2 fact:1 quantity:1 larkin:1 phenomenon:2 show:3 escobar:3 random:9 cnpq:1 x2:6 relation:3 solutions:1 find:2 parameters:5 state:2 should:1 only:2 acknowledge:1 hopf:2 do:4 his:2 beable:5 notation:1 distance:1 dependent:1 familiar:1 de:7 fluid:3 da:1 dx:1 dt:3 ds:3 areas:1 processes:2 continuum:1 arxiv:1 stuff:1 characteristic:1 proponents:1 distant:1 forster:1 nδ:1 view:2 coefficient:1 vink:3 set:1 ser:1 kolmogorov:3 turbulent:1 bounds:1 see:2 result:3 enhanced:9 recently:2 forthcoming:1 brazil:2 fails:1 still:1 hentschel:1 nuclear:1 opening:1 sites:4 written:2 between:12 villiers:1 approach:1 law:1 side:1 notice:1 terms:5 nature:3 restricting:1 however:3 ji:1 analyzed:1 article:2 halpin:1 come:1 distribution:1 both:1 interpretations:1 last:1 region:1 density:1 equal:2 ln:1 connection:2 purely:1 context:1 expression:1 experimental:2 cm:2 point:3 corresponds:7 walk:2 exploit:1 healy:1 moreover:1 throughout:1 described:2 second:3 basis:1 addition:1 west:1 due:2 been:3 quickly:1 much:3 treat:2 interest:1 basic:1 expected:2 transformed:1 ph:2 hardly:1 pm:7 contribute:1 corresponding:2 observable:2 quantities:2 great:1 gen:1 gap:1 1g:1 2im:1 external:1 fokker:2 present:1 applied:1 pacs:1 indefinitely:1 expanded:1 value:2 heidelberg:1 will:1 euclidean:1 behavior:2 characterizing:1 unitary:1 surface:1 iv:2 ii:1 itself:2 fermion:1 santos:2 governing:1 develop:1 parisi:2 make:1 lett:4 same:3 undisturbed:2 paulo:4 kardar:1 quant:2 arguments:1 2νt:1 mixtures:1 figures:1 several:1 used:3 estadual:1 numerical:2 effect:2 campinas:2 hand:1 phy:1 oversimplification:1 infinite:1 collar:1 mech:1 schr:11 proceed:1 scenario:1 fully:1 macro:5 well:1 analysis:3 bohm:2 burgers:10 without:1 solve:1 position:6 model:23 simplified:1 arising:1 dimension:5 usual:2 distances:1 proposed:1 λt:1 being:1 mandelbrot:3 obtain:4 assigned:1 underlying:1 identify:2 atomic:2 using:4 alternative:1 macroscopic:4 eorie:1 stratonovich:1 previous:2 adding:1 zoller:2 conclusions:2 similarities:1 bell:5 character:1 avignone:1 source:2 disparity:1 other:1 extends:1 treatment:1 transformation:2 momentum:5 real:1 tests:1 iν:1 represents:1 devised:1 showing:1 turbulence:9 fractals:1 replacing:1 particle:6 vis:2 polymers:1 identifying:1 δn:3 always:1 multiplicative:3 become:1 essential:1 acad:1 because:2 classical:1 polar:1 garbaczewski:2 some:1 springer:1 growth:4 shortcoming:1 choosing:1 extended:1 neglecting:1 transport:2 provided:2 scale:12 dimensions:1 lead:1 micro:3 shall:1 langevin:1 integration:1 per:1 causal:1 does:3 lattice:2 provides:2 assuming:1 proc:1 tmn:8 noise:12 rep:2 seconds:2 jumps:2 step:1 revtex:1 br:2 found:2 imaginary:3 identifies:1 bz:1 takes:1 comparison:2 om:3 central:1 dzg:1 getting:1 instantaneously:1 freedom:2 discussed:1 dependence:2 o:4 tracer:3 range:1 introduced:3 soc:1 unnoticed:1 follows:2 into:5 within:2 numerically:1 nonsense:1 right:1 references:1 kondrat:1 determine:1 ezard:2 france:1 physical:1 ovchinnikov:1 few:1 support:1 there:8 approximate:1 fast:1 noticed:1 conservation:2 low:1 way:3 brazilian:1 forward:1 was:5 naturally:1 rimini:3 medium:1 complete:1 form:4 memory:1 but:2 hoped:1 gain:1 convergence:1 injection:1 manifests:1 collapses:1 directed:1 made:1 temp:1 pn:7 up:1 us:7 crystal:1 below:1 limit:1 problem:2 hydro:1 similar:4 called:2 stirring:1 gisin:1 mechanics:2 constant:1 reconcile:1 defined:1 abstract:1 describe:2 ao:4 2mν:1 single:2 exist:1 flight:3 universidade:2 regime:3 incorrect:1 grw:5 transitions:2 completeness:1 no:1 dashed:3 edwards:1 when:5 vanishes:1 field:4 valid:1 alber:1 test:1 nice:1 picture:2 francisco:1 models:2 unicamp:1 problems:1 visits:1 chance:1 important:2 variable:1 risken:1 independently:2 anomalous:1 algorithm:1 assume:1 evy:5 rs:2 having:1 mass:2 nelson:5 time:24 walker:1 richardson:5 original:1

quant-ph9912008.txt \|@word ibid:2 represent:1 gs:1 consider:7 illustrates:1 induces:1 magnetic:5 eckert:1 results:1 existing:1 leads:2 eds:1 computation:3 consists:2 sci:1 c1:2 causes:2 depend:1 iii:1 shack:1 charge:1 kζ:1 under:2 analogous:1 alternating:1 case:2 supported:1 advantage:1 very:9 frequencies:2 rise:1 springer:2 wave:10 electron:17 drexel:1 experimentally:2 matrices:1 four:1 hamiltonian:17 cause:1 circuit:3 vector:3 phase:6 science:2 small:3 configurations:1 grateful:1 deutsch:5 second:2 eiϕ:9 implemented:3 scientific:2 even:1 will:5 what:1 trapping:1 apparatus:1 uniform:1 current:3 axial:20 experiment:1 above:4 berman:1 new:2 net:1 consisting:1 contrast:1 edited:4 degree:8 respectively:2 loose:1 lange:1 here:6 ranges:1 iσy:1 cylindrical:2 possibility:2 represented:1 along:2 table:1 appears:1 obtained:3 instituto:1 shift:2 prior:2 procedure:1 usually:2 resonance:2 implement:4 suitable:1 changes:1 king:3 iy:2 via:1 useful:1 marked:1 turchette:2 achievable:3 apply:1 ipx:2 unit:2 standing:8 use:3 superpositions:1 would:3 positive:1 fortson:1 next:1 therefore:2 m2:1 magnetron:3 until:1 today:2 more:4 separated:1 introducing:1 kˆ:2 initial:4 operators:3 stable:1 problem:1 particular:1 foundations:1 given:2 antinode:3 high:1 none:1 quantized:1 permits:1 recall:1 work:2 cat:2 kinoshita:1 following:2 strategies:1 dec:1 example:1 decoupled:1 numbers:2 control:3 ions:2 give:2 process:2 arise:1 neglected:2 haroche:1 respective:3 states:13 performed:4 sense:1 spanning:1 times:2 tan:1 axis:2 motion:11 needs:2 rather:1 technology:1 get:4 write:1 how:2 fourth:2 opt:1 gate:10 flow:1 sin:7 classify:1 oscillatory:1 proc:2 blocks:1 description:1 information:18 oscillators:1 ζk:2 celoria:1 stefano:1 hence:1 plane:3 coming:1 concerns:1 natural:2 martins:1 register:4 murst:1 ωz2:1 ghz:1 circularly:1 so:1 fundamental:4 operate:1 order:3 terms:3 typical:1 operations:10 indeed:1 pointed:1 meter:1 course:1 thermal:1 paper:1 through:4 motions:2 affect:1 fidelity:1 still:1 its:2 before:1 superior:1 remark:1 decay:1 chosen:1 gabrielse:4 writing:1 wineland:3 absence:2 degrees:4 systems:7 rabi:1 into:2 correspondence:1 eventually:1 them:2 good:1 propose:1 introduce:2 emphasised:1 framework:1 effects:1 they:1 instead:2 now:2 easily:2 february:1 lies:1 characterizes:1 classified:1 radians:1 2z:1 possibilities:2 ηt:4 trap:5 truth:1 bonifacio:1 2m:5 universit:2 macchiavello:1 side:1 schemes:1 directly:1 series:2 energy:1 ea:1 used:2 static:1 measurement:5 quantum:42 our:2 operation:2 ev:1 eq:6 out:2 divincenzo:2 shown:5 jackson:1 opened:1 space:1 furthermore:1 interference:1 research:1 contained:1 eprint:2 print:1 induced:1 ref:3 ladder:1 wiley:1 theory:1 interactions:1 mechanisms:1 fisica:3 free:1 completely:1 york:1 md2:1 hand:2 jozsa:2 milburn:2 union:1 interaction:6 could:7 similarly:1 positioning:1 feasible:1 counterpart:2 turn:1 int:2 place:1 δij:1 corrections:1 retain:1 programme:1 neglect:1 first:2 already:1 manuscript:1 encoding:1 omitted:1 variables:1 waves:1 flipping:1 done:1 caves:1 quadrupole:1 open:2 angular:2 hood:1 differ:1 reference:1 hyperbolic:1 introduction:1 leading:2 dipartimento:2 amsterdam:1 system:19 construct:1 unruh:1 their:2 cooling:1 dichotomic:1 realization:3 bits:2 2ωc:1 store:2 gives:4 preserved:1 imperfect:1 trapped:12 observable:1 transverse:3 part:1 simulate:2 manipulation:1 x2:1 number:1 eliminated:2 traps:2 iωt:12 polarized:1 target:3 showed:1 cimento:1 transferred:2 tecnico:1 final:1 preparation:1 amplitude:2 were:3 enables:1 ana:1 electrodynamics:3 correction:2 modern:1 cyclotron:11 say:1 conjugate:1 any:6 generic:1 built:1 depending:4 efficient:2 latter:2 indexes:1 k2:4 potential:3 comment:1 hs:1 destroy:1 switching:1 sure:1 electric:2 investigations:1 who:1 reach:1 centro:1 aext:5 most:2 exploited:1 claims:1 pair:1 measured:2 ekert:3 interacting:2 considered:1 milano:2 physica:1 traditional:1 feynman:3 electrons:5 error:1 exp:1 kz:1 charged:1 penning:4 logical:1 fact:2 quantity:2 structureless:1 show:4 authors:1 anyway:1 rotating:4 registers:1 relation:1 lloyd:2 networks:1 fifth:1 ground:1 feng:1 slow:1 dehmelt:2 implementation:3 situations:1 state:11 negligible:1 should:3 only:4 wood:1 candidates:1 factor:1 constant:2 hamiltonians:1 interested:1 equilibrium:1 do:2 over:2 means:2 familiar:1 zurek:1 de:3 infm:3 joint:1 ones:1 international:1 becomes:1 evolution:2 precession:2 settings:1 fields:3 arxiv:1 network:1 investigate:1 experiments:1 london:1 dyck:4 set:1 electrodes:2 frame:3 hζ:1 operates:1 see:1 computer:5 radius:1 result:2 successive:1 lisboa:1 close:1 2πn:1 best:1 project:1 suffer:1 commutation:1 subsequent:1 mabuchi:1 motional:2 eigenstates:1 written:1 between:7 reading:1 brune:1 barenco:2 recently:2 controllable:1 qubits:8 however:4 scalability:1 selectively:1 jr:4 distinguish:1 news:1 configuration:1 ωc:8 both:1 cos:8 last:1 zoller:2 brown:1 uncertainty:1 against:1 flipped:2 σz:5 σy:2 σx:7 raimond:1 logic:21 qubit:13 expression:1 schroedinger:1 experimental:2 unitarily:1 relevant:3 cn:6 simple:5 ca:1 harmonic:2 simply:1 moreover:1 san:1 considering:1 pp:1 tuning:1 cavities:1 basis:2 pz:3 px:1 py:3 three:1 been:4 ai:1 basic:2 itano:3 ph:4 mωc:2 choose:2 direction:3 controlled:8 received:1 coherence:1 search:2 external:7 plasmas:1 c0:2 spin:18 obtainable:1 present:2 applied:1 novel:1 laser:1 kimble:1 value:1 aim:1 while:2 shall:3 promising:1 aid:1 di:4 hωm:1 khz:1 landauer:3 ive:1 unitary:1 portugal:1 coupled:1 almost:1 characteristics:1 thus:2 non:1 iv:1 ii:1 claimed:1 ie:1 monroe:3 different:1 formalism:1 italy:2 perform:2 radiation:3 lett:9 same:1 checking:1 another:1 quant:4 pauli:1 regime:1 consequence:1 european:1 literature:1 unconventional:1 singapore:3 nondissipative:1 upon:3 effect:2 possible:4 v0:3 action:4 moving:1 purpose:1 unpublished:1 entanglement:1 4d2:1 contribution:1 relies:1 lower:1 off:1 modes:2 charges:1 well:8 academic:1 kells:1 allow:1 bottle:1 position:2 model:4 dimension:1 comprise:1 usual:1 gates:6 routinely:1 appropriately:2 being:1 accurate:1 rotated:1 obtain:1 stored:4 atomic:1 world:3 yet:3 previous:2 enters:1 candidate:2 conclusions:1 iϕ:10 advancement:1 boston:1 internal:3 questioned:1 easy:1 iπ:1 mod:2 transformation:4 momentum:2 real:4 iθ:2 around:1 represents:1 read:1 devised:1 term:3 possibly:1 entangled:2 press:2 using:3 bit:6 advanced:1 apart:1 loss:1 theor:1 necessary:1 particle:1 follows:2 reduces:2 performing:1 camerino:2 cochrane:1 mhz:1 either:1 always:1 nonintegrability:1 reduced:3 cooled:2 mathematical:1 satisfactory:1 because:5 qed:2 classical:7 discrete:1 understood:1 choosing:1 respect:2 oscillations:1 myatt:1 provided:1 tmr:1 scale:1 cnr:1 cavity:6 eiθ:1 measurements:5 microwave:1 defined:1 critical:1 bessel:1 minimal:1 refer:1 nmr:1 obey:1 equivalent:1 oscillating:2 step:2 although:1 hadamard:1 cory:1 comparison:1 about:2 actual:1 extension:2 freedom:9 o:1 addition:2 plus:1 stand:1 act:1 introduced:2 vi:1 soc:1 rev:20 previously:1 image:1 within:2 obtaining:1 due:3 down:2 device:1 appropriate:2 right:1 elementary:3 proportional:2 domokos:1 letts:1 statistics:1 van:4 transfer:3 flying:1 low:1 way:7 ed:1 was:3 function:1 complete:2 form:2 positioned:3 but:4 hu:1 hk:1 matematica:1 munro:1 technologies:1 level:1 partially:1 paolo:1 ωz:9 applying:2 ωs:11 up:1 us:2 theoretical:2 frequency:9 ωm:2 fluctuations:1 embed:1 mechanics:2 ac:8 cirac:2 associated:1 devise:1 detectors:1 universal:2 describe:1 am:3 deep:1 single:4 mωz:2 az:12 approximated:1 physical:4 again:2 no:1 codex:1 extract:1 there:2 nc:2 when:5 meekhof:2 field:7 other:7 diego:1 spatial:2 mathematics:1 nonexistence:1 conclusion:1 node:3 symposium:1 superposition:2 models:2 center:1 problems:1 precision:1 generated:1 claude:1 tombesi:4 structure:1 impurity:1 building:1 implies:1 coupling:3 practically:3 assume:2 physics:1 factors:1 mancini:3 impossibility:1 leibfried:2 mass:1 time:11 observables:1 decoherence:4 laws:1 nuovo:1 once:1

quant-ph9912009.txt \|@word concept:1 customary:1 consider:7 priori:1 squared:3 lack:1 results:3 four:1 entropy:10 reasoning:1 whose:1 careful:1 leung:1 alamos:5 concerned:1 deterministic:1 send:3 environment:1 according:1 th:5 under:2 kwong:1 analogous:2 presentation:1 resources:4 conjecture:10 saves:1 appointment:2 evolves:2 far:3 seemingly:1 choice:1 corollary:2 novel:2 hewlett:1 emphasized:1 difference:5 condition:2 leads:2 induced:1 presented:1 transmission:3 turns:1 presumably:1 michael:2 fewer:1 large:6 indices:1 optics:1 noted:1 degeneracy:2 measuring:1 dilute:1 direct:2 suffices:2 second:13 cost:37 further:4 even:5 index:4 what:6 xor:1 sub:1 rate:1 qip:2 d2:2 section:1 shares:2 current:2 public:1 suspect:1 above:7 new:3 avenues:1 increasing:1 consisting:1 contrast:2 satisfy:1 full:3 degree:1 respectively:2 teleportation:29 here:11 refinement:1 objects:4 groups:1 concluding:1 consideration:2 equations:1 knowledge:4 sending:5 remark:10 barnum:1 remarks:1 technical:1 akr:1 study:10 studied:2 allows:1 los:5 prior:7 amount:17 schumacher:6 bob:75 studies:1 segments:1 involves:1 boykin:2 via:3 useful:2 divide:3 forbid:1 private:5 outcomes:1 apply:4 total:1 neumann:2 use:2 asymptotic:5 would:14 prove:2 always:2 contains:1 a51:1 roychowdhury:2 partite:3 noting:1 call:2 therefore:7 type:1 until:1 more:9 knows:5 outputs:1 naive:1 cooperate:1 appendix:1 normalized:2 particular:3 known:14 cases:2 iii:1 high:2 science:1 work:1 nonmaximally:1 measures:5 values:3 sent:1 following:10 strategies:1 dec:2 example:10 proof:13 control:1 claim:4 give:2 process:11 expanding:1 bennett:7 share:15 pieces:1 states:20 numbers:3 scheduling:2 phrase:2 occur:1 information:25 goal:7 rather:4 discussion:3 get:1 hoi:1 strikingly:1 very:3 pure:19 answer:2 optimal:2 ensemble:12 brassard:2 circular:1 inputs:2 product:2 de:2 huge:2 may:3 ancilla:14 coined:1 earlier:1 applications:1 gottesman:5 date:2 data:3 types:2 short:1 natural:2 third:1 spiller:3 acknowledged:1 compressing:3 buhrman:1 complexity:11 cannot:2 negligible:1 allow:4 subsequently:2 divided:1 typical:5 operations:1 exotic:1 six:1 help:12 indeed:4 pointed:4 move:1 vary:1 years:1 paper:6 including:5 thesis:1 during:2 fidelity:2 still:1 avenue:1 its:6 derive:2 group:4 thank:1 maps:1 chosen:2 lo:5 actually:1 better:3 offers:1 differently:1 latitude:1 main:5 might:2 focussed:1 them:4 skipped:1 combination:1 powerful:1 introduce:1 primary:1 couples:2 a0i:3 they:6 instead:2 now:17 february:1 gets:1 name:1 2s:1 fully:2 university:1 a53:1 divides:1 orthonormal:1 transmitted:2 each:28 2n:2 higher:2 side:2 constraints:3 just:1 directly:2 weight:4 2e2:2 hard:1 reduce:6 idea:4 related:3 obtains:2 combining:1 quantum:53 laboratory:1 eq:6 special:4 out:5 divincenzo:2 shown:6 acknowledgment:1 space:8 restricted:1 furthermore:3 since:7 crucial:1 holevo:2 research:1 daniel:2 performs:2 denoted:1 receiving:1 issue:2 common:1 proviso:2 log2:21 theory:2 written:3 seventh:1 attempt:1 free:1 standard:6 small:1 reason:2 york:1 put:2 jozsa:3 e2:6 advance:5 pairs:2 prepare:13 could:1 similarly:1 consequence:1 onto:1 first:20 separable:1 initial:6 saving:3 manuscript:3 blown:1 coding:5 number:9 infinite:2 smaller:1 done:8 another:4 impossible:1 a3i:4 precisely:1 size:2 given:9 necessarily:1 interesting:2 needed:10 introduction:1 unknown:9 system:6 remotely:1 their:6 too:1 show:1 scheme:7 bits:36 unpublished:2 gives:1 exactly:2 manipulation:2 x2:4 x3:1 x1:4 than:7 coefficients:7 distance:1 bei:1 ben:1 target:1 dam:1 wiesner:1 double:4 require:2 zero:2 limiting:2 preparation:35 individual:2 were:2 outcome:12 decompose:1 seminal:1 motivation:8 sam:1 well:2 modern:1 beforehand:1 argument:1 generalization:5 already:2 say:7 archive:5 need:1 concentration:3 constrained:2 any:3 decomposing:1 subsystems:1 lies:1 depending:1 studying:1 able:1 note:1 instance:4 k1:1 subjects:1 take:5 analogy:1 transmit:5 so:5 unconstrained:1 wonder:2 modulus:1 channel:8 fundamental:5 opposite:1 who:1 systems:1 singlet:1 satisfying:1 encodes:3 pair:6 segment:4 takes:1 surprising:1 clear:1 partition:3 ebits:5 order:1 kr:5 principle:1 usual:6 sum:3 fact:4 laws:6 precise:2 saying:2 probl:1 particularly:1 exclusive:1 agreed:3 random:3 cheap:1 rotating:1 inconsistent:1 subtle:1 trivial:2 find:3 completion:3 tapp:6 satisfies:2 causality:2 simulating:1 hope:1 distributed:3 state:54 purification:1 being:1 only:22 developed:1 employed:1 local:6 over:1 achieve:2 do:2 his:2 subspaces:1 quantph:2 di:13 convert:2 simplest:1 overall:1 truly:1 unimportant:1 ones:1 words:1 shared:6 ali:2 applying:1 trade:1 packard:1 processes:1 resource:3 arxiv:1 summary:2 fuchs:1 eiθi:1 she:16 fixed:3 ignored:1 moduli:4 set:6 exists:2 violated:2 j1:4 j2:4 ancillas:1 namely:2 computer:1 result:12 enhanced:1 discussions:5 nonlocality:1 subject:7 closer:1 invoked:1 subsequent:2 label:2 halves:1 behind:2 various:4 between:11 probably:1 2n1:5 notice:3 recently:3 sections:1 qubits:5 however:2 gratefully:1 vanishing:4 no:4 key:3 distribution:5 motivations:1 both:4 dates:1 braunstein:3 improved:1 desired:3 many:1 equal:4 σz:1 context:3 im:13 qubit:15 expense:2 expression:1 workers:1 ji:4 pre:3 ci:13 relevant:1 co:1 cm:2 point:2 simple:6 wootters:2 asymptotically:2 cf:2 community:1 dimensional:5 simply:4 xi:3 moreover:1 expensive:1 considering:1 forms:1 complication:1 perspectives:1 basis:8 addition:1 locally:3 copies:3 been:9 reduction:4 much:4 combined:1 interest:7 ph:5 xn1:3 define:1 arises:1 corresponding:1 sufficient:3 subspace:5 essentially:1 locations:2 observers:1 understand:3 external:1 hughston:1 c2:7 c1:1 maximally:1 those:4 case:13 k2:1 schmidt:2 unlike:3 pacs:1 value:5 will:8 while:3 suppose:13 shall:1 applies:6 situation:2 θi:5 procedure:8 maximal:1 unitary:11 mexico:1 vi:1 von:2 chau:1 thus:5 non:3 iv:1 ii:5 skipping:1 experts:1 dual:1 vanish:1 different:2 recover:2 lemma:6 author:4 perform:2 things:1 a4i:4 aki:1 same:8 tells:1 member:3 randomization:1 parts:3 quant:4 emphasize:1 pauli:1 conversations:1 party:1 several:2 difficult:1 independent:2 used:4 bristol:1 see:4 trivially:1 i1:10 i2:10 hand:7 codes:1 uses:2 entanglement:42 a2i:4 totally:2 implement:1 normalization:1 recent:3 lower:1 task:1 off:1 proceed:1 scenario:1 nevertheless:1 halve:1 floor:1 epr:3 asked:1 without:3 montreal:2 sets:3 laboratories:1 dimension:3 researchers:1 know:2 tim:1 popescu:9 less:2 transmitting:2 when:4 half:2 rotated:1 obtain:4 distant:2 thanks:2 immediately:1 yet:1 projection:1 adding:1 cut:1 preprint:5 application:1 regarded:8 conclude:2 except:1 mathematically:1 signals:8 apr:1 concerns:1 lett:6 easy:1 theorem:19 usage:1 input:3 transformation:12 nielsen:6 big:2 decomposed:4 spanned:4 possibly:3 entangled:15 using:7 bit:10 advanced:1 mod:1 necessary:5 like:9 semi:1 follows:6 interestingly:1 performing:1 alice:87 ignore:2 communications:2 steps:4 either:1 arbitrary:4 output:4 dilution:13 works:7 signal:4 grouping:1 sketch:1 because:2 often:1 classical:96 people:1 sends:4 phenomena:2 somehow:1 examples:5 b2:1 b3:1 2log:1 specific:2 dense:3 dimensions:1 lead:3 investigations:2 manipulations:2 does:1 decomposition:2 manipulate:2 provides:1 minimal:1 illustrate:2 object:2 power:1 problems:2 equivalent:1 processing:18 bi:28 discount:1 step:30 hadamard:2 ntot:3 hilbert:3 after:1 stage:11 about:1 2o:1 constraint:2 theorems:2 o:1 deserves:1 idm:2 wolf:2 concentrations:1 introduced:1 consequently:1 rev:9 communication:85 into:24 within:1 a54:2 phase:1 appropriate:2 right:1 accounts:1 parties:3 operator:1 proportional:1 reducing:1 initially:5 qed:5 van:1 compression:3 her:14 few:2 support:1 there:8 question:3 transform:1 start:1 ψi:3 inner:1 way:4 labelling:1 ψn:1 was:7 a2:1 synthesis:1 function:4 complete:1 form:11 some:21 smolin:1 alain:2 but:7 26th:1 larger:1 helpful:1 technologies:1 trying:4 inverse:1 made:4 compute:1 tems:2 intuitive:1 whether:1 up:2 us:7 theoretical:1 below:2 converted:1 limit:3 problem:5 piece:2 similar:2 called:2 expect:1 mechanics:2 ab:47 ai:20 abstract:1 describe:1 proven:3 general:12 transm:1 single:5 diverse:1 our:9 inf:1 a1i:3 check:1 inc:1 mosca:2 compared:3 locality:1 fixing:1 whereas:2 wavefunction:1 generally:3 ny:1 other:8 role:1 details:1 happens:1 elements:3 denote:1 generates:1 provided:1 nonclassical:1 ultimately:1 prepared:2 a3:1 important:4 allowing:1 vectors:6 prepares:2 ago:1 remote:34 partitioned:2 2d2:1 assume:1 starting:3 proposed:1 required:8 together:3 equivalently:2 cleve:3 n1:8 requires:11 labelled:1

quant-ph9912010.txt \|@word partial:26 consider:9 rev:11 results:15 subscripts:1 four:2 ψ1i:6 scalar:1 ρt2:1 lewenstein:2 follow:2 premises:1 whose:1 dimensionality:1 calculate:2 33a:2 eˆ:13 tr:5 ρs:8 29a:1 thapliyal:1 finally:6 according:14 those:8 th:2 under:11 33b:1 norm:2 ta:13 random:1 g2:4 g1:4 ρta:93 far:2 rise:1 none:1 corollary:13 should:3 difference:2 matrices:5 condition:16 treating:1 dim:3 34a:3 34b:3 presented:1 tra:1 turns:1 solution:2 deals:2 transposing:1 small:1 der:1 smaller:8 says:1 direct:2 sign:1 second:7 displays:1 further:1 substitute:1 linear:3 even:1 established:1 what:1 invertible:4 giving:3 trivial:5 section:15 analogously:1 expressed:1 3n:14 subspaces:6 3c:1 3b:1 3a:2 method:2 filled:1 27a:1 27b:1 full:2 degree:22 pseudoinverse:1 respectively:10 equals:1 here:9 ranges:1 desired:1 q11:1 q12:3 equations:9 deduced:1 obtained:4 search:1 arrive:1 institute:1 study:2 vectors:74 allows:5 suggests:1 amount:1 resulting:3 hospitality:1 composed:1 formulated:3 useful:4 transformations:1 family:1 29b:1 explained:2 highly:1 austria:1 analyzing:2 apply:1 total:1 linearly:13 use:23 projector:2 would:6 prove:10 ψr:14 positive:17 contains:8 induction:2 next:3 few:2 ψi:4 m1:17 therefore:10 m3:1 m2:12 taken:2 a58:2 until:8 more:5 linden:1 bennett:2 composite:1 operators:20 appendix:8 particular:6 known:1 cases:6 iii:10 must:4 high:1 keeping:3 science:1 equation:17 work:2 det:9 remain:4 minimum:2 values:1 ρt:1 erb:1 concepts:1 following:15 fulfill:2 dec:1 example:7 proof:21 give:5 allowed:1 states:11 contradicts:2 assumptions:1 numbers:3 sense:1 a1a:2 information:2 needs:1 fonds:1 end:2 quantph:1 particularize:1 divided:4 orthogonal:7 orthogonality:1 recovers:1 write:11 how:4 nontrivial:1 criterion:14 fourth:1 simplifies:1 optimal:1 map:2 product:85 singular:1 may:2 max:1 after:5 different:5 applications:1 physik:2 fi:16 fk:1 parallel:1 ψi0:1 ψi1:1 hannover:3 biorthogonal:1 whenever:3 lemmas:1 deutsche:1 st:1 perhaps:1 so:9 fundamental:1 decreasing:2 definitions:2 order:4 holds:3 subsections:2 developed:2 pointed:1 choose:1 years:1 paper:7 thesis:1 mentioned:1 existence:7 still:2 its:19 roots:24 before:2 derive:4 thank:1 maps:3 chosen:1 interesting:1 erators:1 writing:2 parts:2 systems:8 decreased:1 hidden:1 main:1 outside:1 non:6 greater:1 combination:5 introduce:2 number:12 mention:1 they:4 instead:1 now:12 easily:2 february:1 several:5 stated:1 hereafter:1 a3b:3 always:17 university:1 2x:6 orthonormal:2 sufficiently:6 iff:14 each:5 found:3 universit:2 european:1 mean:1 subsystem:5 ei:16 directly:1 ej:2 doing:1 series:1 reduce:10 idea:3 related:5 measure:1 quantum:6 our:7 eq:29 out:5 large:2 shown:9 divide:3 matrix:4 space:11 quantify:1 furthermore:1 since:29 crucial:1 rz:3 denotes:1 rd:1 acting:12 vector:35 get:1 ref:4 occurs:1 math:2 shows:3 theory:3 differ:1 clarify:1 reason:2 ψ2i:4 besides:1 span:1 phd:1 jozsa:1 definition:3 could:1 impose:2 times:1 thing:2 terhal:4 a223:1 δij:1 first:21 separable:53 xk:7 already:1 third:1 variables:4 powerful:1 flipping:1 rank:28 theoretische:2 infinite:3 a3a:6 multiplying:1 simplified:1 least:1 another:5 a2i:1 q02:4 impossible:1 ring:1 q01:1 illustrate:2 given:20 checked:1 kluwer:1 forschung:1 fmrx:1 introduction:1 eqs:1 system:5 construct:3 needed:1 assumption:2 tell:1 statement:4 wootters:1 really:1 gives:8 fˆi:5 exactly:3 proving:2 part:4 too:1 than:11 coefficients:1 unfortunately:1 fuchs:1 sections:2 zero:2 contrary:1 6th:1 p20:1 7c:1 7b:1 7a:2 py0:1 zyczkowski:1 say:3 close:3 seen:2 recover:4 any:7 generic:10 realm:1 min:4 studying:2 popescu:1 able:3 ψei:3 note:11 instance:1 erator:1 take:6 finding:4 pyx:1 spectral:3 play:1 sure:1 transposes:3 ts:1 opposite:1 reach:3 most:13 pyk:4 germany:1 pair:1 sfb:2 why:1 subtracted:5 dordrecht:1 clear:2 later:4 implications:1 multiqubit:1 kx:2 sum:5 fact:10 wissenschaftlichen:1 shor:3 particularly:1 show:24 emphasize:1 supported:27 spaces:2 solutions:10 decompositions:1 substituting:2 d2:1 find:33 subtracting:10 q1:1 q0:2 q2:7 based:7 criterium:1 situations:2 written:10 separability:41 lemma:53 only:16 going:1 subsection:10 indeed:2 local:2 achieve:1 do:4 mixture:2 above:3 cubic:1 means:6 spurious:2 de:1 q31:2 cannot:2 words:1 despite:1 vein:1 αk:5 regarding:2 determinants:1 transposition:12 arxiv:1 summary:1 fulfilling:3 common:3 qi:2 valid:2 kernel:21 set:11 constructing:1 exists:11 imposing:3 see:3 27c:1 result:7 p22:1 discussions:1 terms:2 acts:1 wonder:1 αp:1 satisfying:2 ei2π:2 inequalities:1 αy:1 positivity:4 αa:2 qubits:2 state:8 between:2 invariant:4 subscript:1 caves:1 conditions:19 counterexample:1 notice:1 recently:1 importance:1 complement:2 p2n:1 transpose:11 inseparable:1 wi:3 however:1 concentrate:1 unnormalized:1 distinguish:1 31b:2 31a:3 cirac:1 a232:1 both:8 braunstein:1 last:5 2n:9 gmbh:1 many:2 taking:1 infinitely:1 equal:9 fulfilled:3 connection:1 exceeds:1 qubit:1 whole:1 otherwise:9 among:2 ci:5 ch:1 bell:1 simple:3 cf:1 dimensional:6 werner:2 simply:4 universitat:1 polynomial:28 respect:6 throughout:3 kernels:1 ct96:1 generality:3 leads:1 basis:16 addition:1 px:4 locally:1 three:5 been:7 reduction:3 treat:2 contained:1 pj:1 ph:5 pi:11 define:7 determinant:2 arises:1 corresponding:4 sufficient:13 formed:1 subspace:4 yk:1 systematic:1 efficients:1 general:6 present:1 case:35 intriguing:1 expanded:1 value:2 will:37 while:3 situation:5 ful:1 property:5 procedure:5 larger:6 vi:8 conjugate:4 thus:21 them:14 iv:3 ii:15 itself:2 properties:12 ia:1 rid:1 vanish:1 containing:2 ing:1 35b:2 35a:2 perform:2 qutrit:1 make:2 belong:4 same:20 complex:10 quant:5 arguments:1 finite:3 higher:3 independent:17 used:2 trivially:3 i1:2 i2:10 upon:1 i4:1 hand:6 pita:1 entanglement:4 changing:1 invariance:1 recent:1 suffices:1 p11:1 expression:1 depending:2 well:2 analysis:2 obviously:3 academic:1 without:4 solve:3 sets:1 very:5 model:1 dimension:12 know:10 just:6 less:2 nd:1 sanpera:4 obtain:15 via:1 thanks:1 immediately:1 facts:1 λi:6 yet:1 previous:11 integer:1 density:26 regarded:2 point:1 confirmed:1 belongs:1 conjugated:3 lett:9 easy:1 theorem:15 det1:5 schack:1 det2:4 remaining:1 real:5 acta:1 mor:3 innsbruck:2 decomposed:1 possible:4 vidal:4 21b:1 entangled:7 21a:1 using:21 unique:2 apart:1 loss:3 necessary:9 28a:2 follows:3 reduces:3 28b:3 separately:1 continue:1 steps:1 either:7 arbitrary:3 decrease:4 28c:2 exceed:3 right:1 methods:2 namely:1 some:9 begin:1 q21:1 q22:5 examples:2 moreover:2 provided:2 tmr:1 dense:1 dimensions:3 does:1 decomposition:7 provides:2 minimal:2 rep:1 equivalent:2 bi:2 illustration:1 constructive:3 step:2 substitution:1 p30:2 p31:1 subtract:17 hilbert:6 proceed:6 zur:1 simplify:2 practical:1 remains:2 range:13 a2:3 ensure:1 done:2 woronowicz:1 mixed:2 projectors:11 automatically:3 op:2 py:1 h2:6 into:4 h1:8 obtaining:2 bound:5 multiply:7 hermitian:2 because:1 determine:5 ppt:2 operator:41 actually:2 utility:1 argumentation:1 rows:4 institut:2 deal:3 ψk:2 assumed:2 there:48 transform:3 start:3 noting:1 low:3 way:13 forward:1 analyze:6 was:5 2ρs:1 medium:1 complete:1 form:7 smolin:4 regard:1 tarrach:3 but:12 a59:2 construction:1 b1b:1 line:1 true:4 partially:1 made:1 horodecki:20 whether:8 wish:1 up:2 us:20 ur:3 assume:9 problem:12 similar:1 called:3 entropies:1 mechanics:1 ab:1 constant:1 ai:5 certain:4 convex:7 proven:2 denote:14 peres:6 proves:3 exist:10 barcelona:1 a1b:1 b1c:1 check:5 again:5 no:7 rains:1 allow:2 whereas:1 when:11 vanishes:1 application:2 other:10 role:1 unextendible:1 er:8 concerning:5 calculating:1 divincenzo:4 polynomials:14 prepared:1 a1:4 important:5 a4:5 variable:1 structure:2 network:1 implies:1 imposes:1 b1a:1 ranks:6 together:2 original:3 4n:1 decoherence:1 4b:2 having:1

quant-ph9912011.txt \|@word limited:7 chinese:1 rev:4 global:1 alternatives:1 focus:1 tested:1 existing:10 disc:1 legal:3 computation:3 talks:2 hate:1 issues:1 compact:1 equipment:1 certainly:3 amplification:1 depend:1 electricity:1 alamos:3 factoring:1 preprint:3 list:1 finally:1 critical:1 promoting:1 protocols:3 elliptic:2 kwong:1 fatal:1 me:5 lack:1 risk:3 very:8 springer:1 liability:2 wiretap:1 putting:1 invent:1 strictest:1 emphasized:2 exact:1 governments:2 presented:1 transmission:1 ref:1 companies:2 solution:3 standards:2 large:2 convenience:2 circuitry:1 small:2 challenge:1 application:2 employing:3 says:1 ten:1 bb84:1 scientist:1 feasibility:2 go:3 zero:2 invention:1 design:6 further:2 repeaters:1 even:7 will:15 what:6 hide:1 business:1 rate:4 giving:1 cryptographers:20 expressed:1 current:10 version:2 scientists:1 new:7 firms:2 increasing:2 ever:7 public:11 contrast:2 told:1 niche:1 full:1 degree:1 exchange:1 never:1 commercial:5 teleportation:3 here:2 understanding:1 following:3 operating:1 address:1 active:1 november:1 quite:5 equations:1 appears:1 box:7 vazirani:1 engage:1 incoming:1 rigorously:1 technical:2 losses:1 experience:2 credit:1 amount:2 simultaneous:1 products:9 suggestion:1 social:1 military:1 implement:1 proof:1 inspires:1 patents:1 criticism:1 useful:1 secure:11 logical:1 highly:2 psychological:2 put:3 history:1 fbi:1 analyses:1 market:3 conventional:26 criminals:1 eye:1 working:1 army:1 remains:2 sends:1 ingenuity:1 throw:1 few:2 live:1 therefore:3 a56:1 black:7 type:5 theoretical:2 today:1 more:16 pencil:2 bennett:3 door:2 alastair:1 successful:1 company:1 apparent:1 limitation:1 phone:1 needed:1 implementations:7 particular:2 known:4 iii:1 potential:4 must:3 customer:2 involve:2 none:2 include:1 extension:1 science:1 equation:1 package:1 insists:1 london:1 eavesdropper:1 remain:1 achieve:1 transparency:2 already:1 making:1 dec:2 my:6 example:6 unconditional:3 something:3 control:6 claim:1 dedicated:2 division:1 garbled:1 preserving:1 share:1 near:2 accept:1 high:3 heard:1 assumptions:5 numbers:2 arise:1 potentially:1 counting:1 worse:1 information:9 viewpoint:2 keen:1 rather:5 discussion:2 breaking:3 feature:1 hoi:1 how:2 hardness:1 answer:4 instead:1 widespread:3 verlag:1 brassard:4 hopeless:1 inputs:1 product:6 designer:2 irrational:1 may:20 insecure:1 earlier:1 applications:9 curiosity:1 date:1 data:10 types:1 efficiently:2 natural:3 commodity:1 computations:1 goal:2 fibers:2 appreciate:2 robot:1 think:3 attacker:1 coal:1 ones:1 so:4 ultimate:1 fundamental:7 pay:1 stakes:1 order:4 talk:4 wavelengths:2 enk:1 radiations:1 office:1 laboratory:1 indeed:3 over:4 years:1 course:1 paper:1 including:2 looks:1 signs:1 argued:2 cold:1 still:1 avenue:1 its:10 perfect:7 member:1 emits:1 john:1 personal:1 lo:6 cryptology:1 actually:3 better:3 parts:1 systems:22 remarked:1 pad:2 hidden:3 main:7 might:4 overcome:1 focussed:2 them:7 someone:1 than:7 views:1 conversations:1 practice:1 introduce:2 encouraging:1 break:2 leaks:1 they:13 advantages:1 communities:1 now:2 ther:1 nor:2 february:1 van:1 level:2 crypto:10 realistic:2 good:1 magnitude:2 transmitted:1 mode:1 each:2 colleagues:1 entirely:1 side:1 mean:1 schemes:7 financial:3 generation:1 series:2 energy:1 hard:3 reduce:2 idea:1 inverted:1 used:5 expect:2 measurement:1 quantum:116 our:2 operation:1 beyond:1 out:6 principles:2 try:2 ultimately:2 fundamentally:1 factors:1 since:3 crucial:1 research:7 increase:1 internet:2 receiving:2 issue:4 foundation:1 fiber:2 theory:1 state:1 confidence:2 seventh:1 little:2 possibility:3 standard:2 labs:2 reason:2 management:1 complicated:1 york:1 besides:4 imagine:1 ask:3 org:1 inevitable:1 card:6 director:1 her:1 could:1 computers:1 messages:2 feasible:2 thing:1 massive:4 threat:1 signature:3 corrections:1 stimulate:1 first:1 major:6 industrial:2 nigel:1 researcher:1 powerful:1 number:5 miniaturization:1 intuitively:1 set:1 done:4 idealizations:1 another:1 impossible:1 electronic:1 size:4 received:1 given:2 necessarily:1 officials:1 practitioners:1 privacy:1 introduction:1 opportunity:1 top:1 system:8 adopted:1 their:17 attack:2 rates:1 too:2 passed:1 siam:1 scheme:5 bits:1 gives:1 interests:8 distribu:1 selling:1 imperfect:1 continuous:1 esoteric:1 opinion:1 obsolete:1 optical:4 somewhat:1 review:1 probably:2 believe:1 versatility:1 distance:4 encrypting:1 perfectly:1 unfortunately:2 princeton:1 require:2 second:4 matter:1 cost:8 tion:1 feeling:1 solely:1 html:1 kilometers:1 risky:1 behaviors:1 deciding:1 motivation:1 consistence:1 briegel:1 epr:2 correction:1 mind:3 argument:1 say:4 substantial:1 variable:1 need:3 seen:2 seem:2 clearly:2 complete:1 sell:1 forced:1 built:1 output:1 dollars:1 able:1 ideas:1 note:2 instance:6 concerns:5 take:3 forces:2 negligible:1 concern:2 channel:2 begin:2 added:1 advances:1 normal:1 price:1 plugging:1 most:5 involving:1 importantly:1 significant:1 nothing:1 oil:1 payment:1 subjective:3 consumers:1 loopholes:8 clear:2 untrusted:3 face:1 part:1 tech:4 principle:1 enterprise:1 voting:1 naively:1 fact:3 laws:3 sector:1 saying:1 signatures:1 particularly:3 show:1 cheat:1 encrypted:2 nec:1 discovered:1 stringent:2 businesses:7 solutions:1 subtle:2 tempted:2 trivial:2 find:1 impact:1 abandoning:1 based:7 securing:2 implementation:1 outside:2 should:5 only:4 going:1 generators:1 identification:1 bernstein:1 thousands:1 interested:4 hope:2 do:7 his:3 dominant:1 cryptography:58 means:1 familiar:1 designing:1 assumed:1 likely:1 cannot:3 words:1 international:4 timing:1 him:2 appeal:1 arxiv:1 method:1 banking:1 bad:2 experiments:1 though:1 contain:3 through:1 shl:1 view:6 ignored:1 multiplying:1 computed:1 achieved:1 national:1 innovative:1 mentioned:1 see:6 individual:5 horse:4 usefulness:1 discussions:2 contains:1 ur:1 untested:1 best:2 subject:12 hilbert:1 said:1 extend:1 philosophy:2 nuclear:1 nightmare:1 behind:2 future:17 various:5 relayed:1 closed:1 between:1 tens:1 progress:1 neither:1 outsiders:1 mayers:2 infrastructure:6 recently:2 ability:3 notoriously:1 nature:1 qubits:1 component:1 sole:1 however:9 agencies:1 hypothesis:3 key:23 news:2 hundreds:1 distribution:10 thank:1 both:5 essentially:3 last:1 resistant:1 many:18 taking:2 theoreticians:1 according:1 against:3 foreign:1 assure:1 receives:1 interesting:1 contribution:1 argue:3 whole:2 ease:1 experimental:10 comment:1 flies:1 point:9 wall:1 others:1 period:1 community:1 cd:1 directions:2 cirac:1 simply:2 oblivious:1 trust:1 conference:1 strong:3 perspectives:2 tremendous:1 encryption:3 acceptance:2 political:2 due:2 been:8 mark:1 apologize:1 immense:1 workshop:3 eraser:2 basic:1 threaten:1 ph:5 hardly:1 a356:1 misunderstandings:1 life:7 occupancy:1 controlled:1 etc:4 unsafe:3 offered:4 photon:2 collaborators:1 gap:1 offers:1 understand:8 disruptive:2 worked:1 those:9 quotation:1 case:2 commerce:1 trojan:4 photons:1 fur:1 look:2 pacs:1 neal:1 value:2 employ:2 receive:1 while:6 slippery:1 policies:1 error:1 supply:1 chau:4 non:4 iv:1 ii:3 vs:2 experts:3 commonly:1 weakest:2 primitives:1 vendor:1 technology:25 worry:1 really:1 different:13 develop:2 players:5 things:2 make:4 reconstructed:1 lett:3 same:4 any:11 beside:1 locally:1 authentication:4 complex:1 quant:5 emphasize:1 widely:6 material:1 party:1 trans:1 higher:3 development:4 extended:1 http:1 keys:1 malicious:1 hand:1 driven:1 levels:1 user:1 discouraged:1 totally:2 bob:3 thoughts:1 relies:1 whose:1 scenario:1 largely:1 los:3 com:1 addressed:1 no:9 well:8 increases:1 analysis:1 without:2 academic:3 observations:1 academia:4 solve:1 components:1 claims:1 researchers:2 justify:1 opinions:1 construct:2 burden:1 just:3 being:3 money:1 competitive:1 sources:1 underlying:1 kill:1 using:2 yes:1 divide:1 designers:1 cus:1 zoller:1 field:1 thinking:1 regarded:3 bell:1 guaranteed:1 except:1 discuss:1 signals:3 source:1 governmental:2 subjects:2 adoption:4 developments:2 technological:6 usage:3 input:1 smart:6 real:15 pair:2 customers:5 consumption:1 aspects:1 government:2 read:2 big:4 term:1 dark:1 game:1 philos:1 private:4 background:1 deployment:2 world:11 bit:1 accepted:1 unwilling:1 ruled:1 strengths:1 like:8 success:2 sciencemag:1 signal:2 alice:1 communications:10 audience:1 individuals:1 offices:1 either:1 become:3 security:39 towards:1 replacement:1 mathematical:2 www:2 because:4 theorists:1 often:6 deal:2 people:7 foreseeable:2 some:5 back:1 supplementary:1 understood:1 economic:1 export:3 nonetheless:1 moreover:1 classes:1 employment:1 counts:1 scale:1 dimensions:2 electromagnetic:1 decision:1 investigations:2 integration:4 comments:1 manipulations:1 when:1 leap:1 does:4 provides:2 understandings:1 benefitted:1 run:1 power:3 performed:1 journal:1 processing:2 notable:1 use:6 constructive:1 devil:1 viewpoints:3 experimentalists:1 post:2 voluntarily:1 plug:1 faith:1 about:3 actual:1 would:5 anything:1 getting:1 attacks:5 industry:1 theorems:2 discussed:2 practical:1 deserves:1 range:2 plus:1 greatly:1 trapdoor:1 illuminating:1 introduced:1 software:1 soc:1 own:3 cracking:2 communication:5 into:1 commitment:1 combine:1 assess:1 lies:3 parties:2 computational:4 lesson:1 reducing:1 shrinking:2 your:1 methods:1 fortsch:1 criticisms:2 computer:2 additional:3 possible:2 area:1 transfer:1 there:6 question:2 cherished:1 long:4 doing:1 vendors:7 much:5 low:2 way:11 forward:1 conceivable:1 war:1 happy:2 function:5 interest:6 form:1 offer:2 simplifications:1 smolin:2 regard:2 but:6 sophisticated:2 26th:1 construction:1 survive:2 technologies:4 trying:1 he:1 lncs:1 owing:1 made:3 rejection:1 embedded:1 whether:4 markets:1 up:4 us:5 until:3 record:1 convince:1 limit:1 grasp:1 highlight:1 problem:8 agree:2 mechanics:6 marketplace:3 lanl:4 hellman:1 reconcile:1 computing:1 devise:1 certain:1 describe:2 am:1 advancements:1 general:1 single:3 diverse:1 exist:1 file:1 walks:1 work:1 quantph:1 archive:3 inc:1 unwelcome:1 compared:1 ideally:1 floor:1 ekert:1 peace:3 generally:5 ny:1 other:9 teleported:2 you:4 developers:1 acceptable:2 hacker:1 users:11 sided:1 welcome:1 problems:1 shown:1 inherently:1 helpful:1 regulations:2 hardware:1 important:10 prepares:2 koblitz:1 sides:1 acknowledgment:1 cryptographic:34 glass:1 photonics:1 age:2 space:1 curve:2 departments:1 having:3 impossibility:1 compete:1 time:4 far:1 requires:3 original:2 classical:5 once:1

quant-ph9912012.txt \|@word ibid:1 determinate:2 a400:1 consider:2 over:2 supported:1 reversibility:1 symbols:2 paper:1 relation:1 ozawa:1 edu:2 existence:1 funci:3 research:1 its:3 q1:1 cell:6 q2:1 la:3 temporal:2 deterministic:8 complex:1 writing:1 only:6 tm:45 tape:8 marks:1 local:12 ın:1 real:2 finitely:1 non:1 componentes:3 means:8 read:5 de:12 february:1 introduce:1 lanl:1 every:4 step:2 during:2 instructions:2 represents:4 evolution:16 necessary:3 conclusion:1 proc:2 university:2 arxiv:1 iff:2 probabil:1 inherent:1 london:1 works:1 essential:2 view:3 subsystem:2 el:1 because:3 classical:1 deutsch:2 church:1 some:5 under:2 related:3 operates:2 equivalence:1 depends:1 computer:1 computable:4 interval:1 quantum:30 http:1 operation:2 satisfies:4 es:3 project:1 vol:1 said:1 matrix:1 position:2 computing:2 instantaneous:1 current:6 state:9 vector:1 sus:1 unit:2 goes:1 between:2 ˆi:2 mathematical:2 gov:1 conditions:1 email:2 math:1 satisfy:1 ps:2 theory:2 power:1 computability:1 equivalent:2 nishimura:1 however:1 bi:2 reason:1 address:2 represented:2 evoluci:3 properties:1 observable:4 dec:1 operador:2 rule:1 resumen:1 transition:17 space:1 david:1 motion:4 simultaneous:1 due:1 eigenvalues:1 writes:2 first:1 specifies:1 soc:2 computational:4 co:2 lond:1 probability:5 point:3 into:1 number:1 marked:4 son:1 set:10 references:1 colombia:1 1st:1 operator:10 should:2 cu:1 seen:2 given:8 described:1 introduction:1 distinctions:1 financed:1 there:2 direction:2 three:1 relations:1 hilbert:1 los:2 bases:1 way:1 kronecker:1 taken:1 ph:2 was:1 universal:1 possible:2 andr:1 function:20 head:6 corresponding:1 irreversibility:1 para:1 qp:1 formed:1 immediate:1 summation:1 reversible:13 labelled:1 particular:1 siam:2 present:1 he:1 case:1 equation:11 instruction:3 single:1 value:1 will:1 complexity:2 while:1 values:2 amplitude:3 following:1 meet:1 tres:1 elementos:1 xxx:1 called:2 eigenvector:1 perspective:2 myy:1 unitary:5 proved:1 classic:1 process:1 december:1 abstract:1 bennett:1 spectrum:3 correction:1 states:6 reads:1 application:1 right:1 numbers:4 sense:1 take:2 moves:1 conversely:1 any:8 movements:1 counterpart:2 functions:1 compared:1 requirements:1 form:1 no:1 journal:2 alphabet:4 belong:2 feature:2 same:1 transici:3 machine:13 how:1 other:4 quant:2 machines:9 mx:12 finite:13 unidimensional:2 gill:1 evolve:1 elements:2 infinity:3 description:1 models:2 turing:21 symbol:4 hand:3 mario:1 moving:1 spanned:1 n1:1 infinite:1 changing:1 acknowledgements:1 probabilistic:9 model:1 las:4 implies:1 ags:1 physics:1 ısticas:2 su:2 delta:1 write:5 principle:1 components:4 time:8 observables:2 elez:1 con:3 sigma:2 indirectly:1 se:1 left:1

quant-ph9912013.txt \|@word world:1 axes:1 dx:1 just:2 being:1 constituents:2 major:1 gy:1 discovered:1 sources:1 ge:1 relation:1 klauder:2 2ab:4 follow:1 skill:1 y2:1 trivial:1 find:2 substituting:1 aρ:2 whose:2 calculate:2 zoller:1 located:2 eb:3 laguerre:1 centers:2 except:3 only:3 does:2 coefficients:2 elliptic:9 factor:1 main:1 lz:5 momentum:12 alber:1 identical:2 his:1 dk:1 iωt:5 nauenberg:1 stroud:1 iη:2 wave:12 electron:1 simmons:2 example:1 know:1 words:1 press:1 using:6 superposition:2 progresses:1 exact:1 singh:1 advanced:1 eigenvalue:1 semi:2 particle:1 x0:4 follows:2 university:1 arxiv:1 guo:1 shape:1 roy:1 2d:14 investigate:3 radial:1 mcgraw:2 stationary:1 reduced:2 vision:1 remains:1 benjamin:1 moduli:1 set:1 y0:2 classical:12 ed:2 energy:15 packet:4 lnr:2 b4:2 zero:3 investigated:2 radius:3 b1:1 b2:5 2nr:3 quantum:5 eiϕ:2 eigenstates:2 special:3 tried:1 shown:2 accomplish:1 describing:1 3rd:1 morse:1 αy:1 αx:1 rep:1 since:1 rev:5 peking:1 expressed:1 yet:1 naturwissenschaften:1 method:1 state:14 difficulties:1 hill:2 between:1 get:3 x20:1 shows:2 expand:1 terms:2 theory:2 respectively:1 eab:1 however:2 expansion:2 its:2 x2λ:1 china:1 jr:1 key:1 correspondence:1 along:11 vanish:2 eimϕ:2 cos:3 r2:1 eiπ:1 optics:1 must:1 motion:3 thing:1 αx0:1 simultaneous:2 isotropic:8 retarded:1 usually:1 connected:1 first:2 ηe:1 computational:2 letters:1 point:3 rydberg:1 communication:1 into:1 iη0:5 integral:1 harmonic:9 due:1 dimensional:1 infinite:1 en:1 references:1 polynomial:1 respect:2 clockwise:2 angular:15 y02:1 second:1 similarly:2 introduction:1 initial:1 question:1 approximate:1 been:1 plank:1 therefore:2 calculations:1 expected:2 ψc:2 ph:1 was:5 unchanged:1 minor:1 1d:2 function:2 direction:4 corresponding:7 complete:1 fundamentals:1 neglected:1 huo:1 odinger:4 coherent:17 optical:1 nieto:2 normalized:1 atom:2 known:1 natural:1 line:1 careful:1 nonuniformity:1 those:1 he:1 ii:3 kind:1 showed:1 pacs:1 science:1 straight:1 oscillator:18 ωt:4 value:4 theoretical:1 aim:1 assume:1 note:1 frequency:4 values:1 amplitude:1 were:2 believed:1 nonstationary:1 dec:1 calculated:2 result:1 mechanics:5 beijing:2 motivation:1 ab:1 constant:1 wang:1 calculation:2 well:1 abstract:1 thus:1 spectrum:1 zeng:1 general:2 states:6 conserved:1 kepler:1 imϕ:3 numbers:1 anr:1 seen:3 moves:1 hydrogen:3 constructed:3 functions:1 maybe:1 because:1 δnr:3 means:2 2iωt:1 detail:1 same:4 someone:1 x2:2 liu:1 sixties:1 hω:5 quant:1 generalized:1 widely:1 quantities:1 department:1 nr:37 circular:10 node:1 independent:1 used:1 description:1 see:1 singapore:1 may:5 max:1 june:1 orbits:3 a1:3 hence:2 a3:4 a2:11 moving:6 a4:1 letter:2 potentials:1 phase:3 cases:2 ξe:1 structure:10 scientific:2 schr:4 center:3 considered:1 light:1 average:5 counter:1 packets:5 orbit:15 london:1 without:1 appendix:3 feshbach:1 american:1 exp:9 time:3 position:1 dϕ:3 physics:2 lett:2 ψmn:1

quant-ph9912014.txt \|@word limited:1 epeau:1 interspecies:1 consider:2 switched:1 particular:1 results:2 leads:2 quadrature:2 higher:2 grateful:1 finesse:1 stronger:1 integral:2 γs:5 γq:12 microwave:2 send:1 containing:1 γi:2 efficiencies:1 squeezing:10 those:1 x02:3 must:1 schori:1 zhang:1 frequencies:2 msec:1 conditions:1 wave:1 stays:1 resonant:2 2γq:1 condition:2 inset:2 level:9 solution:1 damped:1 small:6 ueda:1 setup:3 programme:1 upper:2 smaller:1 force:1 direct:1 pulse:10 approximation:2 rate:3 further:2 kitagawa:1 spectral:4 ˆq:5 plays:2 detuned:1 clock:1 sun:1 sum:1 near:1 uniform:2 above:3 new:1 contributes:1 method:3 satisfy:1 full:1 simultaneously:1 degree:1 exchange:1 respectively:1 component:1 teleportation:11 atoms:22 ramsey:1 operating:1 free:1 address:1 entire:1 strong:9 equations:1 institute:1 mostowski:2 allows:2 completely:1 reports:1 leaving:1 suggests:1 amount:1 cesium:1 resonance:1 implement:1 suitable:2 plotted:1 via:3 projection:1 replace:1 linearization:1 achievable:1 should:1 cloud:3 figure:1 finally:1 next:1 comparing:1 opposed:1 memory:11 type:4 theoretical:1 more:2 pencil:1 becomes:1 operators:1 furusawa:1 varying:1 isat:3 fermionic:1 states:5 integrating:1 science:1 equation:1 ik:1 remain:1 following:2 making:1 dec:1 spontaneous:2 example:2 stimulating:1 synchronized:1 process:2 sample:14 application:1 council:1 standard:4 information:5 end:1 decaying:1 verify:1 means:1 feature:1 delay:1 maps:1 interrogated:1 dotted:1 instead:1 parameter:1 ensemble:2 brassard:1 profile:1 map:2 ft:1 may:4 after:5 mapping:6 collection:1 applications:1 deviates:1 requirements:1 short:1 effective:3 light:47 introducing:1 so:3 correlation:2 representation:1 subsequently:1 order:7 restriction:1 over:2 utilize:1 paper:2 pulses:1 mentioned:1 cold:1 activating:1 its:1 perfect:1 write:1 lc:1 decay:1 lo:1 unity:1 hz:2 wineland:2 window:1 offers:1 itano:1 fig:5 h3:1 rabi:1 main:1 eur:1 non:1 greater:1 splitter:6 propose:4 processes:1 bound:1 band:2 sω:1 hald:1 now:2 discuss:2 reconstruction:1 represents:3 term:7 finite:1 university:1 capability:1 2e:1 transmitted:2 2a:2 2b:2 fields:2 found:1 polzik:4 2i:2 lorentzian:1 domain:1 schemes:2 illuminate:1 significantly:1 simplicity:1 barnett:1 gaussian:2 decays:2 measurement:5 quantum:45 wavelength:1 operation:1 beyond:1 eq:8 es:16 out:5 emerges:1 shown:2 space:1 req:1 rev:20 research:2 dominated:2 integrated:1 ree:1 linear:1 interactions:1 gardiner:1 contain:1 possibility:2 quite:1 approaches:1 intermediate:2 estimate:1 interaction:6 widths:1 times:1 length:1 harris:1 place:1 transfer:3 hence:1 onto:10 first:3 simplifies:1 features:2 variables:1 number:3 infinite:2 kuzmich:1 parkins:1 simplified:1 gases:1 carry:1 reached:2 thick:1 given:1 start:1 leading:1 eqs:1 attenuated:1 system:5 1a:3 their:1 1b:3 calculations:1 realization:2 scheme:2 loudon:2 store:1 gives:1 danish:1 asymmetric:2 employ:1 optical:13 off:4 sublevels:1 than:3 population:1 past:1 kind:1 second:4 levels:1 classes:1 fˆ:8 enables:1 decompose:1 raman:8 7b:1 7a:1 reduction:1 turned:4 spectrum:2 dash:1 depleted:1 santarelli:1 recover:1 depending:1 efficient:1 lin:1 note:2 ideal:2 absorbed:4 take:1 switching:1 accuracy:1 even:1 probed:1 most:2 but:3 letter:2 device:1 probes:1 observation:1 salvail:1 steady:3 face:1 ks:2 braunstein:3 kq:3 principle:2 parenthesis:1 physics:1 section:2 fact:1 thomas:1 intensity:2 probe:2 degraded:1 x0:3 ground:3 based:2 parameters:1 distributed:1 written:1 operational:1 only:5 factor:1 do:1 mixture:1 dk:1 cryptography:1 get:1 dependent:1 beams:5 simplest:1 beam:12 dz:8 dv:1 dt:1 quantifies:1 evolution:1 denmark:1 arxiv:1 clocks:1 mapped:2 through:1 nδ:1 doublet:1 shapiro:1 set:2 achieved:2 correlations:2 j0:5 j1:4 aarhus:2 transferred:1 detection:1 see:2 result:4 sobolewska:1 discussions:1 3c3:1 subject:1 γi2:1 macroscopic:2 mabuchi:1 dipole:1 symmetric:1 state:30 determined:1 various:2 between:5 approach:3 comparable:1 nature:1 eˆq:5 weak:3 residual:1 efficiency:6 incident:2 analyzed:2 suggested:1 both:1 last:2 limits:1 region:2 infinitely:1 propagation:3 hω:2 variance:4 contribution:4 expression:2 experimental:4 splitters:2 relevant:3 simple:1 each:2 homodyne:1 dimensional:1 cirac:1 simply:1 cr:1 ct:1 broadening:2 ensures:1 described:2 sam:1 cavities:1 basis:1 due:2 been:4 iκ1:1 iκ2:3 describes:1 slowly:2 treat:1 ph:2 define:1 field:33 direction:1 arises:1 corresponding:1 mind:1 sufficient:1 transferring:1 photon:1 coincides:1 observe:1 detuning:1 wavevectors:1 spin:11 present:2 case:5 laser:1 solid:2 value:2 will:4 dephasing:1 squeezed:12 eik:2 projecting:1 funded:1 chau:1 thus:3 them:1 walmsley:1 couples:1 unit:1 different:1 bollinger:1 perform:1 suggest:1 cross:3 same:2 fountain:2 stimulated:2 imoto:1 quant:2 schematic:1 mølmer:3 dimensionless:2 utilizing:1 grows:1 difficult:1 used:2 i1:3 i0:3 possible:3 compared:1 σr:3 munkegade:1 recent:1 lower:1 kept:2 center:1 acknowledge:1 epr:5 roughly:1 analysis:3 vaidman:1 entry:1 model:2 restore:1 protocol:1 proposed:1 moments:1 storage:7 obtain:2 bandwidth:4 stored:2 atomic:45 scattering:2 λl:1 µ1i:2 zoller:1 density:1 absorption:4 photons:1 realize:2 valid:1 treatment:1 samples:1 pair:1 sectional:1 excited:2 opt:3 rescaled:1 saturation:2 iκ:1 read:3 february:1 entangled:1 vacuum:8 bit:1 highly:1 necessary:1 shaped:1 signal:1 either:2 become:1 security:1 works:1 collective:7 spins:1 because:2 qed:1 classical:7 fresnel:1 some:1 back:3 growth:1 jeffers:2 duration:1 matching:1 scale:2 broadband:1 broad:1 langevin:2 exceeding:1 per:1 esf:1 does:1 eliminate:1 prof:1 propagating:4 bessel:1 demonstrated:1 lowest:1 kozhekin:1 noise:15 reasonable:1 power:2 processing:2 mayers:2 how:2 step:1 qˆ:1 analyses:1 raymer:2 carried:1 discussed:1 dependence:1 reduced:1 carrier:1 ensure:1 cooled:1 bloch:1 soc:1 h2:1 maxwell:1 into:1 within:1 numerically:1 commitment:1 down:1 dissipation:2 operator:9 bosonic:2 prepare:2 area:3 assumed:1 support:1 initial:4 faithfully:1 long:6 lidar:1 width:3 much:1 low:1 fraction:3 assumes:1 µji:1 function:3 medium:3 enough:2 adjusting:1 removes:1 delayed:3 overlapping:1 atom:2 line:4 proposal:5 made:1 ωq:2 wish:1 ωs:2 up:1 us:2 2πn:1 frequency:4 verification:1 semiclass:1 similar:2 strongly:1 storing:3 qin:1 associated:3 computing:1 certain:3 ak:1 describe:1 am:1 zeng:2 kimble:3 our:12 qit:1 regime:3 high:2 functions:1 transitions:2 nl:7 ideally:2 sørensen:1 dashed:1 when:5 ne:1 ny:1 narrowband:1 other:3 role:2 spatial:2 optically:1 briefly:1 coherence:7 separate:1 variation:1 includes:1 meaning:1 important:1 allowing:1 variable:1 astronomy:1 correlated:2 coupling:4 assume:4 dτ:9 required:1 cavity:3 depth:12 c8:1 time:5 decoherence:2 requires:2 lett:12

quant-ph9912015.txt \|@word consider:11 springer:5 caused:1 brownian:4 results:1 gy:1 leads:1 eds:1 entropy:1 controversial:1 francesco:3 mesoscopic:1 causes:1 whose:2 preserves:1 finally:1 preserved:1 under:1 stochastic:46 norm:1 me:1 fax:1 comm:1 very:1 reversibility:2 siena:1 differently:1 wave:7 ρb:1 every:2 fall:1 difference:3 condition:10 χd:1 preuss:1 solves:12 hamiltonian:3 suffices:1 notes:5 t2:59 solution:22 t0:26 t1:137 large:1 solved:1 phase:4 dealt:1 markov:2 der:1 falco:1 osmotic:2 employing:1 force:1 lecture:5 measurable:4 l2n:2 past:1 byrnes:1 second:3 further:1 dynamics:1 odd:1 canonical:1 even:1 established:1 what:1 nonlinear:3 sum:2 xρ:18 transforms:1 find:7 current:2 experiment:1 xvii:2 above:1 sitzungsberichte:1 new:23 equivalent:1 satisfy:1 edited:8 mea:1 respectively:1 never:1 here:8 understanding:2 tremor:1 along:1 quite:2 equations:2 appears:2 change:5 knowledge:1 obtained:4 increments:3 suitably:1 technical:3 changed:2 action:1 suitable:1 changes:2 explain:1 bayes:2 via:1 useful:1 family:4 marginal:5 vii:1 marchetti:1 moral:1 apply:1 ollmer:4 planck:5 everybody:1 derivatives:1 use:1 proceed:2 would:1 probabilities:9 positive:1 contains:1 predictions:1 next:5 linear:1 kinematics:9 therefore:2 taken:1 associated:6 care:1 type:2 theoretical:1 more:2 introducing:1 duality:1 ecole:1 thus:9 acceptable:1 apparent:3 odinger:12 berlin:1 particular:3 foundations:1 iii:16 must:4 logarithm:1 account:1 valued:9 permits:3 recall:2 equation:17 mi:6 modified:1 theories:1 dei:1 mv:1 probabilit:2 concepts:1 following:12 dec:1 my:1 stimulating:1 proof:2 control:4 transition:9 cosmological:1 give:2 process:41 preserving:2 accept:1 indicates:2 employs:1 overbar:1 absolute:1 counterpart:1 rather:1 purpose:1 holds:3 write:1 get:11 significance:1 verlag:5 de:10 information:2 may:9 after:7 derived:2 mapping:1 expectation:1 produce:1 physik:1 italy:1 minimizes:2 law:1 data:1 plank:1 stress:1 natural:1 dynamical:2 whenever:2 sq:9 lines:1 so:2 fundamental:2 representation:5 integrand:2 words:2 order:6 legitimate:1 ito:4 s0:4 interpretation:5 dx:2 produces:1 indeed:5 over:10 satisfied:2 interpreted:1 wiener:2 paper:4 through:4 existence:1 satisfies:12 before:4 bridges:1 derive:2 symmetry:1 la:1 conjugation:1 parts:1 systems:9 pena:1 jacobi:1 mail:1 might:1 crucial:4 combination:1 flour:2 outlined:1 evolution:2 introduce:4 reflected:1 hamilton:5 effects:1 postulated:1 now:5 discuss:1 association:1 february:1 several:1 lies:1 always:2 university:2 magnitude:1 l2:1 each:3 2m:11 universit:1 side:1 reproducing:1 subset:2 differential:3 ed:1 energy:11 idea:2 related:3 t3:3 extended:2 obtains:1 measurement:26 quantum:33 beyond:2 eq:2 es:2 shown:7 carlen:1 matrix:1 space:2 gradient:1 xv:2 rep:1 since:7 lagrangian:3 denotes:1 particles:1 participants:1 reader:2 formula:7 rn:10 induced:1 issue:1 correct:1 math:6 shows:1 foundation:1 39a:1 theory:7 variant:1 little:2 possibility:1 standard:7 admits:1 completely:2 complicated:2 term:3 ask:1 estimate:1 shreve:1 rewritten:2 interaction:2 derivation:3 could:1 impose:1 running:1 motion:4 turn:1 hence:5 undergo:1 support:1 first:7 origin:1 initial:12 features:1 probability:14 martin:1 variables:4 number:1 will:1 general:1 another:2 impossible:2 precisely:2 open:2 given:11 reference:8 needed:1 introduction:2 dipartimento:1 amsterdam:2 system:5 least:1 their:1 assumption:2 saint:2 justified:1 variational:20 final:1 gives:2 collapse:5 discussion:1 serva:2 tool:1 continuous:1 immediate:1 somewhat:1 than:1 coefficients:1 outline:1 diffusion:17 distance:1 holland:1 princeton:4 see:11 aims:1 minimize:2 appealing:1 future:1 publ:1 were:1 providing:1 motivation:1 rewrite:1 boston:2 michele:1 argument:1 generalization:1 increment:3 keller:1 need:7 seen:1 constrained:4 apparently:2 any:5 viewed:1 complete:1 zero:4 efficient:1 lim:2 calogero:2 csisz:1 thorough:2 instance:1 klasse:1 take:1 analogy:1 feshbach:1 reals:1 calculus:1 formulas:2 play:1 sure:1 led:1 shall:2 lively:1 measures:1 birkh:2 most:2 boltzmann:2 multiply:1 probabilistic:6 class:6 martino:2 observation:1 surprising:1 considered:1 coincides:2 drifts:6 possesses:1 construction:1 principle:15 exp:14 mechanical:1 velocity:2 physics:6 section:17 fact:1 bell:1 show:2 supported:1 anyway:1 purely:3 minimizing:1 relation:6 substituting:2 agrees:2 paradoxes:1 based:4 just:2 title:1 writes:1 original:3 should:4 terminal:2 lemma:2 only:2 developed:1 employed:2 padova:2 combe:1 equilibrium:2 continuity:1 do:3 notation:1 di:3 hopefully:1 db:5 elettronica:1 nonequilibrium:3 reversal:1 dt:26 girsanov:1 boundary:1 dp:1 dq:1 processes:10 arxiv:1 nauenberg:1 method:2 twice:1 shalit:1 hydrodynamic:1 including:1 fixed:4 qo:4 view:8 coefficient:6 multiplying:1 exists:2 guerra:9 frame:2 packet:1 relative:1 namely:8 result:7 y0:6 discussions:1 terms:1 subject:3 satisfying:4 review:1 pavon:9 definite:1 functionals:1 blanchard:3 symmetric:5 state:2 karatzas:1 between:3 enjoys:2 previous:9 choose:1 notice:3 recently:1 adding:1 however:1 york:6 hypothesis:2 wq:13 modeling:1 configuration:1 come:1 distribution:3 thank:1 both:3 reverse:3 limits:1 uncertainty:3 according:2 quantization:1 admit:1 present:1 context:3 coh:1 estimation:1 expression:2 experimental:1 among:1 key:1 conclude:2 simple:3 connection:1 2kt:1 except:1 dimensional:2 simply:1 lagrange:5 moreover:4 specializing:1 pp:8 perspectives:1 agree:2 observing:1 due:1 been:5 strategy:1 springerverlag:1 reduction:3 cauchy:1 basic:4 ph:5 improve:1 hardly:1 universal:1 define:5 corresponding:5 quantities:1 concerning:1 coherence:2 observe:2 understand:1 deep:1 albeverio:1 repetition:1 fokker:5 those:1 case:4 wakolbinger:1 replaces:1 look:1 exponential:1 pacs:1 akad:1 empirical:1 value:7 wissen:1 employ:2 while:1 suppose:10 viii:1 applies:1 situation:1 property:3 procedure:1 played:1 vol:5 vi:20 von:1 iu:3 iv:25 ii:38 vq:22 reads:2 casati:1 im:4 conf:1 elsevier:1 σd:1 confirmed:1 formalism:2 develop:3 author:1 seek:2 granted:1 leibler:1 same:15 complex:6 quant:1 arguments:2 finite:14 status:1 independent:3 investigated:1 singapore:1 trivially:1 hand:2 moment:1 hydrodynamics:1 changing:1 invariance:2 opportunity:1 identity:1 recent:1 weakly:1 schr:12 acknowledgement:1 nevertheless:2 modeled:1 well:1 analysis:2 obviously:1 without:1 solve:5 temperature:1 thoroughly:1 position:4 model:3 latter:3 diffusions:5 proposed:1 being:2 xρ1:5 observed:1 obtain:1 underlying:1 mechanism:7 using:2 facts:1 macroscopic:2 cn:1 vρ:1 kluwer:1 density:17 auser:2 point:4 seems:2 drawback:1 transparent:2 thermodynamics:1 add:1 lett:3 theorem:7 iσ:1 transformation:1 momentum:2 real:3 aspects:2 rules:1 evaluate:1 iγ:2 papers:1 extremization:7 possible:3 possibly:1 expecially:1 background:1 press:2 immediately:2 unconstrained:4 advanced:1 cexp:1 appearing:1 particle:1 semi:2 follows:6 serves:1 yields:5 integrals:2 arbitrary:1 pointwise:2 essential:1 lends:1 therein:1 because:1 old:1 neumann:1 classical:3 absolutely:1 conditional:1 some:2 back:3 born:1 zheng:1 sight:1 respect:11 cnr:1 nonempty:1 measurements:1 integration:1 does:3 decomposition:1 tends:5 unipd:1 proc:1 refer:2 noise:2 scientific:1 minimization:4 problems:1 informatica:1 pose:1 imaginary:1 properties:1 bz:1 science:1 chapter:1 comparison:1 world:1 constraint:5 universe:1 capable:1 discussed:2 o:7 rev:3 letters:2 markovian:1 maxwell:1 into:5 integral:4 functional:15 auerbach:1 pair:6 appropriate:3 right:2 references:2 laplacian:1 operator:1 proportional:1 van:1 log:23 assumed:1 strictly:1 there:3 question:1 extremizing:2 quadratic:1 regarding:1 way:2 series:1 forward:15 call:1 hen:1 was:3 function:17 north:1 elsewhere:1 form:4 2iβ:1 regard:1 but:3 principles:2 mysterious:1 repeated:2 hi:4 becomes:2 removed:1 considerable:1 he:1 made:3 versions:1 wish:2 gravitational:1 up:4 us:9 different:2 verification:1 continuously:1 fluctuations:1 problem:35 similar:3 called:5 mechanics:34 interval:2 constant:10 factor:1 defined:5 certain:1 abstract:1 measure:1 am:1 proven:1 denote:9 ar:1 exist:2 formulation:1 hennequin:1 ing:1 physical:3 functions:1 thermodynamical:3 differentiable:1 seminar:1 no:1 amounts:1 wavefunction:3 when:4 vanishes:2 field:4 other:5 role:2 details:2 spatial:1 hove:1 mathematics:4 kullback:1 northholland:1 deviation:1 elements:1 kt:1 drift:25 important:5 variable:2 structure:1 bilateral:2 assume:4 dτ:13 required:1 pseudo:1 masi:1 dρ:4 equivalently:2 dramatic:1 nelson:25 time:44 serious:1 backward:13 requires:1 having:10 once:1

quant-ph9912016.txt \|@word remarkable:1 equalities:1 1ev:1 2c:2 results:1 purely:1 ge:1 grateful:1 mentioned:1 lysov:1 d2:1 its:1 calculate:1 ln:4 alamos:1 written:1 short:1 analytic:2 only:1 condition:2 easy:1 under:1 mail:1 hidden:1 main:1 solvable:2 euler:1 above:1 easily:2 lambert:1 introduce:1 wave:1 ze2:1 electron:2 putting:1 know:1 dx:2 formula:1 richards:1 penetrate:1 nieto:3 now:2 exact:1 dielectric:1 yu:1 eigenvalue:1 february:1 equality:1 helpful:1 2s:2 transmission:1 notes:1 pacs:1 solution:2 arbitrary:2 2m:1 2n:1 university:1 view:1 mathematical:1 exceed:1 arxiv:1 determine:1 prudnikov:1 national:1 hypergeometric:1 phenomena:1 idea:1 related:1 observed:1 value:2 quantum:2 our:1 ev:1 whittaker:1 index:1 rev:2 find:1 models:1 state:1 closed:1 new:2 boundary:2 acknowledgments:1 coefficient:1 confluent:1 recently:1 attention:1 given:1 here:2 ws:2 references:1 eigenvalues:2 interface:1 consideration:1 e0:8 additional:1 suggested:1 both:1 about:1 cot:3 impose:1 discussed:1 according:1 o:5 marichev:1 range:2 2x0:1 mean:1 whole:1 schroedinger:2 ch:1 probability:1 point:2 rydberg:3 into:2 right:1 h2:1 another:1 e4:1 brychkov:1 precisely:2 realistically:1 use:1 asymptotic:1 πs:1 positive:2 msu:1 there:1 noticed:1 los:1 call:1 identity:1 πz:1 ph:2 e2:1 energy:1 more:1 function:2 resting:3 shell:1 form:3 b23:1 moscow:3 continuous:1 gas:1 but:2 spectrum:4 borisov:1 part:1 everywhere:1 dubious:1 somewhat:1 atom:2 x0:5 than:1 he:2 polygamma:1 account:1 unfortunately:1 permits:1 equation:4 work:1 us:2 different:1 will:1 near:4 vega:1 values:1 behavior:1 aid:1 problem:3 dec:1 russia:1 mz:1 constant:6 nauka:1 abstract:1 describe:1 thus:1 defect:2 surface:5 denote:1 states:1 discussions:1 itself:1 ghz:2 laboratory:1 close:3 helium:5 physical:2 functions:2 s2:1 make:1 get:1 isolated:1 same:1 write:1 potential:2 quant:2 take:1 electrons:3 dimensionless:1 axis:2 nye:1 infinity:1 slightly:1 singular:1 may:2 dx2:1 sx0:1 3n2:1 faculty:1 normalization:2 task:1 liquid:1 dφ:2 established:1 well:1 su:1 think:1 solve:2 coordinate:2 model:4 lett:1

quant-ph9912017.txt \|@word consider:2 amplifier:1 results:1 entropy:1 computation:1 contributions:1 whose:2 certainly:1 subjected:2 nonlocal:1 γt:1 γj:2 does:1 squeezing:2 present:3 under:1 nodes:1 include:2 cm2:1 sent:1 ρa:2 confirmation:1 advantage:1 very:3 frequencies:1 implicitly:1 account:1 choice:1 print:5 experimentally:6 condition:4 presented:1 transmission:9 welsch:1 pacs:1 solution:1 large:4 convenience:1 small:11 enhance:1 noted:1 smaller:4 foundation:1 direct:1 hillery:1 jump:2 rate:7 greenberger:1 dynamics:1 eigenspaces:1 even:1 abi:2 bo2:4 expressed:1 current:1 lights:1 experiment:2 goes:2 method:7 coefficient:4 slotine:1 respectively:3 promising:1 component:3 teleportation:3 here:1 met:1 plenio:1 china:2 ratio:1 strong:1 equations:1 imperfections:3 deduced:1 obtained:1 bt:4 great:1 institute:1 losses:1 resulting:1 published:2 resonance:1 implement:3 uniquely:1 useful:2 projection:2 outcomes:1 austria:1 apply:1 total:13 circumvent:1 unit:1 readily:1 use:4 asymptotic:1 would:3 properties:1 depicted:2 call:1 m2:2 taken:1 today:1 more:5 formally:1 operators:2 occurred:2 berlin:1 normalized:1 cases:2 analogous:1 me:1 states:28 none:1 science:4 equation:1 work:2 cav:1 paragraph:2 values:1 iheff:1 following:4 duan:2 arrive:1 example:3 attain:1 compare:1 mirrors:1 process:1 bennett:4 high:7 effectively:1 numbers:1 want:1 allowed:1 times:2 occur:1 verlag:1 information:2 requirements:2 goal:1 demolition:1 discussion:1 enk:1 feature:1 hampered:1 how:2 pure:4 optimal:1 parameter:2 product:1 may:1 after:3 physik:1 fj:9 grangier:1 λ2j:2 realized:1 physical:1 effective:2 light:9 purify:2 yielding:1 ghz:3 purification:23 so:6 turnstile:1 order:1 operations:2 wigner:1 help:1 alternation:1 ities:1 paper:2 through:3 austrian:1 still:1 its:2 probability:8 till:1 interesting:2 lu:1 systems:5 imbalance:1 inefficiency:1 maximal:1 puts:1 non:1 propose:3 subtraction:1 cosh2:2 instead:1 now:2 realize:3 bigger:1 easily:3 term:2 finite:3 always:2 university:1 hamiltonian:2 kerr:13 imamoglu:1 realistic:2 transmitted:1 mode:11 reasonable:1 each:6 found:2 universit:1 european:1 side:12 2j:1 mean:2 schemes:3 directly:2 generation:3 gaussian:9 extended:2 measurement:26 quantum:23 laboratory:1 nonlinearities:1 1ni:1 special:2 standard:1 bility:1 100m:2 network:1 driving:4 space:2 furthermore:1 since:1 rev:9 denotes:1 increase:3 modulation:4 contained:2 gaussians:1 denoted:1 ref:1 sinh2:4 i2:4 interactions:3 gardiner:1 quite:1 difficulty:2 put:2 generate:6 pairs:12 interaction:1 language:1 keep:2 onto:2 first:6 there:4 symmetry:1 variables:1 number:16 reaches:1 system:1 another:2 carry:1 ring:10 xt:3 illustrate:1 given:8 necessarily:1 rewritten:1 obtainable:2 equa:1 eqs:1 theoretische:1 relations:1 needed:1 assumption:3 master:1 listed:1 realization:1 rates:2 white:1 scheme:7 1m:2 final:4 store:2 gives:1 imperfect:1 asymmetric:2 continuous:18 required:2 optical:4 favorable:1 kept:1 unrealistic:1 than:5 coefficients:1 detection:1 kind:3 device:1 aai:2 second:4 distill:2 annihilation:2 represents:1 tion:1 outcome:8 projections:1 hz:5 correction:1 measure:1 ming:1 need:5 twomode:1 any:2 efficient:2 self:2 note:3 heff:2 ideal:2 erator:1 take:3 transmit:1 negligible:3 subject:1 channel:1 begin:1 exactly:1 gγ:1 though:1 pair:2 measured:2 class:2 nonlinearity:1 considered:3 clear:1 later:1 steady:1 posterior:1 dent:1 braunstein:2 part:1 bo1:2 typically:1 fact:2 quantity:2 parker:1 intensity:1 show:1 supported:1 rotating:1 bring:1 spaces:2 lloyd:1 find:1 based:2 just:1 parameters:5 implementation:1 distributed:1 enough:2 should:6 being:2 only:3 factor:2 local:5 over:1 do:2 mixture:1 above:7 cryptography:3 get:8 express:1 quantified:1 satisfied:1 joint:1 cannot:1 preparing:1 despite:1 kurizki:1 during:3 dt:2 adiabatically:1 arxiv:1 common:1 setup:4 parkins:2 exists:1 sep:1 problem:1 frame:1 observed:1 see:1 result:2 enhanced:3 discussions:1 techniques:1 instance:1 satisfying:2 resonantly:1 nondegenerate:1 state:38 between:8 αi:4 boundary:1 conditions:2 email:1 choose:2 extend:1 nature:3 modify:1 however:2 hefei:1 efficiency:3 incident:1 concentrate:2 key:2 bose:1 configuration:4 ja:6 jb:6 thank:1 both:2 last:1 many:1 taking:1 decay:1 propagation:1 qubit:3 estimation:2 experimental:2 otherwise:1 relevant:1 cm:1 point:1 simple:3 homodyne:2 dimensional:3 cirac:2 simply:1 aαi:2 ensures:1 χni:1 described:3 cavities:11 basis:1 three:2 been:5 pb:5 ai:39 pa:5 damping:4 interest:1 pj:3 ph:5 fig:4 γb2:1 γb1:1 corresponding:2 observable:2 photon:9 coherent:2 maximally:14 protocols:2 case:4 multi:1 tanh:1 kimble:1 value:1 will:3 error:1 squeezed:9 procedure:1 larger:1 von:1 thus:4 them:1 ii:4 obstacle:1 im:4 technology:2 different:2 perform:6 media:1 make:1 cross:9 same:8 quant:4 schematic:1 party:3 dimensionless:2 several:4 couple:1 pan:1 difficult:1 used:3 infinity:2 ni:3 i1:4 trajectories:1 4m:1 uses:1 purpose:1 entanglement:24 recent:1 relies:1 finesse:3 modes:11 ccs:1 obviously:1 quantitative:1 model:1 parametric:1 effects:2 stringent:1 protocol:17 they:1 proposed:2 transmitting:1 storage:5 abbreviation:1 distant:8 immediately:1 λj:1 reality:2 bi2:2 λn:1 bi1:11 signal:1 zoller:2 density:4 absorption:1 seems:2 cc:2 transformed:1 lett:6 easy:1 hau:1 real:1 eigenvalue:1 innsbruck:2 possible:3 corresponds:2 entangled:38 vacuum:2 using:3 projects:1 loss:9 like:1 collective:1 performing:3 discarded:1 either:1 output:4 reduced:1 exceed:1 right:1 neumann:1 classical:2 conditional:1 some:3 springer:1 n2:9 b1:4 b2:4 nonzero:1 δn:2 tmr:1 describing:2 confirm:1 cavity:14 measurements:1 langevin:1 integration:1 efficiencies:1 eliminate:2 provides:1 unavoidably:1 moderate:1 straightforward:1 o2:1 demonstrated:2 measuring:2 noise:10 bm:1 jumps:4 bi:45 qnd:12 instability:1 hilbert:4 bz:1 takes:1 about:1 working:1 extension:1 getting:1 uibk:1 practical:3 extensions:2 mixed:7 sumed:1 op:1 considerations:1 ηb:13 ηa:12 communication:6 into:2 cascaded:1 due:2 phase:6 operator:8 proportional:2 institut:1 log:4 area:1 assumed:1 initial:1 start:1 much:3 analyze:1 was:1 assumes:1 function:2 medium:3 form:2 but:6 hk:1 repeated:2 hi:1 proposal:1 partially:3 directed:1 made:1 whether:1 inside:1 ur:1 limit:3 continuously:1 distribution:1 aa:1 ariano:1 ac:1 ab:1 constant:1 choosing:1 defined:2 detectors:1 describe:3 am:2 proven:1 denote:2 single:2 our:1 ing:1 quantph:2 defines:1 inci:1 functions:1 no:2 eq:4 when:2 nam:1 field:3 other:1 generates:2 excitation:6 provided:1 symbol:1 prepared:2 a1:3 generated:2 a2:3 variable:7 sides:8 feasible:1 assume:5 factors:1 furusawa:1 na2:1 na1:1 time:6 n1:7 decoherence:1 requires:2 original:1

quant-ph9912018.txt \|@word represent:2 homomorphism:1 consider:1 chain:1 induces:1 global:25 results:2 existing:3 four:23 obstruction:9 commute:1 c2:1 intricate:1 partial:4 reasoning:2 row:4 relationships:4 whose:2 pˆc:5 inverse:2 pˆe:1 pˆd:2 pˆg:2 pˆf:2 pˆi:2 pˆh:2 pˆj:2 tp:1 ıa:10 under:2 pˆy:1 pˆx:1 analogous:1 belonging:3 lack:2 advantage:1 orthogonal:20 linked:1 exception:1 induce:1 geometrical:1 medicine:1 every:1 figs:1 matrices:1 condition:5 interlocking:1 generalised:2 rotating:2 34c:1 list:1 joined:2 fewer:3 pˆ1:2 pˆ3:2 vector:4 rj:2 small:1 eigenvalues:2 rk:1 round:1 upper:1 smaller:2 zh:4 verifiable:1 ten:5 harder:1 zf:5 prediction:5 elegant:1 zero:3 perspective:2 invariant:1 specker:18 d4:1 eigenspaces:1 spectral:2 diamonds:2 incompatible:3 d2:1 sum:2 axes:1 above:8 new:12 consisting:1 body:2 pˆa:13 full:1 certainly:1 fairly:1 pˆb:11 others:3 directions:7 along:1 19f:1 table:5 morphisms:2 obtained:1 involved:3 larger:6 contradiction:4 suggests:1 amount:2 products:1 sw7:1 pick:1 usually:3 nullifies:1 examining:1 projection:7 extra:2 boolean:16 contradictions:1 nonlocal:1 mabc:7 resolutions:2 predicted:3 use:4 projector:15 would:10 cohomological:2 nine:1 contains:3 bundles:1 predictions:1 properties:1 therefore:8 taken:1 black:1 simpler:1 type:4 until:1 diagrams:2 more:15 r5:3 brings:1 operators:19 getting:1 appendix:1 labelled:4 varying:14 known:1 hold:3 must:11 mf:1 join:1 38b:1 science:1 originally:1 constraint:1 values:8 following:3 dec:1 example:4 proof:7 f1:1 f2:1 f3:1 f4:1 dual:4 figure:18 stated:2 preserving:1 share:2 states:2 contradicts:1 tetrads:2 numbers:2 degenerate:29 arise:4 occur:2 rays:25 r10:2 rather:2 discussion:1 hom:1 orthogonality:2 write:1 maps:8 sin:2 map:6 product:2 description:1 algebra:34 may:26 derived:1 containing:15 collection:3 top:1 diagram:10 produce:3 choice:1 types:4 physical:1 third:2 light:2 correspond:6 element:16 provide:2 ones:1 so:12 interpreting:1 restriction:2 holds:1 over:22 insight:1 produced:3 paper:2 london:1 68c:1 statistical:1 mentioned:1 existence:3 still:1 its:2 before:1 lf:1 imc:4 lb:1 imd:4 fit:1 how:8 chosen:3 interesting:1 forms:2 hidden:4 into:2 lx:2 ly:2 maximal:33 yh:4 non:13 greater:4 combination:1 severely:1 care:1 yb:4 garc:10 hamilton:1 they:8 now:6 easily:4 term:1 several:2 homomorphisms:1 university:1 classified:1 b3:1 identified:1 each:33 found:1 referred:1 subset:5 domain:2 directly:1 independent:1 hard:1 mdf:1 related:2 constitute:1 extended:2 expect:1 combining:1 loops:31 laboratory:1 eq:6 out:1 category:10 respects:1 shown:15 space:20 furthermore:1 since:6 kensington:1 denotes:1 looking:2 obstructions:19 contained:3 pˆ2:2 kent:4 l175:1 denoted:3 squares:2 ri:1 red:1 shows:2 creating:1 linear:1 mdef:2 interchange:1 completely:1 base:5 complicated:1 e4:1 subalgebras:10 e1:1 e3:1 e2:1 r4:3 degeneracies:2 r6:3 r7:3 r1:4 r2:3 created:1 could:2 r8:3 r9:1 int:2 hence:7 onto:11 assign:2 south:1 first:2 origin:1 major:1 initial:4 symmetry:1 m123:1 xb:5 xc:6 variables:4 xa:2 sinβ:2 number:5 sinα:2 restrict:1 done:1 least:3 another:5 impossible:1 precisely:1 cosφ:2 given:3 necessarily:1 similarly:4 introduction:1 leading:1 adjoint:1 system:1 construct:2 their:5 statement:3 ordered:5 structures:4 final:2 gives:3 observable:1 17a:1 cosβ:2 cosα:2 than:13 whereby:2 showed:1 accordance:1 require:3 namely:4 sinφ:2 w3:8 minus:1 result:4 objects:6 cabello:10 simulating:1 meyer:3 say:2 violating:1 iw2:10 need:2 seen:8 clearly:1 viewed:3 ray:4 constructions:1 built:2 mermin:5 self:1 r3:3 analogy:1 green:1 circles:1 begin:1 68e:1 unless:1 object:3 reach:1 fca:4 fcb:2 connected:4 why:1 sub:2 give:5 observation:1 considered:1 clear:1 stronger:1 ks:14 principle:3 constrain:2 section:3 fact:8 12d:1 show:3 able:1 discovered:1 bub:1 spaces:2 codomain:1 trivial:6 d3:3 d1:3 fibre:1 q3:1 based:3 2bz:1 eigenspace:1 true:2 explain:1 state:1 should:1 only:5 threefold:1 subsection:1 factor:1 isham:2 do:2 move:1 subspaces:2 triple:3 di:1 dependent:1 between:5 cannot:3 joins:2 shared:1 gen:2 contextual:4 dps:17 arxiv:1 common:3 contain:8 through:2 fixed:3 kochen:18 view:2 predictive:3 requirement:1 set:43 constructing:3 exists:1 reductio:1 connections:1 see:7 college:1 w2:18 w1:26 triples:1 theoretic:1 subject:3 appear:1 ways:1 review:2 currently:1 definite:3 written:3 smallest:1 various:1 simplest:3 conceptual:1 drawn:1 approach:2 email:1 wd:1 terms:7 reproduced:1 attention:1 analogues:1 ld:1 colourable:7 however:3 consists:1 wp:5 outer:1 both:7 cos:1 ila:1 many:4 la:3 equal:3 etc:1 connection:1 unc:2 context:1 whole:1 comes:1 point:1 simple:3 cf:1 dimensional:37 represented:1 away:1 leads:1 fibres:1 math:2 considering:1 described:1 second:3 aˆ:1 addition:2 three:31 been:3 quickly:1 defined:3 pd:2 basic:1 expected:1 ph:2 algebras:62 tan2:1 dots:1 direction:4 relations:3 corresponding:9 valuations:6 restrictions:1 concerning:1 formed:3 subspace:1 essentially:1 else:1 c3:1 57b:1 c1:1 general:1 assigning:2 those:7 c4:1 case:7 presheaf:5 look:2 subsets:3 solid:1 straight:1 appearance:1 examine:1 value:30 will:18 suppose:1 pˆ:15 property:4 loop:6 seven:2 vectors:15 ir:1 thus:1 them:2 ii:1 counterexamples:1 ic:1 subdiagram:1 technology:1 chaining:1 different:3 σz:7 perhaps:2 large:2 σy:2 same:4 any:9 σx:6 quant:2 arguments:1 pauli:1 proved:2 finite:5 subalgebra:3 composition:2 higher:2 meets:2 used:13 l178:1 assigns:2 again:2 assignment:7 interconnections:1 hand:1 action:1 uses:1 colouring:2 changing:1 totally:4 identity:6 recent:1 proceed:2 countable:1 picks:1 thought:2 without:1 sets:14 five:4 dimension:6 usual:1 unified:1 just:7 less:2 being:5 when:2 topos:2 obtain:1 assigned:10 identify:2 world:1 reality:1 previous:1 dpss:9 conclusions:1 bell:1 except:1 reasons:1 belongs:2 collections:4 lett:3 easy:2 theorem:29 input:7 eigenstate:1 match:1 aspects:1 rev:3 showing:3 implications:1 possible:15 vδ:4 know:4 press:1 using:1 unique:2 necessary:3 like:1 follows:4 consistent:1 28d:1 either:5 reduced:4 terminology:1 right:1 old:1 classical:1 butterfield:2 some:10 b4:1 deduce:2 examples:1 b2:1 respect:1 proofs:11 matching:2 dense:1 dimensions:17 measurements:1 does:3 eliminate:1 provides:4 assuming:1 leftmost:1 chains:1 refer:1 particular:4 power:2 extendibility:1 equivalent:1 although:2 hilbert:21 stage:1 central:1 extension:1 most:3 column:6 measurement:1 interlinked:2 a3:1 compatible:1 mutually:1 plus:3 eight:2 introduced:2 projectors:22 cambridge:1 letters:2 inclusion:8 previously:1 h3:3 image:2 within:2 clifton:15 functional:4 h4:6 due:1 appropriate:2 references:1 determine:1 operator:3 particularly:1 existed:1 additional:1 suffice:1 there:23 imperial:2 way:15 presheaves:1 was:3 function:2 complete:5 form:8 forming:2 but:4 construction:21 hb:1 valuation:6 partially:6 fda:1 throw:1 made:1 consist:4 whether:2 up:3 us:1 uk:1 problem:2 called:1 blackett:1 b1:1 mechanics:4 ac:1 associated:4 ad:1 ai:3 certain:6 abstract:1 describe:1 am:1 denote:1 peres:6 quantum:5 single:7 associates:1 exist:7 journal:1 work:1 constructed:4 absurdum:1 47a:1 no:17 amounts:1 generally:1 arctan:1 application:1 other:5 becomes:1 mathematics:1 theor:2 briefly:1 elements:16 pˆ4:2 bundle:2 precision:1 a1:3 generated:4 a2:3 15e:1 a4:1 included:7 needed:2 structure:6 implies:5 required:6 together:4 having:2 far:1 observables:1 starting:1 original:3 once:1

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.