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quant-ph9910112.txt |@word represent:1 katz:1 consider:3 forbidden:1 particular:1 splitting:1 four:2 quadrature:1 woods:1 follow:2 expressions:6 contributions:2 compact:1 depend:1 calculate:1 re:4 groundstate:1 ie2:2 elliptic:1 under:2 include:1 amplitudes:12 very:5 frequencies:6 densitymatrix:1 unchen:2 upstream:1 mixing:6 experimentally:2 difference:1 condition:5 iν1:1 leads:2 iν2:1 incoherent:1 level:2 yin:1 solution:6 integrated:1 large:5 solved:1 vector:1 small:7 hνµ:1 optics:3 noted:1 fleischhauer:8 smaller:3 compensated:1 oscillation:5 deutsch:1 sin2:2 approximation:6 rate:4 a41:1 eik1:1 even:1 nonlinear:10 wavenumbers:2 imamo:4 cell:1 matsko:2 above:8 new:2 consisting:1 κl:7 millisecond:1 simultaneously:1 respectively:2 here:6 atoms:4 china:1 free:2 κz:1 relaxation:1 strong:1 equations:18 obtained:3 stark:2 involved:1 losses:3 allows:1 4wm:4 resonance:4 studies:1 glu:4 via:1 muenchen:6 yuen:1 root:1 vapors:2 electromagnetically:1 total:2 use:2 would:3 tightly:1 few:1 approach:1 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quant-ph9910113.txt |@word results:2 leads:1 entropy:2 edu:1 consists:1 follow:1 preferable:1 reparameterization:1 discern:1 certainly:1 inverse:5 depend:1 equivalence:1 29a:1 charge:1 does:1 alvarez:1 under:1 fax:1 puzzled:1 very:1 choice:1 introduction:1 electron:1 interpreting:1 difference:1 matrices:4 condition:1 presented:1 large:1 demonstrated:1 smith:1 barbara:1 noted:2 findings:1 sin2:1 literature:1 cosh:1 second:2 further:1 canonical:2 established:1 ubner:2 appear:1 near:4 uniform:2 reminiscent:1 grover:1 goes:1 renders:1 gh:1 method:2 3e:1 satisfy:2 multivariate:1 full:2 degree:2 fock:1 here:5 governing:1 sinh:3 others:1 concluding:1 slater:8 along:1 standard:1 appears:1 change:1 obtained:5 contrastingly:1 institute:1 my:1 study:5 studied:2 approaches:1 prior:20 twamley:2 extremes:1 resulting:1 scutaru:2 studies:2 york:2 via:1 convolution:1 marginal:6 logarithmic:2 iz:1 apply:2 univ:1 research:1 aharoni:1 use:4 asymptotic:1 would:3 commun:1 remains:1 chi:1 de2:1 scenarios:3 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quant-ph9910114.txt |@word secondly:2 four:5 localized:1 forget:1 whose:1 const:2 calculate:1 under:1 summarized:1 supports:1 solution:5 admissible:1 vector:11 heading:1 degeneracy:1 force:1 concise:1 estimates:1 approximation:5 second:8 chem:2 even:16 errors:4 forgetting:1 selected:1 above:5 new:17 coefficient:2 simultaneously:2 here:3 diagonal:8 asymmetry:1 represented:1 auxiliary:12 obtained:1 leaves:1 settles:1 couplings:14 suitable:2 rτ:1 propagators:6 linearly:1 would:4 abbreviations:2 m1:2 therefore:1 nagarajan:1 type:1 fractions:1 relax:1 naive:1 odinger:14 must:7 springer:2 language:2 quartic:3 mm:1 mn:1 mh:1 sturmian:1 root:3 example:11 unmarked:1 give:1 table:14 implementations:1 indicates:2 degenerate:5 feasible:1 guarantee:1 end:2 provide:1 verify:1 feature:1 very:9 nontrivial:3 ordinary:1 preferable:1 vollmer:1 description:2 oscillators:4 after:5 wrong:1 anharmonicities:3 summarize:2 constants:1 third:3 algorithms:1 enter:1 order:24 determinate:1 interpretation:3 wut:1 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quant-ph9910115.txt |@word consider:2 rev:2 magnetic:1 four:1 roy:1 entropy:2 computation:4 factorizing:1 certainly:1 white:1 factoring:2 alvarez:2 aut:1 te:1 dϕj:2 very:1 geometrical:1 coprime:1 fac:1 difference:1 condition:1 presented:1 solution:2 discrete:6 smaller:2 miller:1 sin2:1 second:1 design:2 cesar:1 will:12 what:1 above:1 new:1 consisting:1 contrast:1 desired:2 cos2:1 path:13 equations:1 appears:1 change:6 obtained:1 instituto:1 items:1 study:3 changed:1 cte:1 action:2 resonance:1 fourier:2 changes:2 helps:1 projection:3 family:3 alamitos:1 use:1 feb:1 takes:1 would:1 probabilities:2 next:3 type:3 until:1 more:4 introducing:1 company:1 particular:3 known:2 foundations:1 logarithm:1 high:2 science:1 equation:2 work:2 oscillator:1 reviews:1 remain:1 grover:23 following:2 example:1 process:7 preserving:1 conjecture:1 generically:2 states:2 indicates:1 minimum:1 uam:3 performed:3 want:1 feasible:1 normalize:1 information:16 end:3 kwiat:1 provide:1 discussion:1 get:4 answer:1 optimal:2 parameter:3 brassard:1 exemplify:1 after:2 hence:1 data:1 natural:1 liquid:1 computations:1 register:3 serrano:1 omez:1 complexity:9 so:1 playing:2 typical:1 operations:2 approx:1 over:2 cambridge:1 statistical:5 ieee:1 its:1 interesting:1 lj:4 isaac:1 mail:2 defining:4 eventually:1 non:6 processes:1 introduce:1 geodesic:4 symposium:1 now:1 bigger:1 ift:1 represents:1 inversion:1 always:1 university:1 siegmund:1 fφ:5 each:1 2n:1 characterized:1 doing:2 series:1 reduce:1 related:1 frequency:1 measurement:4 quantum:38 our:4 transitions:1 es:2 out:5 shown:1 gomez:1 space:9 lagrangian:2 looking:2 contained:1 induced:1 shows:1 theory:2 ısica:1 standard:2 completely:1 onoma:1 jozsa:1 definition:1 moment:1 used:1 ds2f:1 motion:1 frieden:1 universidad:1 consequence:1 think:1 first:4 xi:2 probability:7 variables:1 number:4 approximate:1 wash:1 done:1 robust:1 zalka:1 given:8 los:1 unitarity:4 their:1 reciprocally:1 ordered:1 variational:1 hoyer:1 way:2 continuous:1 part:1 than:4 scheme:1 holland:1 require:2 likely:1 determined:3 tion:1 modern:1 randomly:1 any:2 angle:1 depending:1 efficient:1 mial:1 sherwood:1 note:3 instance:1 algorithms:6 coincide:1 needle:1 paid:2 involving:1 connected:1 successive:1 nothing:1 class:8 considered:2 kj:4 average:1 order:2 proceedings:1 optical:1 exp:1 χl:1 typically:1 fact:2 quantity:1 shor:10 show:2 random:1 rotating:1 minimizing:1 chuang:1 find:5 tapp:1 slow:1 implementation:1 less:1 should:1 technologically:1 only:1 geodesics:1 constant:12 pointed:1 adiabaticity:1 do:2 means:3 de:2 ϕj:1 during:1 dp:1 evolution:1 arxiv:1 factorization:7 summary:1 exercise:1 view:2 set:2 achieved:1 bounds:1 see:1 computer:4 result:1 recently:1 phases:1 visualize:1 nuclear:1 yannoni:1 xvi:1 state:12 between:1 approach:1 preserve:1 notice:2 terms:2 attention:1 however:1 jr:1 csic:1 x2i:1 annual:1 equal:1 involve:1 whole:1 finds:1 boyer:1 otherwise:2 comment:1 minima:1 conclude:2 wootters:1 period:5 factorize:1 iterations:1 polynomial:2 respect:3 pp:2 transformations:6 basis:1 computing:4 three:1 been:2 mark:1 pj:8 ph:5 pi:7 define:6 corresponding:2 dolores:1 concerning:1 search:1 observe:1 spain:2 case:2 p0:1 exponential:2 bill:1 value:2 intimately:1 fubini:3 orica:1 35th:1 loop:3 unitary:10 metric:4 thus:1 suggest:1 clearly:1 quant:5 polyno:1 finish:1 trajectories:1 running:1 entanglement:1 changing:1 recent:1 appropriated:1 well:1 analysis:1 obviously:2 contact:1 greatest:1 model:1 gates:2 just:1 cj:3 dφ2:1 using:8 previous:1 point:5 lett:1 easy:1 input:2 haystack:1 mod:4 transformation:1 aspects:1 eigenvalue:1 possible:1 harmonic:1 increases:1 unification:1 know:1 dφj:1 press:2 integer:2 you:1 formal:1 like:1 adiabatic:5 steps:2 methods:1 classical:4 madrid:3 some:2 searching:3 2log:1 provided:1 does:2 provides:1 reaching:1 equivalent:1 mitchell:1 step:1 hilbert:7 proceed:1 about:1 constraint:1 discussed:1 dependence:1 o:3 practical:1 remains:4 estimator:1 mechanics:1 computational:1 publishing:1 into:1 references:1 reducing:1 log:9 there:1 transform:3 fast:1 start:1 conservation:2 lov:1 lot:1 function:14 north:1 form:1 schwindt:1 but:2 longer:1 maximum:1 us:5 crystal:1 solvents:1 projecting:1 problem:4 clear:1 strongly:1 associated:3 item:4 defined:4 abstract:1 measure:1 general:1 imately:1 conserved:1 distributions:3 check:1 defines:3 no:2 ekert:1 tight:1 other:1 role:2 np:1 nr:1 christof:1 problems:2 generated:1 fisher:23 brandt:1 faster:1 algorithm:35 dφ:2 physics:2 governed:1 time:10 decoherence:1 dϕ:1 starting:1 once:1
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quant-ph9910116.txt |@word monte:2 concept:2 consider:4 rev:8 magnetic:1 global:1 results:1 leads:1 entropy:1 rebbi:1 computation:1 inverse:3 depend:1 respectively:1 young:1 finally:1 those:2 under:4 tf:6 anharmonic:2 billard:2 conjecture:4 supported:2 amplitudes:2 far:1 wave:1 lyapunov:3 decide:2 experimentally:1 difference:1 fractal:1 dim:1 mc:10 hamiltonian:2 evaluation:1 weinberg:1 solution:9 large:2 solved:1 shuryak:2 small:2 relation:2 upper:1 smaller:1 occurrence:1 renormalized:18 miller:1 prediction:1 zero:5 displays:4 d7:2 rigorous:2 chem:1 carlo:2 analogue:1 spectral:3 what:3 errors:1 appear:1 giving:2 sum:2 expressed:1 goes:2 scientists:1 new:4 increasing:1 method:2 kicked:1 degree:1 galaxies:1 guangzhou:1 here:2 atoms:1 believed:1 china:4 ansatz:1 concluding:1 path:11 standard:1 equations:1 physiology:1 interpret:1 box:1 search:1 tunneling:2 institute:1 study:1 studied:1 allows:1 recently:1 domains:1 makes:1 jackiw:2 departement:1 via:3 useful:1 highly:1 giannoni:1 gluon:1 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quant-ph9910122.txt |@word logarithms:1 partial:11 consider:3 desirable:1 results:5 four:2 entropy:13 computation:1 edu:1 manipulations:1 reasoning:1 row:2 whose:2 calculate:1 aug:1 tr:2 environment:1 thapliyal:4 finally:1 under:2 division:1 conjecture:5 collaborate:1 kraus:1 far:1 corollary:6 every:1 mixing:2 affect:1 matrices:3 condition:5 tra:2 irreducible:5 trb:2 upb:2 small:1 eigenvalues:4 barbara:2 noted:1 prevent:1 smaller:1 lewenstein:2 among:1 direct:2 zero:8 cost:2 further:2 even:3 subadditivity:1 appear:1 bc:3 quantifying:1 expressed:1 pawel:2 above:3 international:1 method:1 contrast:1 paradoxical:1 satisfy:1 bruß:1 full:1 respectively:1 error:1 teleportation:1 understanding:1 following:1 explore:2 plenio:1 based:1 obtained:3 remark:3 ρil:1 technical:1 study:1 vectors:1 approaches:1 leaving:1 amount:5 schumacher:2 action:1 complicated:1 bob:5 cancellation:1 named:1 via:1 dyn:1 scales:1 spooky:1 ask:1 should:2 univ:1 bangalore:1 unit:1 use:4 additive:1 asymptotic:6 would:6 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quant-ph9910123.txt |@word consider:2 r1x:1 leads:2 commute:1 expressions:3 causes:1 concerned:1 finally:1 p2:24 r10:1 very:1 eis:1 condition:1 positions:1 large:2 small:1 says:1 second:1 value:4 appear:1 experiment:1 localized:1 above:4 obvious:1 satisfy:1 outgoing:1 here:1 directions:7 along:3 incoming:1 dp1:2 institute:1 vectors:1 resulting:3 usually:1 fourier:1 explained:1 decrease:1 de0:1 e1:6 nonnegligible:1 m1:2 therefore:1 m2:2 until:1 israel:2 becomes:2 hold:1 recall:2 equation:2 work:1 dej:1 values:4 expanding:2 involve:1 collision:2 sharp:1 occur:1 r20:1 decaying:1 rather:1 six:1 write:3 how:1 sin:6 massive:1 description:1 may:1 after:1 parallel:1 lines:1 correspond:1 so:5 gerard:1 first:1 order:1 typical:1 holds:3 indeed:2 move:1 statistical:1 p1x:1 satisfies:1 still:1 its:2 before:1 perfect:2 decay:1 sergienko:1 vicinity:2 coordinates:3 detected:1 choose:1 main:2 pittman:2 fragment:1 introduce:1 nov:1 now:2 always:1 asher:1 parameters:1 each:5 found:1 ei:3 ej:1 energy:3 decays:2 quantum:2 wavelength:1 eq:8 shown:1 since:1 rev:2 research:1 particles:15 cause:2 rj:1 free:1 standard:1 reason:1 beginning:1 e0:3 e2:6 pairs:1 r0:2 r1:13 r2:9 motion:2 isotropic:2 integrand:1 origin:1 there:4 symmetry:2 variables:1 restrict:1 intuitively:1 angular:2 given:4 cartesian:1 width:2 system:3 relations:2 their:1 behaved:1 gives:1 shell:1 exactly:1 peaked:6 detection:1 zero:2 were:1 ann:1 seen:1 conversion:1 angle:1 latter:2 mid:1 k2:2 k1:2 broglie:1 opposite:12 correlation:1 but:3 pair:2 diametrically:1 why:1 deviations:4 technion:1 considered:1 request:1 points:1 velocity:2 physics:2 show:1 supported:1 radii:1 q1:2 q2:2 dp2:2 spite:1 dp0:1 only:7 explicitly:1 de:1 expectation:1 words:1 dp:2 transversal:1 arxiv:1 yield:1 dpj:1 frame:1 observed:2 namely:4 exponent:5 definite:1 various:1 between:2 caves:1 conditions:1 recently:1 however:7 article:3 problem:3 observable:1 cos:11 uncertainty:1 contribution:1 comes:1 nonrelativistic:2 corresponds:1 simply:1 moreover:1 pr:2 described:1 describes:1 pj:6 ph:1 define:1 θj:1 fund:2 angles:1 demand:1 irrelevant:1 present:4 case:5 eip:1 p0:9 p1:27 straight:2 evaluated:3 will:3 near:2 situation:1 property:2 maximal:1 vj:2 thus:3 encouragement:1 technology:1 different:1 same:2 quant:1 wavepacket:5 φj:1 peaks:1 see:3 appreciably:1 v1:2 v2:2 moving:1 purpose:1 center:1 well:2 experimental:1 components:2 coordinate:1 parametric:1 usual:1 spherical:6 λr:1 rest:1 momenta:6 yet:1 alignment:4 rapid:2 photons:1 point:1 spread:2 swope:1 momentum:4 identical:1 around:3 spectacular:1 evaluate:1 possible:1 increases:1 appearing:1 particle:7 follows:1 stationary:5 reduced:1 because:1 wavepackets:2 classical:4 some:1 respect:2 oscillations:2 provided:1 lead:2 strekalov:1 broad:1 integration:1 does:6 centroid:1 fragments:3 wavefunctions:1 2m:1 simpler:1 discussed:1 letters:1 rj0:1 into:3 integral:4 down:1 phase:6 operator:2 relativistic:1 shells:2 initial:1 approximate:1 start:1 conservation:1 way:2 was:2 hp:1 ht:1 expected:2 haifa:1 line:1 whether:1 variations:1 us:4 below:1 verification:1 distribution:4 similar:2 mechanics:1 shih:1 likewise:3 abstract:1 peres:2 single:1 moves:1 physical:1 stationarity:1 wavefunction:2 when:5 ny:1 other:3 spatial:1 department:1 deviation:1 prepared:1 ξj:6 correlated:2 implies:1 assume:3 mass:1 time:2 having:1
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quant-ph9910124.txt |@word partial:1 consider:14 rev:1 varying:1 results:9 leads:5 proposition:4 computation:1 go:3 follow:1 expressions:5 compact:1 looking:4 c0:1 depend:2 calculate:7 advantage:2 eigenbasis:1 tu:3 tr:59 ts:44 finally:2 tm:3 clones:1 under:2 ρa:2 summand:2 straightforward:2 very:6 ρc:1 choice:1 unitaries:2 every:5 commute:1 fall:31 difference:2 matrices:5 rn:1 condition:1 groups:1 dim:10 level:1 bn:1 turns:2 solution:2 try:1 admissible:2 convenience:1 undone:1 math:1 small:3 eigenvalues:2 equation:36 upper:6 alluded:1 semicontinuous:1 haar:1 summarizing:1 estimates:2 direct:2 cosh:4 approximation:2 fold:3 rate:21 design:1 evaluated:2 infimum:3 gn:1 further:5 estimated:2 odd:1 substitute:1 theory:15 even:7 will:29 what:3 plays:1 stands:1 invertible:1 section:24 near:1 expressed:1 applied:1 reminiscent:1 version:3 reconstruction:3 sup:1 judicious:1 obvious:2 increasing:3 l1:1 method:1 contrast:2 full:4 simultaneously:1 whose:1 respectively:3 never:1 component:3 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quant-ph9910125.txt |@word hull:1 vila:1 concept:1 consider:2 remarkable:1 funct:1 excepting:2 keep:1 illustrated:4 roy:3 ge:1 spiridonov:5 consists:5 denotes:3 whose:1 depend:2 chain:2 aug:1 iii:2 technique:11 simplify:2 finally:1 those:5 worth:3 witten:1 deforming:1 far:1 connects:1 choice:2 manipulated:1 socorro:1 nieto:5 difference:2 fractal:1 leads:4 hussin:2 level:19 skills:3 positions:2 unscaled:2 solution:8 solved:1 eigenvalues:1 subindex:1 der:1 sukhatme:1 α2i:1 direct:1 sign:1 painlev:1 design:2 value:2 further:1 implemented:2 driel:1 shayegan:1 spectral:30 iterating:1 ˆx:2 section:18 selected:1 labeled:1 expressed:2 designing:3 new:12 increasing:1 method:5 contrast:1 satisfy:1 wehner:1 simultaneously:1 degree:1 mechanisms:2 spacing:1 here:1 understanding:1 behaviour:1 explore:2 possibility:3 others:1 concluding:2 based:2 along:1 standard:26 equations:5 change:4 widening:1 obtained:4 instituto:1 dα2:1 institute:1 study:2 changed:3 resulting:1 fernandez:1 action:1 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quant-ph9911001.txt |@word 2m2:2 sector:3 played:2 consider:3 just:1 show:1 over:1 roc:1 course:1 cambridge:1 solutions:5 summed:1 consists:1 taiwan:1 eigenstates:1 pj2:2 q1:1 unique:1 number:2 calculate:1 parameters:1 density:6 chosen:1 tw:1 fix:1 complex:3 should:1 h2:1 only:1 other:3 restriction:1 choose:1 under:1 role:1 hidden:1 playing:1 presentation:1 oct:1 momentum:1 arguments:1 real:3 case:2 momemtum:1 get:3 very:3 frequencies:1 expectation:2 wave:2 p1:1 hamilton:3 words:1 press:2 using:1 nov:1 now:3 dimensionless:1 eigenvalue:1 term:1 2p:3 2q:1 immediately:1 hamiltonian:22 goldstein:1 follows:1 university:1 arxiv:1 large:5 mode:2 always:1 indices:1 2m:15 2n:2 qj:5 bong:1 require:1 mπi:1 because:2 classical:1 physically:1 energy:6 edu:1 some:2 relative:1 differentiation:1 imply:1 frequency:6 value:2 eliminating:1 quantum:8 small:4 approximated:1 eq:17 ep:2 canonical:4 even:1 xψ:1 potential:2 give:2 mentioned:1 oxford:1 furthermore:1 since:1 integration:1 denotes:1 looking:1 comparision:1 various:1 above:2 between:1 new:2 prentice:1 before:1 conditions:1 satisfy:1 exactly:2 terms:3 linear:3 respectively:3 q2j:2 attention:1 interested:1 qi:5 york:2 address:1 put:1 approach:3 imaginary:3 hand:1 ηj2:2 generate:1 eψ:1 obtained:1 pairs:2 yeung:1 prescription:1 wesley:1 institute:1 sinica:2 could:1 larger:1 side:1 motion:3 turn:1 variable:1 rewrite:1 interesting:1 hence:3 2h:2 think:1 taipei:1 first:1 come:1 xh:1 there:1 xn:1 nonrelativistic:1 simple:1 variables:11 obtaining:1 ηj:5 ηi:5 negative:1 dimensional:1 nothing:1 right:2 drawback:1 relations:2 respect:1 electronic:1 planck:6 schrodinger:8 given:3 smaller:1 superpositions:1 wai:1 similarly:1 πj:5 equations:4 πi:5 atomic:1 system:14 construct:2 appears:1 iq:2 much:1 slowly:1 low:2 pj:5 mks:1 ph:1 pi:5 gives:1 function:5 considerably:1 corresponding:3 form:3 regard:1 but:1 repeated:1 dirac:1 dimensionalities:1 varying:2 known:1 x1:5 than:2 must:1 p2:5 fuction:1 ma:1 look:1 roles:1 characteristic:2 equation:10 particle:1 us:3 worth:1 will:13 cast:1 determined:1 limit:1 mp:1 applies:1 following:2 problem:1 more:1 care:1 result:1 mechanics:7 dn:6 constant:5 they:1 coupled:1 mqi:1 ip:1 secondly:1 conventional:1 thus:1 surface:1 evolution:1 ih:3 itself:1 mc2:2 conjugate:3 seen:1 bohm:1 different:2 things:1 divided:1 when:1 same:2 read:1 parts:5 quant:1 take:1 units:2 ensure:1 coincide:2 parameter:5 independent:1 used:2 superposition:1 normal:2 our:5 time:4 radically:1 πj2:2 important:1 pair:1 mpi:1 constants:1 independently:1 natural:1 effective:1 discarding:1 into:3 order:1 4n:1 academia:1 mass:1 principle:1 mechanical:2 firstly:1 quadratic:3 hall:1 physics:1 dimension:3 fact:1
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quant-ph9911002.txt |@word limited:1 sci:1 consider:2 represent:1 hint:4 forbidden:1 global:1 dynamic:1 results:5 fig7:1 mild:1 entropy:1 equalized:2 go:4 follow:2 preferable:1 localized:3 rigidity:1 compact:1 whose:5 certainly:1 inverse:1 calculate:2 deterministic:2 answered:1 finally:1 does:6 analogous:1 include:1 case:2 probe:4 straightforward:1 continues:2 wigner:3 wave:37 figs:8 kcr:1 resonant:1 husimi:3 difference:3 exact:1 conserved:2 induced:4 level:1 positions:3 integrating:1 solution:1 t0:2 pˆ1:8 discrete:1 spaced:2 pˆ2:3 eigenvalues:2 inconsistent:1 averaged:4 force:1 periodicity:1 hk2:1 hk1:1 estimates:1 matrices:1 consists:1 second:5 complicates:1 settled:2 further:6 dynamics:22 estimated:6 canonical:3 even:6 index:1 what:3 nonlinear:1 section:7 axes:1 expressed:1 3t:2 consistently:2 causes:2 roundoff:1 fig1:1 row:2 consisting:1 contrast:2 kicked:19 notions:1 degree:3 ranged:1 respectively:14 gathered:1 never:2 here:3 adachi:7 believed:1 flannery:1 possibility:2 address:1 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quant-ph9911003.txt |@word limited:1 consider:3 remarkable:1 ali:1 magnetic:3 results:5 leads:1 known:2 generalize:1 edu:1 consists:1 follow:1 whose:1 depend:1 eigenbasis:2 tr:1 finally:1 those:2 γm:18 must:1 ingredient:1 mondrag:2 orthogonal:1 very:1 geometrical:3 noncyclic:2 hannay:1 emphasized:1 difference:2 exact:5 condition:6 hamiltonian:31 ref:1 solution:9 integrated:3 discrete:2 vector:4 small:4 eigenvalues:4 originally:1 degeneracy:1 neighborhood:4 consistent:1 approximation:5 zero:1 further:1 dψ1:1 established:1 what:1 stands:2 putterman:1 sum:1 expressed:1 above:2 sup:1 new:6 evolving:5 hern:1 respectively:3 never:1 here:3 atoms:1 explore:1 sinh:2 address:1 directions:1 along:2 equations:4 extreme:2 obtained:3 study:3 vectors:1 allows:1 suggests:1 periodic:17 resulting:2 miniatura:1 changes:1 foundations:1 sire:1 addressed:1 apply:1 total:1 conventional:4 takes:1 distinct:2 e1:3 next:4 ψk:8 ψn:19 therefore:3 ψm:2 torre:2 metric:1 more:2 odinger:2 validity:1 berlin:1 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quant-ph9911004.txt |@word chinese:2 query:1 simon:1 helps:1 r12:2 r13:2 song:1 very:2 exact:2 gui:1 large:2 vector:19 chuang:1 superalgebras:1 sin2:9 zero:2 pass:1 further:2 even:1 what:1 sun:3 celebrated:1 version:1 new:1 3d:1 ψo:1 component:2 here:2 china:3 cos2:3 pati:1 obtained:1 search:8 generalizing:1 institute:1 involved:1 larger:1 usually:1 chang:2 involves:1 explained:1 marked:11 plot:1 commun:1 chi:1 process:2 therefore:1 ψa:1 theoretical:1 particular:1 known:1 kumar:1 rotational:6 equation:1 det:1 grover:8 hansen:1 hosoya:1 beijing:2 figure:1 give:1 calculation:1 neglected:1 states:1 chin:1 tan:1 counting:1 r23:2 r22:2 r21:2 axis:20 orthogonal:1 csc:1 vital:1 optimal:1 explains:1 sin:33 brassard:3 fu:1 applications:2 plane:4 mag:1 summarize:1 data:1 parallel:3 realized:1 remember:1 light:1 su:7 element:1 algorithms:1 order:1 operations:1 gershenfeld:1 interpretation:2 eigen:1 displayed:1 expects:1 through:1 still:1 group:6 solving:2 li:1 lu:1 systems:1 lx:1 mismatches:2 tsinghua:1 gate:1 rotation:8 now:1 yu:1 transparent:1 easily:1 university:3 peking:2 each:3 found:3 heavy:1 spinor:1 ei:1 accelerator:1 measure:1 quantum:14 laboratory:1 operation:1 ru:2 shown:3 matrix:1 space:1 res:1 since:1 rev:3 eprint:2 ra:2 formula:1 ro:3 ref:2 theory:2 r11:2 jozsa:1 arccos:2 throws:1 first:1 origin:2 initial:3 probability:5 number:2 zalka:2 passes:1 given:5 top:1 approximately:1 their:1 1n:2 academy:2 exactly:1 than:1 iteration:1 contrary:1 amplitude:5 gives:1 argument:1 manner:1 any:3 lie:2 angle:6 lin:1 polarization:1 instance:2 generalized:5 finding:2 so:11 formulas:2 multiple:1 trace:7 centre:1 reach:4 most:2 letter:1 phase:14 r31:2 r32:2 r33:2 typeset:1 yang:1 li1:1 physics:3 vandersypen:1 rotating:1 relation:2 d2:1 tapp:2 state:29 iei:1 only:1 factor:1 circle:5 hope:1 continuity:1 di:1 overall:1 satisfied:1 nearly:5 theta:2 during:1 neither:1 arxiv:1 requirement:3 tu1:1 national:1 achieves:1 see:1 computer:1 nuclear:1 written:3 various:1 between:2 drawn:1 geometric:1 luo:1 recently:1 nature:1 qubits:1 however:3 interation:1 uτ:4 distribution:2 cos:28 cot:6 many:1 equal:1 figures:1 qubit:1 boyer:1 arbitrarily:1 simple:2 corresponds:7 dimensional:1 spans:1 crystalline:1 basis:1 been:7 describes:1 ph:13 algebras:1 fig:3 lanzhou:1 understand:2 c2:1 case:4 novel:3 value:2 iτ:2 zhang1:1 near:1 behavior:1 unitary:3 thus:1 xiao:1 cone:1 ie:1 develop:1 clearly:5 quant:13 difficult:1 development:1 phi:2 numerical:1 effect:1 ion:1 kim:1 center:1 well:1 position:1 just:2 being:1 when:7 rotated:1 rotates:2 nov:1 hai:1 han:2 sciences:2 wei:1 lett:4 easy:1 cun:1 transformation:3 aspects:1 iγ:2 entangled:1 press:2 using:1 rotate:1 helpful:1 exploiting:1 mismatching:2 steps:1 arbitrary:7 searching:4 understood:2 b2:2 matching:7 eiθ:1 eiξ:1 demonstrated:1 bd:1 nmr:1 bc:1 bi:1 step:1 substituted:1 revtex:1 eiφ:1 about:2 certainty:1 pu:1 important:1 within:1 rotations:3 references:1 operator:2 tilted:1 fortsch:1 span:1 there:1 approximate:2 long:2 yan:1 lov:1 naturally:1 but:3 failure:1 pi:3 maximum:2 us:1 problem:2 ac:1 ad:1 computing:1 abstract:1 general:1 check:1 constructed:1 mosca:1 no:2 tip:7 department:1 theor:1 picture:7 zheng:1 prepared:1 a2:2 bounded:1 structure:1 jones:1 longer:2 algorithm:19 lanl:2 time:1 n1:2 n2:1 requires:2 original:4 evenly:1
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quant-ph9911005.txt |@word consider:1 varying:2 results:1 comments:1 depend:1 paris:1 finally:1 those:1 under:1 amplitudes:4 frequencies:4 wave:3 print:1 sidebands:1 condition:3 vibrational:7 hamiltonian:5 knight:2 notes:1 proposals:1 solution:1 optica:1 puebla:1 leave:1 optics:1 noted:1 upper:1 dutra:1 divergencies:1 approximation:1 second:1 further:1 dynamics:2 odd:1 even:1 nonlinear:3 below:1 above:1 ˆi:1 respectively:1 spacing:5 here:2 relaxation:1 equations:1 obtained:1 remark:1 maccone:1 vectors:1 resonance:1 changes:1 matos:4 via:2 consejo:1 apply:1 unit:1 use:1 superpositions:5 would:5 remains:1 ψs:12 negative:1 therefore:3 ciencia:1 initial:1 emission:5 particular:3 valued:1 mc:1 decouples:1 equation:2 vibronic:1 following:1 spontaneous:2 example:1 proof:1 control:1 ions:1 states:17 lamb:2 filter:1 fortunato:2 archive:1 describes:2 xˆ:6 write:1 pure:1 instead:2 parameter:2 simplicity:1 cessa:5 may:3 applications:1 wallentowitz:3 realized:1 ionic:1 light:3 correspond:1 element:1 so:1 fundamental:1 representation:1 acknowledges:1 order:1 mexican:1 cerda:1 mainly:1 thermal:1 lasers:2 controllable:2 thank:1 ln:1 lm:3 lk:4 writing:1 choose:2 lq:1 rabi:3 non:1 propose:2 effects:1 they:1 acta:1 nov:1 now:1 n01:2 n02:1 easily:1 term:1 level:1 sideband:6 possibilities:2 stopped:1 trap:1 l1:1 ηs:2 universit:1 macchiavello:1 mean:1 em:1 ej:1 generation:2 energy:2 frequency:3 combining:1 quantum:3 our:1 transitions:1 eq:4 shown:1 tombesi:2 matrix:1 driving:3 space:1 dsw:1 rev:12 denotes:1 mν:1 occurs:1 pue:1 fisica:1 generate:5 milburn:1 interaction:3 geometry:1 could:1 transition:2 linearizing:1 motion:5 undergo:1 interact:1 first:1 major:1 already:1 manuscript:1 laguerre:1 number:16 done:1 changing:1 electronic:4 angular:2 engineer:3 given:3 eqs:1 system:1 avez:1 needed:1 master:1 scheme:3 ranging:1 trapped:2 ch:1 part:1 x2:1 than:1 approximations:1 rate:1 preparation:1 kth:2 treated:1 argument:1 manipulating:1 orders:1 depending:1 note:2 instance:2 potential:1 towards:1 electric:1 sherman:2 kj:1 later:1 steady:2 drive:1 km:1 typeset:1 ks:2 fact:1 spaced:1 show:1 rotating:1 ground:1 based:3 parameters:2 less:1 written:5 should:2 only:1 di:2 de:6 kurizki:3 fields:3 arxiv:1 tuned:2 n12:1 achieved:2 freitas:1 zones:1 see:1 discussions:1 ηk2:1 qth:1 annihilation:1 definite:1 motional:1 qubits:3 state:12 jth:1 barranco:1 limit:1 reading:1 conditions:6 available:1 recently:2 extend:1 initially:1 however:1 concentrate:1 both:3 protect:1 last:1 chosen:1 filho:4 contribution:1 apdo:1 filtering:2 cn:8 dipartimento:1 harmonic:1 nˆ:1 exploit:1 associated:1 cp:1 schleich:2 aˆ:2 three:1 been:5 much:1 detrimental:1 pj:1 ph:2 ariano:1 corresponding:1 tecnolog:1 coherent:2 c0:1 importance:1 present:2 case:5 laser:6 moya:5 value:1 will:1 delle:1 larger:1 vogel:9 mexico:1 vk:1 them:3 reads:1 itself:1 ia:1 madonna:1 technology:1 different:2 italy:1 same:2 any:1 quant:2 inaoe:1 driven:1 ion:12 decouple:1 robust:3 qubit:1 normalization:1 lower:3 schr:1 without:1 λs:1 restore:1 proposed:3 emerge:2 being:1 obtain:6 ldp:1 λe:1 using:3 dicke:2 nacional:1 other:1 conacyt:1 lett:3 mod:1 resolved:1 tests:1 february:1 press:1 integer:1 postal:1 apart:1 like:1 camerino:3 pol:1 specific:3 arbitrary:2 fulfil:1 because:1 methods:2 classical:2 conditional:1 some:1 fluorescing:1 choosing:3 separately:1 lead:1 broad:1 measurements:1 stops:2 assuming:1 noise:3 selecting:1 vitali:1 revtex:1 references:1 ηj2:2 hilbert:1 sacchi:1 ρˆe:1 efforts:1 ρˆs:1 jν:1 ηe:1 ηm:3 ηk:1 ηj:2 accounts:2 operator:3 support:1 there:1 long:2 noticed:1 cats:1 way:3 garraway:1 function:1 but:3 matematica:1 directed:1 infm:1 characteristic:1 flip:1 mth:1 ωj:2 ωm:2 spectroscopy:1 distribution:2 mechanics:1 constant:1 certain:1 abstract:1 aj:2 am:2 single:4 internal:1 regime:1 ekert:1 when:3 field:5 setting:5 conclusion:1 picture:1 generates:1 excitation:3 polynomials:1 odinger:1 generated:3 coupling:1 assume:1 lanl:1 time:2 n0:1 n1:1
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quant-ph9911006.txt |@word represent:1 dsu:1 sci:1 consider:1 caused:1 stems:1 results:4 four:1 roy:3 scalar:7 go:2 3a2:1 expressions:3 2r0:2 const:12 calculate:1 concerned:1 technique:6 factoring:1 passage:1 finally:1 program:1 under:2 a42:1 nodes:3 goodson:1 divergent:1 case:6 r12:1 account:2 wave:6 breit:1 emphasized:1 exact:5 condition:7 leads:1 solves:1 solution:2 large:4 solved:1 vector:7 math:3 perturba:1 small:3 eigenvalues:8 warszawa:1 equation:16 encloses:1 work:1 zh:1 natur:1 sign:2 approximation:6 3a3:2 imply:1 further:3 implemented:1 quite:1 what:1 nonlinear:1 appear:1 foregoing:1 consequent:1 indian:1 above:2 new:6 3a4:2 method:7 contrast:1 notions:1 fiz:2 eksp:1 component:6 here:3 nodeless:1 behaviour:4 pratt:1 address:2 represented:2 consideration:4 standard:5 equations:4 logarithmic:9 differential:1 obtained:5 parameters:1 difficulty:1 involved:1 study:1 stipulates:1 ab2:1 ab3:1 published:1 conveniently:1 suitable:2 makes:1 exited:7 involves:1 york:1 varshni:3 via:1 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quant-ph9911007.txt |@word replacing:1 now:1 descartes:2 vorticity:6 consider:3 pointing:1 maximum:1 rev:8 magnetic:7 varying:1 results:1 bennemann:1 illustrated:1 ginzburg:1 concept:1 broader:1 edu:1 follow:2 depend:2 concerned:1 simplify:1 precession:1 according:1 squeezing:2 those:4 lord:2 dramatically:1 ta:2 advantage:1 orthogonal:2 very:1 wave:75 kaminski:1 every:1 paraboloid:1 summarized:1 difference:3 exact:4 condition:6 leads:2 annihilated:1 mc:1 presented:2 solution:11 travels:1 admissible:1 vector:15 d3:1 small:1 gauge:1 shows:1 optics:1 equation:23 english:1 physics1:1 sin2:1 za:1 sign:1 past:1 zero:6 dynamics:7 linear:3 even:3 what:1 nonlinear:3 plays:1 appear:5 sum:2 8m:1 remain:2 thickness:1 above:2 new:3 method:2 satisfy:1 edited:1 vx:1 full:2 evaluating:1 degree:3 component:3 here:1 atoms:2 met:1 objects:1 tangent:1 separate:1 based:3 along:11 quite:1 respect:6 appears:1 change:4 obtained:7 stringari:1 institute:2 study:7 studied:1 approaches:2 commonly:1 usually:1 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quant-ph9911009.txt |@word discards:1 logarithms:1 concept:2 partial:1 consider:16 chain:3 secondly:1 induces:1 equalities:1 global:3 unique:1 splitting:1 four:3 entropy:61 per:10 computation:2 projective:1 issues:2 whose:1 preserves:1 maximally:1 depend:1 calculate:1 graph:1 equivalence:5 characterises:2 send:2 passage:1 environment:1 finally:1 monotonically:14 preserved:1 th:1 under:3 analogous:2 include:1 sent:2 ingredient:1 overlaps:48 division:1 conjecture:1 deforming:2 string:1 g1:3 orthogonal:8 very:3 results:5 suggesting:1 wishes:3 every:3 entries:3 isi:1 matrices:12 deformations:13 condition:7 common:1 leads:2 school:1 squares:1 altering:1 positions:2 xyz:1 list:1 solution:3 fewer:1 t1:1 noiseless:1 deformed:3 vector:1 math:3 recall:1 small:2 eigenvalues:18 optics:2 noted:1 smaller:4 grateful:2 direct:4 suffices:1 sign:1 equation:1 gmbh:1 pass:1 further:5 lanl:2 choices:2 distance:1 linear:1 even:1 what:3 sub:1 richard:1 brackets:1 giving:7 diag:2 section:2 brief:1 expressed:2 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quant-ph9911010.txt |@word sch:1 leads:3 parker:1 follow:1 depend:1 pˆi:1 pˆj:2 finally:1 spain:1 exposition:1 te:2 applied:1 string:1 g0:1 very:1 choice:1 suggesting:1 electron:2 witten:1 putting:1 nieto:3 difference:1 condition:1 4n2:1 positions:1 solution:4 pˆ2:1 small:2 eigenvalues:1 mangano:2 commented:1 bonnor:2 sin2:1 l2l:2 zb:1 sign:1 me4:1 zero:3 perspective:1 me2:1 further:2 aim:1 appear:2 diag:1 contributed:1 new:3 ever:1 method:2 3d:11 coefficient:1 confluent:1 entailing:1 respectively:2 here:2 atoms:1 ionization:1 tangent:1 free:1 sinh:1 november:1 strong:2 equations:1 κr:5 obtained:3 instituto:1 exemplified:1 algebra:2 study:1 studied:2 allows:1 suggests:2 accomplished:1 hospitality:1 identification:1 useful:1 scales:1 modifying:1 decrease:1 limb:1 herranz:2 planck:2 working:1 recalling:1 positive:10 contains:1 negative:7 going:2 therefore:2 taken:1 type:4 today:1 more:1 flat:4 corrected:1 odinger:12 curvature:21 particular:1 known:1 cases:1 account:2 rotational:1 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quant-ph9911011.txt |@word proposition:3 titech:2 saturating:1 consider:6 pointing:1 desirable:1 gf:1 code:31 generalize:1 computation:1 edu:1 denotes:5 θp:10 gi:4 row:1 whose:1 calculate:1 aug:2 fellowship:1 knill:4 young:1 send:1 environment:2 finally:1 critical:1 present:1 th:1 teaching:1 presentation:1 alternating:4 g1:3 orthogonal:11 ieice:1 choice:1 corollary:1 anonymous:1 lecture:1 sony:1 matrices:2 condition:1 presented:3 notes:2 occurs:1 large:2 vector:3 gruyter:1 β2m:2 mn:2 α2m:2 fold:1 second:1 cost:1 chen:3 eigenspaces:1 pmk:1 bilinear:5 errors:7 appear:1 section:13 decoding:12 nondegeneracy:1 version:3 scientists:1 values:1 method:2 aij:3 modify:2 b2r:1 nonbinary:2 china:1 november:1 obtained:3 search:1 receive:1 shift:3 vectors:2 contradiction:1 aω:2 products:2 via:6 apr:1 merely:1 ookayama:1 outcomes:3 sloane:2 apply:1 linearly:1 use:2 additive:5 would:4 positive:2 readable:1 next:2 vol:11 bases:2 call:1 exhaustive:1 more:1 pless:2 constructs:2 cases:1 iii:1 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quant-ph9911012.txt |@word limited:2 consider:1 results:5 hole:1 technique:1 under:2 worth:1 applied:2 worse:1 advantage:2 very:1 trigonometric:3 putting:2 exact:12 condition:6 turns:1 t2:1 solution:1 t1:1 dealt:1 small:4 estimates:2 approximation:7 second:2 value:1 further:1 chem:4 even:2 giving:1 assistance:1 brief:1 version:2 new:1 method:2 satisfy:2 dman:1 here:2 atoms:1 consideration:1 z1:2 change:1 box:2 great:1 roychoudhury:2 institute:1 study:6 studied:1 p2:1 superpotential:3 products:1 studies:1 oschl:6 varshni:1 poorest:1 useful:1 visible:1 viz:4 unit:1 takes:2 noting:1 taken:2 more:1 binding:1 emission:1 berlin:1 particular:1 cases:2 must:2 high:1 springer:1 science:1 equation:5 work:1 modified:1 values:2 publications:1 give:3 india:2 states:2 council:1 tan:1 eigenenergies:4 chemical:2 far:2 influences:1 opt:1 ordinary:1 sin:3 sommerfeld:4 algebra:1 may:1 thermodynamic:1 earlier:1 singularities:1 dx2:2 barriers:1 wave:4 short:2 outline:1 light:1 so:2 worst:1 acknowledges:1 eigen:3 paper:1 statistical:1 omitting:2 its:2 roots:2 superior:1 energies:6 ionised:1 writing:2 better:2 systems:2 mail:2 non:1 framework:3 walls:2 effects:1 they:4 nov:1 now:1 teller:6 represents:3 l2:2 each:2 2l:9 2m:3 bond:1 en:2 wentzel:2 significantly:1 series:1 energy:5 sinha:2 quantum:10 v01:11 ep:2 special:2 out:1 gol:1 matrix:3 since:1 research:1 investigation:1 formula:2 ref:3 correct:1 red:1 after:1 theory:1 reformulated:1 found:1 b30:1 adhikari:3 formation:1 york:1 put:1 estimate:1 e1:6 times:1 hence:2 first:2 industrial:1 armitage:1 directly:1 given:1 koo:1 similarly:1 introduction:1 system:3 acknowledgment:1 perturbations:1 brevity:1 calculations:2 eqn:1 πx:2 molecular:3 gives:5 ryzhik:1 asymmetric:1 2al:1 optical:1 somewhat:1 authors:3 x2:1 x1:1 than:3 approximations:2 raman:1 motivation:1 modern:1 raj:1 wilson:3 ideal:1 potential:11 added:2 unless:1 though:3 quote:1 wells:4 marin:1 formulae:1 extremely:1 coincides:1 exp:3 physics:2 fact:1 dover:1 precise:1 particularly:2 nπ:1 substituting:1 d2:2 find:3 ground:7 aπ:2 written:3 only:1 indian:1 molecules:1 factor:1 identification:2 aα:2 famous:3 ones:1 dz:2 brillouin:3 dx:10 invariant:1 dt:1 normalizable:1 arxiv:1 analytical:8 fixed:1 exists:1 our:3 observed:3 sec:5 w0:2 recently:1 techniques:1 et2:1 αx:9 symmetric:1 state:7 various:3 between:1 isical:2 approach:5 terms:1 nature:1 importance:4 reproduces:4 extent:1 alters:1 suggested:2 both:6 cos:1 cot:8 v02:11 many:1 quantization:12 improves:1 context:1 comment:2 mechanics:2 had:1 dimensional:2 ley:1 throughout:1 cavities:1 tremendous:2 due:1 been:3 z2:4 ph:1 obtained:1 arises:1 supersymmetric:3 kramers:2 confinement:3 plasmas:1 c0:3 those:1 case:3 ǫn:1 evaluated:1 will:1 cast:2 a21:3 a22:4 wkb:13 thus:3 reads:1 confining:2 eigenfunction:2 lengthy:1 inc:1 flugge:1 periodic:1 quant:1 units:1 gets:1 fairly:1 used:1 functions:2 v0:9 v1:1 v2:1 potentials:10 infinite:3 normalization:2 recent:1 schr:5 well:6 bohr:4 academic:1 solids:1 calcutta:1 dimension:2 usual:2 being:3 accurate:1 obtain:1 press:1 shape:1 atomic:1 scattering:1 tables:1 conclusions:1 absorption:1 help:1 reactivity:1 identical:2 around:1 rules:3 cruz:1 mol:1 confined:2 using:1 tangentially:2 reduces:2 yields:1 either:1 integrals:1 planelles:2 www:2 methods:1 deal:1 some:1 transport:1 scientific:1 infra:1 pressure:1 bs:6 properties:4 impenetrable:1 eqns:1 discussed:3 practical:1 range:1 gradshteyn:1 integral:1 bound:2 gomes:3 references:1 financial:1 mbs:7 gases:1 capacitance:1 function:2 form:5 considerable:1 partially:1 inside:1 different:1 cosec:5 detailed:1 ac:2 taylor:1 int:3 abstract:1 single:1 formulation:3 az:1 physical:1 again:1 radically:1 compared:1 electrical:1 branch:1 spatial:3 mathematics:1 poor:1 problems:1 odinger:5 a1:9 a2:15 impurity:1 4v:1 holes:1 rule:6 dρ:1 n0:3 n2:1 starting:1 once:1
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quant-ph9911013.txt |@word limited:1 consider:1 pointing:1 rev:12 excellent:1 destroyed:1 results:2 existing:3 roy:1 scalar:1 computation:1 follow:2 soc:1 devoted:1 careful:1 integral:1 nonlocal:1 finally:6 present:7 whatsoever:1 analogous:1 include:2 worth:1 resources:1 applied:3 belonging:1 presently:1 advantage:4 orthogonal:3 very:7 rise:1 springer:1 polarization:2 every:2 anonymous:1 experimentally:1 continued:7 treating:2 splitter:1 swapping:3 level:1 turns:2 notes:1 proposals:1 applicable:1 large:5 math:1 noted:3 smaller:1 deutsch:1 dealing:1 opting:1 murao:1 feasibility:4 fold:1 second:12 concludes:3 further:1 ter:1 implemented:3 theory:3 even:3 aim:1 what:6 abc:6 xor:1 sub:2 rate:1 fine:1 assisted:19 brief:1 supplied:8 henceforth:1 suspect:1 goes:1 fractional:1 deal:1 shared:8 method:41 coefficient:1 edited:1 notions:1 component:1 teleportation:2 here:6 desired:4 plenio:2 mes:15 along:1 obtained:8 convert:1 suitably:1 institute:1 involved:1 popescu:6 studied:1 allows:1 prior:1 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quant-ph9911014.txt |@word sergei:1 leighton:1 partial:1 consider:1 remarkable:1 squared:3 particular:2 focus:2 leads:1 avalanche:1 computation:1 edu:1 consists:1 research:2 localized:1 depend:1 tp:17 quasi:1 stable:2 breach:1 maryland:2 worth:1 photocount:3 amplitudes:1 orthogonal:1 frequencies:1 figs:1 condition:13 splitter:3 branca:1 pbs:1 positions:2 brendel:1 t0:1 large:1 coincidences:1 small:3 optics:3 averaged:1 illustrating:1 oscillation:1 dealing:1 pulse:24 second:8 further:1 20cm:2 spectral:8 nonlinear:2 appear:1 rate:6 axes:2 experiment:2 above:1 new:1 method:2 pinhole:1 ibid:1 respectively:2 teleportation:1 here:1 asymmetry:1 operating:1 cos2:1 address:1 represented:1 consideration:1 strong:1 observing:3 sinc:4 obtained:1 naval:1 study:1 larger:4 usually:1 narrow:5 klyshko:4 plotted:1 spatially:4 explained:3 county:1 hardy:1 modulated:1 decrease:1 motor:1 ksz:2 select:1 plot:1 use:4 takes:1 would:1 wiped:1 contains:1 generate:1 calculation:2 therefore:2 doubling:1 selects:1 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quant-ph9911015.txt |@word sci:1 consider:3 pth:1 magnetic:9 lack:1 dynamic:1 results:1 leads:2 obstruction:1 disappears:1 computation:8 vega:1 research:1 whose:3 leung:1 i2:1 spin:19 γp:4 tr:1 quantumness:2 nonlocal:1 does:1 those:1 under:1 identity:1 belonging:1 supported:1 very:1 frequencies:1 rise:3 conditions:1 seemingly:2 wave:1 every:1 difference:1 exact:1 treating:1 hamiltonian:7 turns:2 notes:1 proposals:1 solved:1 vector:2 small:1 vincenzo:1 illustrating:1 lewenstein:1 appearance:1 pulse:1 approximation:1 second:1 evaluated:1 dynamics:2 linear:5 even:4 will:1 what:4 plays:1 witnessed:1 giving:2 sum:1 debate:1 current:1 experiment:1 above:1 acknowledgments:1 condensed:1 led:1 answers:1 reported:1 relaxation:1 consideration:3 strong:1 equations:19 obtained:1 scienze:1 involved:2 popescu:1 vectors:5 suggests:1 poisson:1 permutation:2 action:1 resonance:1 suitable:1 makes:2 sticking:1 via:1 zyczkowski:1 9n:1 explained:1 marked:1 replace:1 analyzing:1 org:1 summation:1 total:1 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quant-ph9911017.txt |@word secondly:1 consider:2 limited:1 caused:1 magnetic:1 splitting:8 leads:2 selection:2 per:2 lewenstein:2 osa:1 research:4 localized:1 looking:1 achieving:1 amplification:2 calculate:2 spin:1 pfau:5 opportunities:1 finally:2 does:3 onderzoek:2 those:2 stable:2 stochastic:1 nodes:1 te:4 heraeus:1 necessary:1 alternating:2 case:3 presently:1 advantage:3 orthogonal:2 far:5 could:4 connects:1 wave:42 p1:2 fall:1 resonant:4 experimentally:4 interleaved:1 entire:1 dominate:1 vibrational:1 level:11 issue:2 proposals:2 correct:2 large:9 vector:10 calibrated:1 science:1 small:7 settings:1 optics:6 degeneracy:3 upper:1 kz0:1 dilute:1 version:1 vasilyev:1 sin2:3 feasibility:2 superimposed:1 rate:24 enhancement:1 equal:2 further:1 implemented:1 zp:7 even:4 will:21 trapping:20 advantageous:1 distance:1 fine:3 section:1 evaporative:1 near:10 uniform:1 current:1 experiment:2 above:3 waals:1 new:1 falling:2 increasing:2 waveguide:2 method:3 contrast:1 edited:1 evanescent:46 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quant-ph9911019.txt |@word represent:1 partial:1 consider:2 rev:5 global:1 reversibility:1 four:1 entropy:1 grateful:1 consists:1 sci:1 careful:1 send:1 presents:2 finally:2 excluded:1 far:1 novel:1 difference:1 condition:14 presented:1 trb:1 insufficiently:1 deals:1 vector:3 eigenvalues:4 equation:2 prevent:1 smaller:1 direct:1 itive:1 imply:1 what:1 plays:1 trivial:5 reminiscent:1 above:2 shared:1 method:4 satisfy:1 respectively:5 teleportation:3 jointly:1 understanding:1 plenio:2 alone:1 equations:1 obtained:3 convert:1 vectors:3 accomplished:1 schumacher:1 bob:2 shaded:5 makes:1 uniquely:1 appropriately:1 via:1 useful:1 decrease:1 use:1 proceed:1 would:1 prove:1 next:4 comparing:1 depicted:1 therefore:5 jonathan:1 tell:1 more:3 composite:1 particular:1 known:1 cases:2 iii:2 must:2 account:1 indicates:3 originally:1 work:1 following:8 example:4 proof:1 heart:1 figure:2 stated:2 process:2 bennett:2 share:1 states:16 contradicts:2 numbers:2 want:2 exclude:1 axis:1 information:2 needs:1 recovery:23 divided:1 holds:1 feature:1 located:1 pure:4 product:1 mar:1 after:1 respective:2 applications:3 plane:1 revealed:2 types:1 majorization:11 natural:1 third:2 explicit:1 summing:1 element:1 so:1 realizes:3 fundamental:6 decreasing:3 order:3 operations:10 satisfied:4 years:1 hokudai:1 y1:1 existence:4 satisfies:1 sapporo:1 before:1 manuscript:1 how:2 decreases:4 systems:2 mail:1 schmidt:3 them:3 yj:2 greater:1 yn:1 fig:8 introduce:1 they:1 now:1 discuss:1 nor:2 represents:1 equality:3 always:6 university:1 orthonormal:1 sufficiently:2 iff:1 inequality:4 2a:2 each:6 found:1 individually:1 directly:1 reduce:1 idea:1 combining:1 quantum:7 happen:1 eq:9 really:1 shown:1 matrix:1 furthermore:1 since:4 crucial:1 increase:1 ref:1 shows:4 theory:1 besides:2 pairs:9 noted:1 consequence:1 first:2 already:1 xn:1 probability:6 striking:1 vedral:1 number:1 done:1 another:6 impossible:4 thick:1 interchange:2 necessarily:1 asymptotic:1 similarly:2 eqs:3 system:14 relations:1 indicate:2 assumption:2 too:1 scheme:13 final:1 recovered:5 gives:1 tool:1 part:4 manipulation:11 x1:1 than:4 transferred:2 matter:2 future:1 tion:1 enables:1 dash:1 say:1 manner:1 need:2 concentration:3 recover:2 seek:1 their:1 take:1 begin:1 investigations:1 rearrange:1 most:2 connected:2 letter:6 pair:23 surprising:1 bipartite:4 points:1 physics:1 notion:2 fact:2 quantity:5 show:2 discovered:1 relation:1 hokkaido:1 find:1 explain:1 state:16 should:1 only:9 bernstein:1 local:6 do:2 goes:1 cryptography:1 means:4 cannot:5 new:1 during:3 resource:1 arxiv:1 implication:2 reveals:3 exists:2 imposing:1 distantly:1 namely:1 individual:4 result:4 japan:1 satisfying:3 inequalities:5 review:1 importance:1 written:1 smallest:2 between:5 neither:2 reading:1 conditions:5 recently:1 nature:1 qubits:1 jp:1 however:4 residual:2 rohrlich:1 both:1 essentially:1 region:16 according:2 connection:2 qubit:3 whole:3 relevant:1 bell:9 corresponds:1 dimensional:1 represented:1 described:2 incomparable:7 second:4 basis:1 addition:2 three:3 been:1 ai:3 much:2 ph:5 define:1 sufficient:1 great:1 observers:1 understand:1 maximally:2 case:5 main:2 solid:2 will:2 contemp:1 suppose:1 irrespective:1 property:9 taking:1 procedure:3 studied:1 von:1 thus:11 procrustean:1 probabilistically:1 ii:2 itself:1 different:1 perform:4 same:1 parts:1 quant:5 widely:1 largest:5 catalysis:1 see:3 purpose:1 entanglement:47 normalization:3 recent:1 concrete:1 without:1 components:1 very:1 popescu:2 less:1 obtain:4 valuable:1 distant:1 density:1 point:2 realize:1 transformed:5 lett:3 theorem:6 transformation:8 real:2 nielsen:7 depends:1 possible:7 increases:1 entangled:31 using:1 recipient:1 necessary:2 particle:1 lost:12 follows:3 collective:8 alice:2 fully:1 dilution:1 works:1 reduced:1 mathematical:2 because:4 neumann:1 classical:7 absolutely:2 provided:1 manipulations:3 does:1 decomposition:2 refer:1 posi:1 equivalent:1 processing:2 broken:1 bq:5 majorized:2 bz:1 rearranging:1 o:1 practical:2 therein:1 previously:1 communication:7 into:9 obtaining:1 nothing:2 references:1 deal:1 prepare:5 transfer:1 there:6 question:1 transform:3 sends:1 way:1 was:2 complete:1 but:1 hk:1 line:4 true:3 partially:11 applying:1 whether:1 wish:1 up:1 limit:1 grasp:1 called:1 detailed:2 ac:1 ab:75 proved:5 defined:1 certain:1 measure:1 am:1 deep:2 general:1 ap:6 exist:3 quantph:1 again:1 dotted:1 no:4 dashed:1 when:2 detail:1 application:3 other:1 role:1 department:1 conclusion:1 elements:7 intend:2 a1:2 important:2 transfers:1 needed:2 implies:2 auxiliary:9 required:1 together:1 having:1 impossibility:1 implied:1 requires:2 original:2
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quant-ph9911020.txt |@word represent:1 partial:2 consider:3 induces:2 global:29 souls:2 interpret:7 4al:1 proposition:37 latter:2 presheaves:7 follow:1 subobject:37 issues:4 compact:9 whose:3 careful:2 concerned:1 equivalence:4 tr:16 tp:1 former:1 finally:1 does:2 preserved:1 excluded:1 under:3 mutandis:1 analogous:5 worth:1 subtleties:1 versus:2 belonging:3 straightforward:1 orthogonal:1 very:1 rise:1 induce:1 results:4 medicine:1 valued:39 every:3 interpreting:3 difference:2 condition:27 disconnected:1 generalised:30 entire:3 obvious:1 grains:4 turns:2 having:3 list:1 large:1 assignments:5 supplement:1 recall:6 mulvey:1 noted:4 upper:1 smaller:1 consistent:1 generalisations:1 second:2 perspective:6 infimum:10 further:1 specker:17 analogue:1 linear:12 even:3 what:1 sub:2 giving:1 section:26 selected:1 favour:1 expressed:1 version:5 above:15 new:3 net:2 neu:1 journal:1 heuristically:1 satisfy:2 relationships:1 focuses:1 ιv:3 doubt:1 never:1 here:1 behaviour:1 objects:15 possibility:1 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quant-ph9911023.txt |@word partial:8 consider:5 focus:1 four:6 scalar:1 entropy:8 go:1 contributions:1 reasoning:16 whose:1 inverse:3 referring:1 alamos:1 29b:2 29a:2 tween:1 nπ:2 efficiencies:1 those:9 under:2 applied:10 g4:2 g3:2 g2:1 g1:2 orthogonal:13 shifters:1 results:5 untenable:2 every:1 condition:2 illustrated:3 level:7 knight:1 correct:1 restoring:1 generalize:1 possibility:1 occurrence:1 discriminates:4 10b:1 10a:1 prediction:1 13a:2 nonmaximally:1 zero:5 what:1 appear:1 incompatible:1 section:3 selected:6 analogously:3 version:5 above:1 8c:1 3b:2 3a:2 acknowledgments:1 contrast:1 simultaneously:1 degree:3 respectively:2 never:1 plenio:1 8d:3 address:1 change:5 calculate:2 obtained:4 41b:1 involved:4 study:1 allows:1 contradiction:4 products:1 schumacher:1 andaluc:1 changes:2 transmittance:2 via:1 useful:1 family:1 tr:2 logical:1 hardy:41 ıa:2 use:1 additive:1 takes:3 would:6 prove:3 positive:4 mirrors:2 predictions:2 emits:3 classically:1 examination:1 therefore:15 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quant-ph9911024.txt |@word represent:1 since:2 consider:1 just:2 horne:1 caused:1 supported:1 find:1 results:1 four:1 experiments:4 asserts:1 legal:1 questions:10 affirms:1 mentioned:1 existence:2 yes:12 still:1 methods:1 its:1 dordrecht:3 clarifications:1 perfect:1 like:1 based:1 kluwer:1 alamos:2 bell:2 seems:1 ıa:3 only:6 other:1 those:2 excluded:2 theorem:9 hidden:6 ought:1 loophole:2 into:3 lx:1 real:9 non:4 handle:1 rational:1 means:1 very:1 de:4 possible:5 criticized:1 matters:1 cannot:2 legitimate:1 combinations:1 affect:2 nov:1 dialectica:1 advanced:1 contextual:3 shimony:1 version:1 february:1 indeed:1 assignation:2 fqm:1 always:2 conceive:3 arxiv:1 irrational:1 deals:1 realistic:1 roger:1 reasonable:1 2n:1 qm:3 island:1 view:2 mathematical:2 reidel:2 set:7 modulo:1 aspect:2 classical:2 achieved:2 experiment:3 some:2 aplicada:1 finiteness:1 individual:1 result:3 measurement:1 quantum:4 comments:1 specker:4 proofs:1 ucm:1 es:1 out:2 even:6 dense:2 space:4 affects:1 sum:4 measurements:11 rev:11 counterfactual:1 kochen:3 contained:1 does:5 currently:1 kent:6 assuming:1 print:2 new:2 author:1 approach:2 math:1 edited:2 refutation:1 predetermined:1 theory:4 gedanken:1 ısica:1 however:4 answers:5 quite:1 admits:1 difficulty:1 departamento:1 address:1 represented:1 hilbert:4 bz:1 meyer:2 both:1 about:2 regarding:1 world:2 efficiency:1 involved:1 vectors:1 assumed:1 greater:1 local:1 compatible:3 mutually:1 admit:1 historical:2 universidad:2 weird:1 andaluc:1 los:2 grounds:1 comment:1 subset:2 mechanics:3 initial:1 useful:1 projection:5 point:1 communication:1 variables:1 garc:2 private:1 outcomes:2 dimensional:2 infinite:2 because:2 long:1 impossible:2 resolutions:1 precisely:2 electronic:1 illustrate:1 my:1 city:1 described:4 takes:1 would:5 prove:1 illegal:1 there:1 system:5 construct:1 inevitable:1 their:1 linear:1 assumption:1 identity:2 way:1 was:1 taken:2 ph:3 type:2 theoretical:4 assumes:1 lett:10 refuted:1 allow:1 corresponding:1 statement:1 operators:5 holt:1 hooker:2 precision:7 but:1 volume:2 hk:1 demand:1 known:1 trying:1 than:1 spain:1 me:1 peres:3 account:3 evolution:2 thanks:1 pacs:1 plain:2 work:2 empirical:1 submitted:1 theories:4 will:1 matter:2 determined:2 three:2 none:1 concepts:2 following:1 situation:2 problem:1 concludes:1 example:1 numbers:1 pre:2 required:1 ad:1 defined:2 cabello:3 sevilla:3 grant:2 argument:1 equal:1 ii:1 clauser:1 assumptions:1 exist:1 performed:2 analysis:1 orthogonal:2 vanish:1 any:5 physical:7 sis:1 generalizes:1 smallest:1 no:15 archive:2 imprecision:2 holds:1 when:3 junta:1 instance:1 ideal:3 concerns:1 quant:3 arguments:2 instead:1 finite:5 nonexistence:1 conflict:1 conclusion:1 superposition:1 see:1 opposite:1 models:2 english:1 santos:2 hand:1 nullify:1 algebraic:2 preparations:1 letter:1 variable:5 grangier:1 normalization:1 recent:1 mech:1 consequences:1 assume:2 reprinted:1 clear:1 refute:1 detectors:1 questioned:1 rule:3 mod:1 ks:8 lhv:4 points:3 so:3 principle:2 components:2 sets:1 far:1 model:2 physics:2 dimension:1 fact:1 once:2
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quant-ph9911025.txt |@word epeau:1 partial:1 consider:4 results:10 existing:2 four:6 computation:1 reasoning:1 send:1 environment:1 spain:1 ingredient:2 supported:1 zhang:1 very:1 electron:1 securely:1 illustrated:2 swapping:8 level:1 altering:1 knight:1 guo:1 eve:40 fewer:2 large:2 solved:3 small:1 3b:2 round:1 grover:1 feasibility:2 second:2 even:1 adds:1 version:1 3c:2 shared:2 3a:2 public:8 contrast:1 revealing:2 edited:1 ibid:3 never:1 teleportation:2 here:2 address:1 represented:1 change:1 obtained:5 vernam:2 popescu:1 goldwasser:1 allows:1 accomplished:1 bob:53 andaluc:1 makes:4 useful:2 secure:1 transit:1 hardy:1 cereceda:1 alamitos:1 ıa:1 use:1 would:5 prove:1 next:2 comparing:1 therefore:8 encode:1 goldenberg:1 type:1 theoretical:1 more:1 possession:2 abrams:1 knows:4 started:1 becomes:5 occurred:1 tested:4 particular:2 known:6 foundations:1 cases:1 iii:2 must:5 science:1 work:2 modified:1 ij:7 learn:1 following:4 example:7 performed:1 compare:1 boschi:1 process:3 bennett:5 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quant-ph9911026.txt |@word partial:1 consider:4 forbidden:5 results:6 gy:1 four:2 vmax:6 generalize:1 contributions:1 whose:2 certainly:1 schiff:1 elliptic:3 divergent:2 division:1 b181:1 very:4 choice:2 exact:5 condition:18 entire:1 tanh:4 solution:2 large:1 differential:1 interpolating:1 eigenvalues:3 originally:1 oscillation:2 sukhatme:5 miller:1 consistent:1 literature:1 cosh:3 approximation:8 zero:2 further:1 chem:1 even:2 established:1 appear:1 chicago:4 section:2 selected:1 above:4 new:2 increasing:1 method:6 satisfy:1 condensed:1 justification:1 ibid:1 shankar:1 nodeless:1 sinh:3 quite:1 equations:2 obtained:4 tunneling:1 antisymmetric:4 kruglov:1 institute:1 study:2 studied:3 minsk:1 resulting:3 makes:4 winkler:1 followed:1 requiring:1 plenum:1 univ:1 readily:1 derivatives:6 use:3 takes:1 usa:2 probabilities:1 positive:1 whittaker:1 negative:1 tabulated:1 classically:10 ψi:7 type:1 successful:1 becomes:1 apparent:1 odinger:1 tested:1 known:6 cases:1 account:1 ma:3 equation:4 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quant-ph9911027.txt |@word partial:1 consider:1 maximum:1 caused:1 idealised:1 chiao:1 go:1 revealed:1 violate:2 finally:3 icx:1 those:7 indicating:1 orthogonal:1 far:1 none:1 wave:2 putting:1 orientations:1 gdansk:1 entire:1 swapping:3 presented:2 did:2 ref:1 coincidences:1 dip:2 upper:1 1x:3 pragmatic:1 ten:1 sin2:1 prediction:2 second:2 insertion:1 further:1 port:1 even:6 will:3 what:4 stands:1 experiment:9 above:2 shared:1 ever:1 90o:1 full:1 led:1 respectively:2 here:4 reported:1 possibility:1 directions:1 based:1 along:5 quite:1 calculate:1 obtained:1 incoming:1 rests:1 fernandez:1 usually:3 mz:1 changes:1 caro:1 emerge:1 via:1 spatially:1 highly:1 hardy:1 inequality:4 counts:3 use:3 takes:1 probabilities:3 predictions:3 next:1 ψk:1 therefore:1 taken:1 themselves:1 ψf:1 theoretical:1 more:2 separated:1 trait:1 operators:2 visibility:1 cases:1 hold:1 must:1 account:2 eberhard:1 permits:1 setup:2 work:1 arrangements:1 values:3 following:5 arrive:1 could:1 unconditional:1 proof:1 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quant-ph9911028.txt |@word interpretation:2 just:3 enter:1 indeed:3 half:1 ignoring:1 gda:2 attempts:1 via:2 facts:3 kbn:1 rotates:1 find:2 postulates:1 teoretycznej:1 proposed:1 application:2 chosen:1 polarizing:1 photons:7 presence:1 behind:3 should:1 originality:1 matrix:1 only:3 explicitly:1 fig:1 employed:1 plate:1 them:1 his:1 motivated:1 around:1 dependent:1 multiport:3 possible:2 wave:1 distinguishing:1 zukowski:1 altogether:1 own:1 using:2 nov:1 february:1 like:1 fizyki:1 textbooks:1 always:3 university:1 arxiv:1 alice:4 correct:1 verdict:1 either:1 fires:3 arbitrary:1 quick:1 output:3 uniwersytet:1 reduced:1 erroneous:1 fired:1 lectures:1 some:1 second:2 sands:1 ignores:2 measure:2 discussions:1 our:1 operation:1 port:6 p03b:1 happens:1 what:2 said:1 pinpoint:2 reasoning:1 distinguishes:1 students:1 state:9 difficulties:1 exit:6 above:1 between:1 print:1 reading:1 method:1 measuring:1 marek:1 noise:1 terms:1 opening:1 each:1 however:2 analyzer:1 wesley:1 completely:2 bw:1 complicated:1 reappears:1 beginning:1 properties:1 chapter:1 both:1 about:1 last:4 suitably:1 many:1 leaves:2 density:1 allows:1 according:1 side:1 calculations:1 place:1 context:1 bob:1 mz:1 first:6 nsk:1 beamsplitter:10 probability:2 bell:2 reasons:1 communication:3 within:1 plain:1 replace:1 device:9 because:1 spotting:1 would:1 gdansk:1 initial:1 pedagogical:1 leighton:1 ports:1 going:1 statement:1 basic:1 ph:3 perfectly:1 type:1 final:1 pl:1 gives:1 addison:1 michalski:14 kaszlikowski:1 share:1 registered:1 exactly:1 photon:9 but:2 hh:3 optical:1 excellent:1 cases:1 irrelevant:1 than:4 those:1 case:2 was:3 transmits:1 nski:1 measures:1 macroscopically:1 limit:1 following:1 more:1 root:1 could:1 mistake:3 claim:2 motivation:1 entering:1 figure:1 vol:1 detectors:3 abstract:1 measurement:3 mind:1 telephone:1 states:1 quantum:2 single:1 way:1 claimed:1 exiting:2 any:1 dk:1 information:1 paradox:1 no:3 supported:2 when:2 same:2 polarization:9 field:1 other:1 quant:3 orientated:1 simplified:1 mathematics:1 detector:2 events:2 independent:1 infinity:1 description:1 see:2 may:1 who:1 wrong:2 instytut:1 pair:1 totally:1 recent:2 forgets:2 younger:1 correlated:2 faster:4 sets:1 nevertheless:1 light:4 poland:1 grant:2 epr:4 physics:1 feynman:2 observe:1 does:1 time:2 very:1 its:2 having:1 fact:4
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quant-ph9911029.txt |@word schumaker:1 consider:4 rev:8 results:1 ge:3 parameterization:4 whose:2 depend:6 aug:1 recurrence:1 quasi:7 γm:2 under:2 p2:1 stud:1 song:4 wave:11 rotational:1 every:1 stays:1 affect:1 exact:8 condition:5 hamiltonian:16 turns:1 solution:4 t0:10 culation:1 optics:2 originally:1 upper:2 force:2 periodicity:9 sign:2 approximation:1 zero:2 plenum:1 enclosed:2 dynamics:1 canonical:5 sug:1 nec:1 version:1 above:3 new:1 method:1 coefficient:2 edited:2 mea:1 here:1 cos2:1 path:1 along:1 change:2 great:1 generalizing:1 thirty:1 study:3 studied:3 gle:2 periodic:15 poisson:1 action:16 changes:1 formulated:1 useful:1 4a2:1 worthy:1 compare:1 total:1 linearly:3 use:8 would:1 positive:1 linear:6 therefore:2 ψm:6 more:1 formally:1 thus:6 odinger:1 particular:3 cases:7 must:1 parameterize:1 none:1 valued:1 equation:5 averaged:1 oscillator:14 london:1 values:1 flo:1 cal:1 following:1 making:6 trans:1 def:1 f2:8 give:1 states:2 ter:2 tan:3 divided:2 get:1 significant:1 sin:4 description:1 algebra:1 may:5 oscillators:2 after:4 mapping:5 choice:4 meaningful:1 branches:1 acknowledged:1 so:5 over:2 move:1 satisfied:4 years:1 paper:2 through:8 looks:1 hannay:33 existence:7 satisfies:1 vari:1 its:1 thank:1 gen:6 derivative:1 gilkey:1 defining:1 dae:1 return:3 nation:1 effects:1 half:1 oxford:2 now:2 easily:2 february:1 2p:2 always:2 university:2 level:1 2a:1 found:1 2i:5 homogeneous:5 differential:1 overdots:1 gaussian:2 frequency:3 ex:1 quantum:5 eq:3 out:1 shown:2 driving:1 space:8 rep:1 since:1 lagrangian:2 denotes:1 re:1 rational:2 ref:4 math:5 shows:2 mρ:2 theory:1 reason:1 york:1 definition:2 derivation:1 could:2 motion:5 length:1 applica:1 first:1 origin:2 benefited:1 variables:6 number:1 xp:32 tively:1 aharonov:2 wilczek:1 passes:1 given:17 their:1 system:5 relations:1 needed:1 2ωi:4 molecular:2 gives:2 2ab:1 exactly:1 part:1 x2:2 natural:1 anandan:2 than:1 coefficients:1 cyclic:1 require:1 depends:1 submitted:1 sured:1 were:1 tion:2 generalization:2 spect:1 angle:42 lin:1 note:1 liu:2 ideal:1 generalized:6 finding:3 multiple:2 though:2 price:1 object:1 jarzynski:1 letter:1 phase:25 axp:2 considered:3 calculated:1 later:1 bracket:2 exp:3 χm:2 physics:3 fact:4 quantity:1 show:1 lewis:2 purely:1 relation:8 solutions:5 find:6 aρ:3 feng:1 ratio:2 parameters:1 should:4 combi:1 only:2 explicitly:1 corresponds:1 integrable:1 ied:1 do:2 di:2 dependent:4 pois:1 overall:1 expectation:2 dz:2 dx:1 mul:1 dt:11 interpreted:1 geometric:14 dp:1 dq:1 evolution:6 arxiv:1 summary:1 qc:12 common:1 qh:7 kernel:1 set:11 ser:1 exists:4 mension:1 national:1 ables:1 see:3 w2:5 corre:1 discussions:2 recently:1 surfaces:1 phases:2 satisfying:2 case:7 written:6 closed:5 between:1 invariant:3 subscript:2 korea:1 terms:11 however:2 jr:1 solu:3 relying:2 suggested:1 both:3 cos:5 pdx:1 many:1 equal:3 berry:6 passing:1 expression:1 x2p:2 comes:1 con:1 point:1 simple:2 ca:1 period:12 2i0:3 semiclassical:3 respect:2 tracted:1 li:1 pp:11 described:3 transformations:2 addition:1 trajectory:1 px:1 due:2 been:13 pb:1 describes:1 interest:2 pe:3 ph:2 define:1 sical:1 generating:4 timeperiodic:1 relaxing:1 curves:7 func:1 child:3 general:5 applied:1 pacs:1 straight:1 value:4 will:5 while:6 replaced:1 real:1 unitary:2 averaging:1 eral:1 tions:4 iv:1 itself:1 im:1 zhang:1 ric:2 agarwal:1 containing:1 pay:1 make:1 lett:4 same:5 any:3 quant:2 dimensionless:2 finite:1 independent:3 used:1 suggestion:1 singapore:1 i0:5 effect:1 possible:1 driven:1 recent:1 lower:2 schr:1 center:2 well:1 evolves:1 without:2 model:3 dimension:1 just:1 being:1 shape:1 atomic:1 world:1 differentiation:2 adding:1 family:4 transformed:1 treatment:2 theorem:3 har:1 transformation:1 momentum:1 identical:1 represents:1 showing:1 term:4 harmonic:9 early:1 press:1 using:1 unique:2 mod:1 like:2 differentiations:1 adiabatic:1 arbitrary:1 works:1 clas:1 inition:1 classical:7 some:1 back:1 gilmore:1 evaluated:1 b2:1 unless:1 happens:1 ported:1 shall:1 does:4 unit:1 provides:1 mined:1 proc:1 scientific:1 2m:13 analyses:2 bx:2 bz:1 stokes:2 discussed:1 dependence:1 compatible:2 range:1 2iω:1 os:1 soc:1 orthog:1 dξ0:1 integral:7 son:1 chris:1 hermitian:1 square:1 operator:1 ellipse:9 theoretically:1 additional:1 area:3 there:9 long:1 u2:1 2πi0:2 way:2 analyze:1 was:2 function:11 complete:10 form:1 shapere:1 respec:1 tally:1 hu:1 cycle:1 hm:1 line:5 removed:2 made:1 applying:1 2πi:1 smooth:2 up:1 below:2 similar:2 average:2 iqc:1 mechanics:1 diverges:1 constant:9 choosing:2 af:1 defined:10 packets:1 proven:3 denote:4 single:1 exist:4 eralized:1 reflecting:1 check:1 physical:1 again:2 functions:7 experimen:1 no:3 when:2 other:1 ellipses:4 branch:3 department:1 models:2 problems:1 polynomials:1 generated:2 bounded:1 variable:15 sider:1 structure:3 ago:1 implies:1 monic:1 curve:1 mass:2 time:21 transports:1 original:2 external:1
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quant-ph9911030.txt |@word partial:2 consider:6 magnetic:2 results:3 mnw:1 ge:2 schumaker:1 expressions:1 contributions:2 whose:10 depend:3 calculate:2 mwc:1 program:1 indicate:1 γn:4 γm:2 under:22 tb:2 ta:2 case:8 straightforward:1 song:5 wave:23 wishes:1 every:1 summarized:1 hannay:3 exact:1 condition:1 hamiltonian:3 bn:4 knight:1 solution:14 small:4 joshi:1 noted:2 force:6 oscillation:5 sign:1 zero:2 linear:1 even:3 section:8 above:2 new:3 method:3 satisfy:1 respectively:2 pati:3 path:1 equations:1 remark:1 divisor:1 study:5 studied:10 suggests:1 periodic:12 adopting:2 fourier:1 changes:1 examining:1 classification:1 2wt:1 univ:1 linearly:6 use:3 graphs:1 additive:2 asymptotic:1 would:4 positive:2 give:1 next:2 comparing:1 ψn:14 therefore:3 ψm:6 squeezing:1 ψe:5 introducing:1 sons:2 operators:1 stable:1 odinger:3 particular:8 known:2 cases:4 balakrishnan:1 must:2 equation:18 oscillator:21 mw:6 following:2 making:2 example:2 compare:2 reasonably:1 stated:1 calculation:1 states:4 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quant-ph9911031.txt |@word scalapino:1 consider:3 generalize:1 λik:1 finally:3 stochastic:12 analogous:1 result1:1 exact:2 condition:1 hamiltonian:3 arnesano:2 solution:1 succession:1 λi1:1 configurations:1 sapienza:2 jump:8 second:1 dynamics:2 ode:1 scientific:4 index:1 plays:1 above:2 increasing:2 jumps:6 component:4 here:3 active:8 along:1 observing:1 appears:1 obtained:3 allows:1 poisson:6 via:2 family:2 total:2 use:1 takes:1 probabilities:1 γi:2 e0:1 definiteness:1 therefore:2 taken:1 associated:3 until:1 introducing:1 anticommuting:1 operators:1 site:6 nkσ:1 particular:1 cardinality:2 fermionic:2 valued:1 ρe:1 ρi:1 mt:14 ρs:3 values:2 following:2 example:1 dn:3 links:5 process:2 expanding:1 numbers:4 seattle:4 s2:1 s1:12 s0:1 how:1 ordinary:2 parameter:1 replacing:1 ζk:3 different:2 collection:2 jumping:1 choice:2 natural:1 sk:13 algorithms:1 representation:2 order:2 holds:3 indeed:1 over:2 course:1 its:2 derive:1 la:2 energies:1 choose:1 inspecting:1 them:1 integral:9 evolution:3 introduce:1 nov:1 february:4 each:1 done:1 universit:4 characterized:1 stieltjes:1 extract:1 special:1 out:1 shown:1 matrix:3 factors:2 since:2 rev:1 cancels:1 may:2 i2:1 interactions:2 fisica:4 estimate:1 markov:1 interaction:1 derivation:1 determining:1 times:2 place:2 exponentially:1 first:3 initial:2 probability:4 number:3 iht:6 set:3 angelis:2 braces:1 given:3 ordering:1 dipartimento:4 system:3 construct:1 rates:1 fermions:1 dt2:1 destruction:1 final:1 continuous:1 part:1 akσ:1 than:1 coefficients:2 submitted:4 rewrite:1 say:1 any:2 strength:1 depending:1 efficient:1 note:2 take:1 performance:1 modulus:1 shall:2 remarks:1 probabilistic:2 considered:1 clear:2 later:1 points:1 principle:1 exp:2 usual:1 presilla:2 quantity:1 random:1 relation:1 occupation:3 parameters:1 only:3 a1σ:4 factor:2 continuity:1 do:1 di:8 dependent:5 de:3 expectation:5 dt:20 ds:1 processes:6 arxiv:1 europhys:1 multiplying:1 j1:8 j2:1 see:2 best:1 exponent:1 sites:1 ciσ:3 terms:2 nature:1 however:1 jk:3 configuration:1 σk:3 last:3 taking:1 equal:1 iv:6 contribution:6 expression:3 ci:2 relevant:1 dimensional:1 simply:1 ordered:1 considering:2 described:1 piecewise:2 addition:1 trajectory:4 due:1 ijσ:3 interest:1 ph:1 systems:1 corresponding:1 lecce:4 systematic:1 spin:9 those:1 case:1 value:1 suppose:2 evaluating:2 error:1 situation:1 property:1 thus:1 non:1 according:2 ik:1 ij:2 vanish:1 containing:1 hubbard:4 italy:4 quant:1 finite:4 independent:1 i1:4 trajectories:3 functions:2 parametrized:1 moment:1 sandvik:1 recent:1 hopping:2 analysis:1 roma:4 model:3 left:2 just:1 cjσ:2 obtain:2 assigned:1 world:4 differentiation:1 density:2 lattice:2 interested:1 lett:1 iσ:3 real:3 rules:1 iγ:1 possible:1 iη:1 integer:1 mod:1 niσ:8 δn:19 remind:1 integrals:1 arbitrary:1 disorder:1 some:2 separately:1 per:1 njσ:5 obey:1 equivalent:1 imaginary:2 piazzale:2 beccaria:2 o:1 within:1 numerically:1 functional:1 son:1 references:1 log:4 dnt:1 assumed:1 there:1 start:2 was:1 moro:2 function:1 repeated:1 link:6 ns1:2 applying:1 builds:1 up:2 us:2 fermi:1 jσ:2 constant:2 defined:2 ak:1 lasinio:2 elog:1 conserved:1 check:1 ni:2 nj:1 no:3 when:3 jona:2 other:1 role:1 ns:3 nt:11 elements:2 provided:1 symbol:1 a1:4 bounded:1 independently:1 algorithm:1 interval:3 rule:1 paper1:1 time:12 n1:4 having:1
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quant-ph9911033.txt |@word holds:4 partial:1 just:2 show:1 being:2 guided:1 system:2 representatives:1 spaces:3 through:2 solutions:1 aspect:1 mentioned:2 follow:1 analogue:1 eigenstates:6 subspace:1 proposed:1 representing:1 equivalence:1 should:5 only:4 other:3 those:2 much:1 under:1 adequate:1 main:2 accurate:1 momentum:3 take:2 correspondence:6 do:1 non:1 publication:1 than:1 easily:1 dependent:2 introduce:1 choice:2 among:3 framework:2 ones:2 hamilton:1 negative:1 they:5 ˆi:1 affect:1 nov:1 now:4 discuss:2 condition:1 formal:1 wider:1 dimensional:1 february:1 eigenvalue:1 necessary:2 particle:1 hamiltonian:1 altering:1 analogs:1 arxiv:1 appropriate:3 established:1 investigate:1 commute:1 δi:1 indices:2 eigenvalues:2 fixed:3 qm:26 qo:6 mean:3 mathematical:1 too:1 meaningful:1 coordinate:3 belgrade:1 exposed:1 serbia:1 direct:1 related:2 calculated:1 namely:1 submitted:1 picked:1 quantum:3 our:1 dynamics:1 expressions:1 after:1 points:1 ˆp:8 ˆq:7 sudarshan:2 cp:10 rp:10 commutation:1 over:1 space:10 gautam:1 since:2 rev:4 liouville:1 find:1 manifestly:1 state:1 does:1 harmonic:1 dqdp:2 above:4 between:1 understood:1 new:1 ri:5 rj:1 satisfy:1 secondary:1 degree:2 initially:1 respectively:2 equivalent:4 each:1 identical:1 differ:1 here:4 standard:8 rigged:3 ansatz:1 elsewhere:1 address:1 represented:3 proceeded:1 beginning:1 hilbert:4 bz:1 takes:1 box:1 both:3 essentially:1 kinematical:1 last:1 concretely:1 desired:1 institute:1 freedom:2 vectors:3 discussed:1 o:1 nonvanishing:1 etc:1 ensure:1 derivations:1 poisson:1 act:1 mixed:1 firstly:1 introduced:3 projectors:1 first:1 arbitrarily:1 considerations:3 features:2 cm:22 nonrelativistic:1 reasons:1 within:1 number:2 due:1 semiclassical:5 hermitian:2 because:1 done:1 proposing:1 operator:8 respect:3 cq:10 precisely:1 planck:1 neumann:1 kernels:1 given:1 toward:1 bracket:1 classical:4 basis:5 sake:1 aˆ:1 there:1 mari:2 relations:4 properties:3 ordered:1 intention:1 appears:1 ψi:3 therefore:1 ph:2 extreme:2 was:2 po:6 preserved:1 function:1 arena:1 sponds:1 formally:1 complete:1 form:1 observable:2 hr:3 becomes:3 operators:9 hq:6 serve:1 odinger:1 but:1 sherry:2 ordering:1 part:1 ho:8 hold:2 spin:1 proposal:2 present:2 ρa:1 coefficients:3 anything:1 pacs:1 equation:4 work:1 oscillator:1 depends:1 value:2 will:8 matter:1 while:2 limit:5 norm:1 shall:1 were:1 following:2 problem:1 more:3 similar:1 example:2 eigenvector:1 proof:1 mechanics:7 real:2 addressing:1 constant:1 commutative:1 give:1 defined:8 characteristics:1 abstract:1 neglected:1 interpretation:1 denote:1 states:7 single:2 pˆ:15 formulation:16 seen:4 dard:1 physical:2 polynomial:1 iˆ:18 different:2 formed:1 no:2 formulations:2 when:3 same:5 how:2 priori:1 quant:2 generalized:3 pure:1 collapse:1 place:1 most:1 expresses:1 parameter:1 hp:6 irreducible:2 simplicity:1 product:1 used:4 altered:1 algebra:11 translated:1 remarked:1 problems:1 polynomials:2 hand:2 algebraic:1 meaning:1 important:1 purpose:2 representation:7 phase:6 representations:1 von:1 rq:12 eigenvectors:2 schr:1 dynamical:2 third:2 values:5 sq:1 without:1 mimic:1 hi:2 so:2 principle:2 mechanical:1 very:1 observables:9 physics:1 order:1 fact:1 normalized:2
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quant-ph9911034.txt |@word represent:2 consider:5 rev:3 magnetic:8 splitting:2 four:1 gc:1 expressions:1 causes:1 depend:1 ty:3 subjected:3 γi:2 under:2 suffered:1 lre:1 2γi:2 g1:6 orthogonal:1 very:1 frequencies:2 induce:2 results:2 refractive:1 resonant:3 leads:1 incoherent:1 level:4 transmission:1 anisotropy:2 large:13 vector:1 indices:1 enhance:1 fleischhauer:2 enhancement:12 further:3 dynamics:1 even:1 cell:3 experiment:2 gi:1 above:1 new:2 modify:1 here:3 atoms:1 asymmetry:4 free:1 alone:1 consideration:1 along:2 strong:2 obtained:2 reports:1 resulting:1 published:1 domains:1 chang:1 via:1 scaled:2 welch:1 manipulate:1 use:1 takes:1 commun:1 next:1 therefore:5 inguscio:1 emission:1 controlling:3 normalized:1 particular:2 ahmedabad:1 equation:1 averaged:1 oscillator:1 crossed:1 spontaneous:3 example:3 control:20 india:1 states:3 degenerate:2 axis:1 needs:1 advantage:1 navrangpura:1 s0:3 regions:3 how:1 parameter:1 circular:2 simplicity:2 after:2 derived:1 diagram:1 applications:1 plane:3 response:1 efficiently:1 drop:2 light:2 counter:2 su:1 element:1 cascade:1 switch:6 negligible:1 vapor:2 order:2 over:1 symbols:2 through:4 mentioned:1 its:4 derive:1 decay:1 chosen:1 interesting:3 exhibits:1 absence:1 production:1 fig:8 rabi:1 mail:1 anil:1 polarizations:1 nov:1 inhomogeneously:1 several:2 hamiltonian:1 identified:2 magnitude:2 each:1 found:1 side:1 significantly:2 magneto:11 ec:3 decays:1 laboratory:1 transitions:1 eq:2 out:1 shown:6 matrix:2 induces:1 research:1 increase:1 re:2 rb:2 induced:4 cause:1 shows:1 doppler:7 written:1 birefringence:5 diagonal:1 possibility:5 small:2 interaction:1 created:1 could:3 transition:4 length:1 isotropic:2 hence:2 number:2 another:1 given:2 introduction:1 system:6 intermediate:3 brevity:1 realization:1 scheme:3 gives:2 part:1 sublevels:4 polarized:15 see:3 spectra:1 prl:1 say:3 autler:1 clearly:1 cataliotti:1 illuminated:1 strength:2 note:2 ulrich:1 probed:1 involving:1 propagate:1 significant:4 average:1 broadened:4 steady:1 optical:13 exp:2 velocity:1 fact:1 quantity:1 emerging:1 particularly:2 intensity:3 show:3 probe:14 solutions:1 ground:1 parameters:5 state:5 factor:2 coherences:1 do:1 beam:5 nearly:1 zhu:1 fields:2 arxiv:1 townes:1 analytical:3 enhances:2 set:1 observes:1 observed:1 depends:1 result:2 enhanced:1 pump:1 between:5 conditions:1 αl:5 terms:1 component:3 however:1 analyzer:2 incident:1 article:2 configuration:4 problem:1 both:2 many:2 zeeman:2 quantization:1 propagation:1 passing:2 otherwise:1 relevant:1 ca:5 corresponds:1 represented:1 scully:3 keitel:1 respect:1 broadening:1 addition:1 west:1 create:1 due:3 ansch:1 detuning:1 describes:1 ph:2 field:35 controlled:1 coherence:1 coherent:2 determination:1 present:2 case:3 p1:2 laser:7 will:4 ein:1 opt:3 almost:1 thus:3 couples:1 im:2 ernet:1 agarwal:5 different:1 circularly:2 realizing:3 same:1 quant:2 split:1 physical:1 independent:1 used:2 effect:1 hand:2 action:1 levels:2 recent:2 off:1 center:1 pavone:1 solve:1 components:3 2gi:2 model:3 left:4 rotated:2 obtain:2 rest:1 identify:1 atomic:2 tilde:1 gaeta:2 rotation:11 polarization:10 density:3 absorption:3 had:1 other:2 lett:3 input:4 suominen:1 excited:1 real:1 saturation:1 patnaik:4 mor:19 iγ:2 press:1 using:2 loss:1 rotate:1 signal:4 susceptibilities:4 output:4 right:2 back:1 dense:1 electromagnetic:1 does:1 linearly:2 expressing:1 propagating:3 demonstrated:1 detuned:1 stenholm:1 plots:1 imaginary:1 properties:1 magnetooptical:1 discussed:1 o:3 range:1 act:1 experiences:1 block:1 inclusion:1 references:1 proportional:1 switches:1 assumed:1 there:2 dispersion:1 bianchini:1 analyze:1 energy:1 function:1 medium:15 complete:2 but:2 atom:2 elliptically:1 lukin:1 inside:1 eout:1 frequency:3 pumped:1 demonstrate:1 distribution:1 strongly:1 defined:1 abstract:1 denote:1 corresponding:2 defines:2 compared:1 no:1 when:4 application:1 kp:1 details:1 conclusion:1 optically:1 important:1 coupling:1 assume:2 values:1 demonstrates:3 having:3
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quant-ph9911035.txt |@word limited:3 footing:1 partial:1 consider:12 illustrates:1 believed:1 caused:2 forbidden:1 both:3 people:1 results:7 holevo:1 four:15 future:1 quadrature:5 entropy:4 gb:6 computation:2 edu:1 causes:1 equiprobable:2 devoted:2 whose:1 amplification:5 barnett:1 calculate:2 vaidman:2 producing:1 concerned:1 tr:6 acting:1 send:2 environment:2 finally:2 behave:2 device:3 protocols:1 under:3 analogous:1 fatal:1 sent:3 detect:5 activities:1 probe:7 string:1 straightforward:1 orthogonal:15 far:2 p0:3 seemingly:1 theo:1 physics:4 valued:2 mixing:1 ρe:8 kazuo:1 exact:3 condition:2 common:1 shimony:4 nonselective:1 indicate:1 subsets:1 presented:1 transmission:10 positions:2 notes:1 trb:4 tre:3 eve:53 correct:2 large:7 math:1 nonn:1 small:7 eigenvalues:1 optics:2 caltech:1 upper:15 work:3 occurrence:1 oscillation:1 protect:1 coefficient:4 direct:2 hillery:5 sign:2 feasibility:1 rate:8 cost:2 evaluated:3 subtle:1 rigorous:1 further:2 estimated:1 mor:2 leakage:16 theory:7 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quant-ph9911036.txt |@word externally:1 consider:1 chain:1 illustrates:1 rev:9 four:10 avalanche:4 computation:1 consists:1 gn:1 expressions:1 whose:2 certainly:1 paris:3 subjected:1 technique:1 tr:1 passage:1 finally:3 program:1 preserved:1 under:1 impinges:1 orthogonal:2 wave:2 summarized:1 experimentally:2 switches:1 pbs:5 turns:1 large:1 phase:6 minimal:1 small:2 optics:2 pulse:1 sign:2 discriminated:2 second:4 further:3 port:1 nonlinear:8 apparatus:1 section:2 above:1 utkenhaus:1 new:1 method:2 κn:2 respectively:2 teleportation:2 ors:1 plenio:2 κz:1 address:1 directions:1 path:3 strong:2 incoming:1 shift:4 popescu:1 larger:1 leaving:1 resulting:2 usually:1 birefringent:1 involves:1 via:2 useful:1 outcomes:2 hardy:1 eiφn:3 fed:2 superpositions:4 would:1 remains:1 mirrors:1 depicted:2 examination:1 therefore:2 m2:2 a59:2 a58:1 jonathan:1 type:1 theoretical:1 reflects:1 more:2 stable:1 odinger:2 high:1 valued:1 setup:7 work:1 fock:9 values:1 concepts:1 following:2 spontaneous:1 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