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quant-ph9912072.txt |@word limited:1 interference:1 results:14 existing:1 quadrature:24 commute:2 go:1 amplified:1 adjustment:1 causes:2 faridani:1 content:1 certainly:1 amplification:4 depend:2 pˆf:3 spin:3 nonlocal:1 environment:1 does:9 squeezing:1 preserved:1 ti:5 circumstances:1 case:4 amplitudes:1 outside:1 very:2 rise:1 p0:6 seemingly:1 focus:1 summarized:1 experimentally:3 difference:4 splitter:2 smithey:1 presented:1 yˆm:7 integrating:3 leave:1 discrete:2 yˆs:6 eigenvalues:2 setup:6 application:1 strongly:3 approximately:2 prediction:1 pulse:2 jump:16 zero:10 further:1 dynamics:1 kitagawa:1 even:18 index:1 what:1 ˆs:14 appear:1 ˆx:1 section:6 expressed:2 find:1 current:12 experiment:1 above:4 ˆi:1 contributes:1 equivalent:1 ˆn:1 paradoxical:1 raymer:1 exchange:1 applies:1 component:24 understanding:1 reported:1 inverse:1 separation:1 relaxation:1 based:1 strong:1 equations:1 appears:2 change:5 obtained:6 laporta:1 holger:1 leaves:1 changed:1 allows:1 suggests:2 amount:1 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quant-ph9912073.txt |@word partial:1 consider:1 alternatives:1 expressions:1 contributions:1 concerned:1 γt:6 finally:1 under:1 belonging:3 far:1 condition:1 hamiltonian:2 notes:1 occurs:1 solved:1 pˆ2:1 dealt:1 eigenvalues:3 larly:1 cosh:2 further:2 canonical:3 ˆu:1 foregoing:1 expressed:1 ˆb:64 en:2 above:2 method:3 satisfy:1 condensed:1 respectively:1 here:1 xθ:1 operating:2 sinh:2 equations:7 differential:1 obtained:1 clarendon:1 institute:1 my:1 study:1 studied:1 resulting:1 symmetrical:1 apply:1 kobayashi:2 would:1 positive:1 anticommutation:1 becomes:1 operators:7 odinger:1 curvature:1 known:1 gadella:1 springer:1 work:3 oscillator:4 fock:4 values:1 following:2 dec:1 root:1 give:6 suggestions:1 toshiki:1 degenerate:1 verify:1 logunov:1 xˆ:9 instead:1 may:1 earlier:1 orbits:1 4th:1 law:1 lines:1 correspond:1 so:1 decreasing:1 interpretation:1 help:4 schwartz:1 vary:1 satisfied:2 paper:3 mentioned:1 japan:1 satisfies:2 before:1 rapidly:1 decay:1 chosen:1 coordinates:7 writing:1 gel:3 them:1 introduce:3 they:2 now:6 eigenvalue:3 inversion:1 dirac:2 gamow:1 university:1 l2:2 2m:2 square:1 ed:2 energy:2 principles:1 quantum:12 our:1 out:1 space:5 since:1 rev:1 re:1 mγ:9 lecture:1 integrated:1 math:1 antiunitary:1 benjamin:1 theory:4 barrier:8 standard:5 nth:6 put:1 βx:2 motion:1 first:1 origin:1 transform:1 πb:1 interchange:1 given:1 hyperbolic:1 introduction:1 adjoint:3 system:2 relations:4 πu:5 gives:1 reversed:1 continuous:1 x2:2 dx2:1 ˆˆb:4 coefficients:3 normalizing:1 annihilation:3 matter:1 states:15 determined:1 modern:1 conjugate:2 any:2 self:2 able:1 note:1 potential:8 generalized:11 bogolubov:1 sakurai:1 heisenberg:5 multiple:1 axiomatic:1 shall:4 phase:3 acknowledgements:1 tensor:1 pˆθ:1 physics:2 show:2 spaces:4 relation:2 solutions:3 corner:1 find:2 state:1 should:1 only:1 factor:1 parabolic:8 dn:2 do:1 his:1 get:3 express:2 cannot:1 reversal:5 dt:2 takahashi:2 evolution:1 arxiv:1 contain:1 view:1 see:2 result:4 satisfying:2 commutation:4 representatives:6 written:1 invariant:1 xˆ2:1 conditions:3 triplet:2 terms:3 essentially:2 instant:1 limits:1 many:1 taking:1 according:1 iℏ:4 finds:1 kets:1 ibaraki:1 point:1 cf:2 dimensional:2 been:2 treat:1 ph:2 define:1 addison:1 subspace:1 assert:1 θu:6 applied:6 will:2 iξ2:2 unitary:1 vol:2 thus:5 equal:1 ii:1 examined:1 vanish:1 twofold:1 belong:1 same:2 unity:1 complex:4 quant:1 products:2 numerical:4 hand:1 purpose:1 schr:1 well:1 bohm:1 todorov:1 coordinate:4 model:1 fand:3 being:3 obtain:1 valuable:1 thanks:1 eigenstates:5 lebesgue:1 except:1 versa:1 momentum:3 iξ:7 showing:5 iβ:1 spanned:1 harmonic:4 press:1 integer:1 like:2 unstable:2 arbitrary:2 parity:5 right:1 methods:2 classical:1 creation:3 b0:3 iˆb:1 tsukuba:1 lead:1 normal:7 integration:2 connecting:1 provides:1 inserting:1 bn:2 wesley:1 properties:2 stone:1 getting:1 dˆ:10 extensions:1 because:1 references:1 operator:15 proportional:1 there:1 u0:2 width:1 physicists:1 way:1 triplets:1 dx:7 function:3 form:3 but:1 hu:3 hn:3 us:5 un:2 problem:2 similar:1 mechanics:2 constant:1 defined:2 abstract:1 dξ:7 examine:1 pˆ:9 physical:1 functions:2 field:2 book:1 nu:1 picture:4 polynomials:1 commutator:1 meaning:1 vectors:1 proceeding:1 sides:1 anticommutator:1 vice:1 assume:1 factors:2 mass:1 time:10
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quant-ph9912074.txt |@word operations:1 represent:4 code:12 protocol:1 unbreakable:1 proposed:2 less:1 developed:1 find:1 course:1 concept:2 through:1 statistical:1 go:1 sci:1 trivial:1 its:1 note:1 now:3 based:2 termed:1 exact:1 technique:1 mathematically:1 source:1 only:1 systems:4 marginal:2 mitra:3 columns:2 string:1 cryptography:2 reveal:1 coding:2 measurement:1 economical:1 break:1 mention:1 cannot:1 legitimate:1 using:3 bit:13 py:69 correcting:1 discuss:1 apart:2 easily:2 regarding:2 presented:1 always:1 level:1 solution:1 public:1 communications:2 transmitted:1 she:2 each:1 popular:1 references:1 security:1 works:1 added:1 us:1 ignored:1 arxiv:1 force:1 directly:1 classical:4 sep:1 s1p:1 reduce:1 idea:1 operates:1 see:1 elements:3 devices:1 choosing:1 measure:1 quantum:3 our:1 extended:1 might:1 provided:1 fails:1 sub:14 apparatus:1 ways:2 measurements:1 undertake:1 decoding:2 behind:1 does:2 sources:1 above:2 between:2 denoted:2 shared:3 increasing:1 correct:1 minimal:1 publications:1 satisfy:1 noise:5 recently:1 statistically:1 respectively:5 equivalent:1 here:1 statistics:2 than:3 key:6 represented:2 binary:2 amer:1 noisy:1 pβ:3 pγ:2 search:9 fixed:2 sender:4 introduces:1 greater:1 practical:1 pz:80 produce:3 due:1 receiver:5 share:1 introduced:3 distinguish:1 arbitrarily:1 computational:2 secure:6 probability:5 presence:1 simple:3 communication:2 cryptosystem:1 number:4 highly:1 lies:1 done:1 been:1 another:2 sequences:17 message:1 should:1 considering:1 rows:2 similarly:2 introduction:2 measured:1 px:69 sequence:13 system:9 long:2 strategy:2 needed:1 therefore:2 basic:1 ph:2 bits:3 correction:1 more:2 function:1 introducing:1 fake:1 knows:2 s0p:1 becomes:1 further:1 but:4 applicable:1 environmental:1 pα:3 repeatedly:1 exhaustive:7 he:3 randomly:1 made:1 pursue:2 type:1 levels:1 will:9 assume:1 itself:1 values:7 three:1 error:17 again:1 problem:2 procedure:1 london:1 piper:1 august:1 hellman:1 corrupted:5 pseudo:5 abstract:1 describe:1 india:1 proven:1 states:2 effectively:1 single:1 minimum:2 numbers:1 manipulating:1 need:1 distinguishable:1 increased:1 information:4 different:6 computationally:3 advantage:2 once:1 when:2 feature:1 same:4 recovers:1 noised:2 how:1 quant:2 mathematics:1 composition:1 independent:1 used:2 users:1 protection:1 shall:3 suppose:1 defeat:1 lengthy:1 cipher:7 uses:1 position:5 device:1 probabilistic:2 natural:1 ke:1 nevertheless:1 cover:1 element:2 without:1 so:2 time:1 firstly:1 calcutta:1 breaker:8 physics:1 having:1 know:1
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quant-ph9912075.txt |@word represent:5 positions:2 concept:1 partial:3 consider:9 springer:1 rev:1 rob:3 desirable:1 results:4 leads:4 eds:3 commute:5 go:1 follow:1 expressions:3 spacetime:2 issues:1 whose:3 depend:2 calculate:1 centres:1 irrelevant:1 subjected:1 deterministic:1 environment:12 finally:2 those:2 under:4 analogous:1 worth:1 norm:1 ta:1 started:1 applied:4 belonging:4 attribution:1 expressing:1 orthogonal:6 very:5 could:1 rise:1 exception:1 focus:1 interpreting:1 allowed:1 condition:19 accompanying:1 turns:1 t2:37 applicable:5 t1:33 ascribed:1 δjj:2 section:4 small:8 noted:2 degeneracy:3 physically:3 approximately:2 says:1 occurrence:1 consistent:27 approximation:1 imply:2 plenum:1 further:3 specker:1 implemented:1 permutations:2 pmi:2 linear:5 spectral:8 index:2 what:9 unavailable:1 incompatible:2 exactly:3 interactions:11 foregoing:1 expressed:1 agrees:1 current:1 summers:1 above:8 retains:1 new:5 consisting:1 contrast:2 thin:1 pioneering:1 subdivided:1 full:1 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quant-ph9912076.txt |@word saying:1 they:2 results:1 benasque:1 gda:4 paper:1 mentioned:1 based:1 state:1 lemma:3 other:1 lett:2 superoperators:1 under:1 oct:1 do:1 bound:2 horodecki:3 entangled:1 distillable:1 vidal:2 presented:1 university:2 arxiv:1 found:1 upper:1 en:3 ed:2 ef:2 some:2 see:1 measure:1 our:2 eq:2 ep:2 nonzero:1 shown:1 rev:4 manipulations:1 increase:1 pawel:1 does:1 ref:9 recently:1 however:1 ryszard:1 log:1 michal:1 institute:1 isotropic:1 hence:1 genuinely:1 nsk:4 family:1 communication:1 cf:1 private:1 werner:6 ppt:1 use:1 additive:1 asymptotic:1 therefore:1 astrophysics:1 ph:3 was:2 theoretical:1 irreversibility:3 appendix:1 authors:1 irreversible:1 those:1 applied:1 showed:1 erratum:2 value:1 technical:1 remain:1 proof:5 cirac:1 calculation:2 preserving:1 states:6 incorrect:1 rains:2 make:1 holds:1 invalid:1 valid:1 quant:3 mathematics:1 independent:1 trace:1 earlier:1 faculty:1 entanglement:2 considered:1 poland:2 physics:2 having:1 fact:1
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quant-ph9912077.txt |@word limited:1 gs:12 consider:1 interference:1 focus:1 gb:2 whose:2 inverse:1 depend:1 γs:15 γu:7 environment:1 present:1 under:1 γb:6 analogous:1 γf:4 indicating:1 prigogine:1 advantage:1 very:1 frequencies:1 rise:1 induce:1 wave:2 cook:2 experimentally:1 exact:2 condition:2 entire:1 vibrational:2 level:7 knight:2 damped:2 large:1 fourier:1 enhance:1 application:1 slower:1 prediction:3 pulse:3 approximation:2 likely:2 enhancement:1 even:1 will:1 stands:1 near:1 experiment:1 above:6 fractional:1 expresses:1 contrast:3 condensed:1 degree:1 here:4 atoms:3 plenio:1 address:2 κt:1 luis:1 along:1 coupling:10 observing:1 sinc:2 κs:5 institute:1 shift:1 larger:2 resulting:1 suggestion:1 published:1 resonance:6 narrow:1 peˇrina:1 via:1 regardless:1 modulated:1 tp:4 achievable:1 qze:20 waveguides:4 commun:1 weizmann:3 hypothetically:1 opposed:1 memory:1 more:3 israel:1 populations:1 rehovot:1 becomes:1 factor:1 emission:4 validity:1 reversible:1 normalized:1 sharply:3 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quant-ph9912078.txt |@word replacing:1 partial:1 consider:13 remarkable:1 woo:1 results:20 leads:1 generalize:1 grateful:1 edu:1 go:1 involved:3 semiconductor:1 depend:10 shanghai:2 behaviours:2 finally:2 does:5 tk:4 under:2 details:2 boll:1 straightforward:1 very:7 connects:3 wave:1 infiniteness:2 2l3:1 difference:4 matrices:3 condition:1 four:2 vidensk:1 hamiltonian:2 transmission:1 gui:1 developing:1 solution:8 t0:2 solved:2 vector:2 small:1 eigenvalues:1 semenoff:1 infinities:1 degeneracy:1 sturm:1 liang:1 sin2:15 sign:2 carefully:1 zero:12 substituting:4 rigorous:1 further:2 odd:16 stdp:1 even:26 established:3 plays:2 appear:2 diag:1 section:6 while:7 expressed:1 lengthy:1 current:1 version:2 above:27 new:3 net:1 method:8 satisfy:7 27a:2 condensed:1 simultaneously:3 relates:1 respectively:2 guangzhou:1 component:3 discrete:2 here:3 understanding:1 behaviour:4 ei:1 china:4 gesztesy:1 address:1 sine:1 equations:10 appears:1 change:1 box:1 arrive:2 kek:3 technical:1 shift:1 study:5 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quant-ph9912079.txt |@word partial:1 remarkable:1 extremes:1 comparatively:1 ge:1 ros:1 reˇ:1 spector:1 const:1 spirit:1 quasi:3 daniel:1 alvarez:1 under:1 case:2 comm:1 far:1 wave:10 sons:1 exact:2 condition:4 immediately:1 hamiltonian:2 solution:4 discrete:1 small:2 biological:1 inspection:1 force:5 methodical:1 sukhatme:2 sin2:2 cosh:5 approximation:1 imply:1 dedonder:1 chem:1 odd:2 linear:1 even:2 what:1 nonlinear:1 appear:2 giving:1 brief:1 uniform:2 current:1 version:1 above:2 illustrations:1 new:10 appeal:1 contrast:3 pioneering:1 respectively:2 component:1 composed:1 cos2:2 sinh:5 represented:1 strong:2 equations:1 appears:1 extreme:1 obtained:1 remark:1 roychoudhury:1 antisymmetric:1 shift:4 inspired:2 studied:2 maioli:1 simultaneous:1 graffi:1 conveniently:1 suitable:1 makes:1 involves:1 jackiw:1 oschl:5 mimicked:1 varshni:1 useful:2 family:2 private:1 analyses:1 sky:1 use:1 asymptotic:1 prove:1 remains:2 positive:2 continuous:1 contains:1 bender:5 scope:1 themselves:1 type:1 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quant-ph9912085.txt |@word spherical:1 distances:2 extrapolated:1 proximity:1 results:2 through:1 using:2 covered:1 reynaud:2 perfect:1 causality:1 knowledge:1 la:1 paris:1 graph:4 better:1 hill:1 coefficients:1 theorem:1 quant:2 pointed:1 eur:1 plate:1 his:2 forces:1 notation:2 distance:2 very:2 frequencies:1 sup:1 expectation:1 focus:1 nearly:1 they:1 press:1 experimentally:1 part:2 discuss:1 dielectric:3 de:1 metals:1 nicely:1 erieure:1 arxiv:1 specific:1 solid:1 academic:1 fig:1 accurate:1 mcgraw:1 universit:1 higher:1 out:1 side:1 therein:1 upper:2 force:9 significantly:1 ed:1 consistent:1 conductivity:1 pierre:1 observed:1 see:1 frequency:4 value:2 measurement:1 our:3 drude:1 techniques:1 surfaces:2 appear:1 fv:1 reflectors:1 since:2 rev:3 integration:1 µm:5 experiment:3 theoretically:1 between:7 new:2 net:1 evaluation:2 shows:2 recently:1 theory:1 do:1 reach:1 attention:2 agreement:2 here:2 quite:1 a59:1 difficulty:1 palik:1 york:2 besides:1 imaginary:2 configuration:1 properties:1 calculate:1 obtained:2 both:2 about:1 kastler:1 geometry:2 optics:1 studied:1 equal:2 reports:2 compatible:1 range:3 coated:1 assumed:1 exceeds:1 experimental:3 functions:2 comment:1 ηe:1 within:1 integrations:1 scientifique:1 restrict:1 references:1 relations:1 national:1 respect:1 thick:1 france:1 cu:12 casimir:8 given:2 astrid:1 additional:1 measured:2 there:1 predictions:1 been:1 response:1 needed:1 reduction:3 handbook:2 low:1 centre:1 expected:3 ph:2 deduced:1 theoretical:6 gives:1 function:3 flat:1 ecole:1 factor:2 recherche:1 validity:1 taken:1 underlined:1 optical:6 discrepancy:2 particular:1 line:2 than:1 present:1 measurements:1 case:1 approximation:1 curie:1 contradicts:1 rad:1 work:1 up:1 evaluated:3 while:1 values:5 mp:1 problem:1 dec:1 similar:1 procedure:1 result:1 layer:2 constant:3 figure:2 mirrors:3 surface:1 ii:1 sphere:2 au:12 numbers:1 recalculated:1 demonstration:1 campus:1 different:1 erratum:1 author:1 dashed:1 lett:2 same:2 metallic:2 dependent:1 compares:1 details:1 pure:1 plates:1 finite:1 interpolation:1 pacs:1 effect:1 jussieu:1 laboratoire:1 numerical:2 derived:1 differing:1 brossel:1 energy:2 plane:6 but:1 letter:1 fits:1 marie:1 data:4 lamoreaux:6 constants:1 recent:1 normale:1 lower:2 reflection:1 lambrecht:2 cedex:1 more:1 solids:1 extrapolation:1 time:1 clears:1 model:1 serge:1
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quant-ph9912086.txt |@word neighbors:2 limited:1 urbana:1 sci:2 consider:4 switched:2 interference:1 magnetic:1 lack:1 results:2 unchanged:3 switches:2 rapid:1 circuitry:2 entropy:1 microwave:2 computation:19 radiation:1 go:1 amplified:2 involved:1 causes:2 whose:4 votes:3 inverse:6 overlapping:1 violate:1 alamos:2 subjected:1 eˆ:2 advances:1 nonlocal:1 environment:1 common:2 neighbours:13 program:2 device:4 swap:3 th:1 under:1 ωia:1 analogous:1 through:1 worth:1 overlaps:1 case:1 updated:1 intense:1 string:4 acoustic:1 very:2 frequencies:19 continues:1 induce:4 fabricated:1 electron:1 manipulated:1 every:1 updates:2 cellular:14 fall:1 resonant:25 difference:2 arrange:1 entire:2 swapping:1 immediately:1 bring:1 bn:6 forth:1 t2:2 t3:2 z10:2 t1:3 try:1 vector:1 phase:4 science:2 small:10 enhance:1 loads:3 optics:1 noted:3 still:1 deutsch:3 probabilities:1 photomultipliers:1 pulse:43 consists:1 zero:7 today:2 design:7 enhancement:1 further:2 chem:1 news:2 shining:1 even:4 trick:1 what:4 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quant-ph9912087.txt |@word epeau:1 partial:3 consider:1 rev:2 equalities:1 results:1 existing:1 four:1 eds:1 proposition:6 entropy:1 dimensionality:1 depend:1 ohya:5 tr:1 γk:2 uniqueness:2 tk:8 th:6 under:4 accardi:5 g1:1 orthogonal:4 choice:3 corollary:3 condition:4 dim:6 school:1 solves:3 solution:7 vector:4 indices:1 equation:3 second:1 pass:1 rigorous:1 further:1 spectral:1 index:1 nonlinear:1 gα:3 section:9 sut:1 above:12 international:1 method:1 satisfy:1 full:1 respectively:1 teleportation:24 here:3 coupling:1 change:1 obtained:3 remark:2 commutant:1 vectors:4 schumacher:1 studi:1 composed:1 via:2 spatially:1 projection:3 family:5 requiring:1 plenum:1 unitarity:1 unitary:12 summation:1 apply:1 tools:1 unit:1 use:2 positive:1 nagoya:3 ψn:2 therefore:3 means:5 volterra:4 type:1 theoretical:4 more:3 separated:1 bennett:2 becomes:3 operators:4 eν:1 normalized:1 particular:2 cases:1 iii:1 must:1 tokyo:1 science:1 ρk:12 ρu:3 ρv:2 following:7 making:1 dec:1 example:1 proof:5 f1:1 f2:1 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quant-ph9912103.txt |@word concept:1 customary:1 consider:1 priori:1 rev:2 results:1 schatten:2 commute:2 entropy:15 comments:2 computation:1 denotes:1 contributions:1 ohya:2 tr:26 those:1 under:2 stochastic:2 sent:2 case:5 orthogonal:1 very:2 seemingly:1 every:15 mixing:1 emphasized:1 difference:3 matrices:3 condition:2 dim:4 presented:2 transmission:7 turns:1 noiseless:7 discrete:1 proposition:4 small:1 eigenvalues:3 anal:1 optics:1 upper:1 encoder:1 smaller:2 says:1 estimates:1 fold:7 rate:6 normed:1 manipulating:1 defines:1 implemented:1 linear:1 will:2 subadditivity:2 stands:1 d2:8 section:4 decoding:5 3i:2 version:1 above:2 sup:2 new:3 here:1 following:2 operating:1 possibility:1 strong:4 appears:1 extreme:1 obtained:2 eij:2 sender:1 forum:1 institute:1 shift:1 economics:1 allows:3 p2:1 amount:6 survey:1 data:1 schumacher:8 bob:3 formulated:2 projection:3 marginal:1 replace:1 unit:1 use:9 asymptotic:1 uniformity:1 codewords:1 probabilities:1 positive:6 negative:3 next:4 call:1 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quant-ph9912104.txt |@word represent:2 externally:1 code:2 partial:2 consider:5 maximum:1 surrounding:3 rev:8 magnetic:9 desirable:1 results:5 produce:2 four:1 eds:2 entropy:14 microwave:2 computation:2 consists:1 follow:2 expressions:1 instantaneous:1 discern:1 particles:3 violate:2 transferred:4 i2:4 irrelevant:1 tr:2 γt:2 environment:10 ℜe:1 matlab:2 stable:3 analogous:1 preskill:1 norm:1 unnormalized:1 digit:1 premium:1 evolves:2 very:3 frequencies:2 rise:2 springer:4 seemingly:1 choice:3 print:2 manipulated:2 mixing:4 experimentally:1 em:5 difference:3 matrices:1 condition:9 cool:6 milburn:1 entire:1 dominate:1 immediately:1 level:6 did:1 schumacher:1 correct:2 large:4 vector:5 science:2 small:2 eigenvalues:7 markov:4 regard:1 optics:4 originally:1 upper:2 slower:2 oscillation:1 excited:17 sign:2 approximation:2 go:1 likely:4 j23:2 further:2 dynamics:12 implemented:3 linear:14 even:3 index:2 what:6 errors:35 adds:1 rate:5 brackets:1 section:4 axes:1 remain:1 find:3 access:1 3i:2 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quant-ph9912106.txt |@word magnetically:1 limited:1 since:1 ron:1 switched:4 magnetic:19 indicating:1 fabricated:3 leads:1 gf:1 concept:1 computation:2 edu:1 issues:1 increase:1 mounted:6 attracted:1 alamos:1 show:3 presents:1 list:1 finally:2 those:2 presentation:1 dramatically:1 sent:1 r13:1 sitting:1 very:3 frequencies:3 hughes:1 iii:2 results:1 electron:1 manipulated:1 orientations:1 sidebands:1 enter:1 encounter:1 cool:1 interferometry:1 pre:1 jhe:1 modulator:1 proposals:2 integrated:3 large:11 millimeters:1 small:7 optics:6 10µm:2 upper:1 smaller:2 slower:1 direct:1 pulse:1 zero:2 design:2 further:4 even:2 what:1 trapping:9 apparatus:1 giving:1 section:1 near:2 access:1 experiment:3 above:8 3c:1 3b:1 3a:1 increasing:3 3f:1 3e:1 3d:3 body:1 edited:3 compresses:1 full:1 transportation:1 lee:1 µm:16 here:2 atoms:37 desired:1 free:1 others:1 along:1 strong:1 respect:1 obtained:1 sending:1 weinstein:1 institute:2 leaves:1 changed:1 robin:1 amount:1 published:1 der:1 uniquely:1 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quant-ph9912111.txt |@word remarkable:1 rev:8 lack:1 desirable:1 results:4 leads:3 eds:1 ge:1 entropy:36 grateful:1 gn:9 expressions:1 gi:10 devoted:1 increase:1 depend:1 chain:2 combinatorial:2 spin:1 corrections:1 critical:25 alvarez:1 preserved:6 include:1 worth:1 g7:2 p2:1 g5:7 deforming:1 advantage:1 song:1 very:4 implicitly:1 ginsburg:1 zachos:1 wave:2 stat:1 sons:1 difference:2 fractal:2 deformations:1 condition:6 entire:1 hamiltonian:6 issue:1 solution:1 correct:4 large:6 discrete:2 small:5 generalize:1 2πmt:1 upper:2 employing:1 evaluating:1 zk:1 ze:1 consistent:5 coefficient:1 past:1 prevails:1 second:4 equal:1 zq:13 goes:3 index:2 nonlinear:1 plays:3 stands:1 sum:2 expressed:7 devoto:1 establishes:1 fractional:3 new:2 principal:1 method:2 pioneering:1 compact:1 condensed:2 full:2 led:1 κi:9 exchange:1 realizations:1 here:3 atoms:2 desired:1 groups:5 ratio:3 observing:4 appears:1 logarithmic:1 calculate:4 obtained:4 derivable:1 great:1 rigorously:2 study:6 studied:2 allows:3 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