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quant-ph9903082.txt |@word limited:1 allowed:1 consider:2 exponentiation:1 caused:2 global:1 results:11 a1:2 adjective:1 quadrature:1 per:2 4n2:2 contributions:5 causes:2 ρss:4 whose:1 certainly:1 inverse:2 calculate:1 co:1 transferred:1 producing:2 concerned:1 technique:1 tr:4 extraneous:1 passage:1 presents:1 finally:2 compensate:1 device:8 helps:1 th:2 under:2 include:1 worth:2 norm:2 me:1 worse:1 straightforward:1 returning:1 far:1 implicitly:2 rise:1 springer:3 semi:2 untenable:1 experimentally:1 difference:3 condition:1 leads:2 obvious:1 exponential:1 exits:1 hamiltonian:16 schawlow:21 turns:1 proposals:1 solution:2 correct:1 large:4 math:1 small:4 optics:1 noted:3 upper:11 smaller:3 consistent:1 sin2:4 ghosh:2 pulse:3 sign:1 past:1 rate:23 perspective:1 pass:3 rigorous:2 invariant:1 dynamics:2 substitute:1 theory:4 even:6 trick:1 what:1 nonlinear:10 adds:2 stands:4 giving:1 sum:2 expressed:2 agrees:3 waiting:1 version:1 localized:1 above:8 new:4 contributes:1 method:6 ihτ:1 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quant-ph9903085.txt |@word partial:2 consider:1 forbidden:1 results:4 emeritus:1 entropy:7 expressions:1 displaying:1 sin2θ:6 tr:3 finally:1 device:1 analogous:1 presentation:2 indicating:1 jensen:3 very:3 wave:1 probability:2 sons:1 resonant:3 experimentally:2 emphasized:1 difference:1 matrices:3 vast:1 notations:1 level:3 tra:1 knight:2 solution:3 large:2 small:4 eigenvalues:1 trr:1 optics:5 noted:1 upper:2 sin2:2 za:1 approximation:1 zero:3 displays:1 further:1 goes:1 even:1 will:2 appear:3 sum:1 near:3 expressed:1 henceforth:1 version:1 above:4 new:8 occupation:1 contrast:1 edited:1 full:1 ibid:3 respectively:1 component:1 residual:1 here:13 atoms:1 reported:2 explore:2 separation:1 address:1 represented:1 strong:1 cerf:4 grandy:2 naval:1 akr:1 reminiscent:1 completely:1 eberly:1 resonance:1 honor:2 blackbody:3 scales:2 marginal:4 scaled:1 decrease:2 rρ:1 total:2 univ:2 use:2 probabilities:1 positive:6 contains:2 negative:12 classically:5 a55:1 therefore:1 memory:1 today:1 more:1 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quant-ph9903086.txt |@word represent:1 consider:1 rev:8 hats:1 results:8 leads:1 roy:1 scalar:1 cooperative:1 consists:1 follow:1 only:1 contributions:1 gj:1 compact:2 whose:1 inverse:3 depend:1 calculate:1 tail:2 present:6 th:3 under:1 include:2 divergent:2 division:1 greiner:1 shielding:1 straightforward:1 very:2 implicitly:1 rise:1 geometrical:1 putting:1 refractive:3 experimentally:1 impressive:1 did:1 turns:2 solution:3 leave:1 vector:1 dealt:1 small:8 equation:2 dilute:4 force:8 dealing:2 consistent:1 prediction:1 cosh:1 approximation:1 zero:1 further:6 chem:9 even:1 index:3 appear:2 dr1:1 sum:3 dr2:1 expressed:1 above:9 waals:6 obvious:1 increasing:1 method:7 body:1 edited:1 degree:1 eksp:1 component:1 here:11 behaviour:4 minor:2 separation:2 others:5 active:1 path:1 along:1 quite:1 equations:1 obtained:10 vectors:2 commonly:1 resulting:5 published:1 πa:1 fourier:6 studies:1 via:2 family:1 apr:1 sign:1 summation:1 total:3 establish:2 causal:1 unit:1 use:5 positive:5 contains:1 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quant-ph9903093.txt |@word partial:2 consider:4 results:1 four:9 generalize:1 edu:2 relationships:1 whose:1 depend:1 calculate:1 γs:3 γk:1 charge:1 under:4 applied:1 fax:1 straightforward:1 dispense:1 void:1 translations:1 wave:8 q1µ:1 difference:2 matrices:7 illustrated:1 exponential:1 did:1 pacs:1 list:1 large:1 vector:2 dealt:1 eigenvalues:2 upper:1 force:1 cosh:7 past:1 affiliation:1 imply:2 theory:2 even:1 what:4 appear:1 richard:1 diag:1 section:2 selected:1 current:1 version:2 flowing:1 new:2 boost:7 public:1 exercise:1 satisfy:3 full:4 degree:2 component:6 here:3 possibility:1 sinh:7 address:2 represented:1 consideration:1 along:1 equations:3 interpret:1 deduced:2 obtained:2 search:1 institute:1 vectors:5 commonly:1 simultaneous:9 suitable:2 makes:3 involves:1 useful:1 fµ:12 requiring:1 replace:1 flexibility:2 wit:2 contradictions:1 summation:2 apply:2 unit:6 derivatives:1 use:2 figure:3 usa:1 ψs:2 contains:2 negative:2 next:1 derivation:1 call:1 therefore:2 compactly:1 more:10 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quant-ph9903094.txt |@word limited:2 gr:1 represent:1 rev:6 global:2 brownian:7 results:1 abramovici:1 consists:1 gillespie:1 whose:1 inverse:1 paris:1 braginsky:1 stable:1 tf:9 γf:6 sent:2 case:2 very:2 amplifier:2 brossel:1 wave:5 sensitivity:1 resonant:2 deformations:1 cool:1 squares:1 modulator:4 level:4 transmission:1 sensor:2 large:5 small:2 equation:1 heidmann:4 force:11 sign:1 second:1 pass:1 spectral:1 plays:1 near:1 experiment:4 sup:1 increasing:3 erieure:1 agreement:2 photothermal:1 eksp:1 residual:1 atoms:1 objects:1 2kb:1 strong:1 appears:1 deduced:1 obtained:10 shift:2 study:1 studied:1 allows:1 resulting:5 walther:1 published:1 resonance:19 fourier:1 changes:2 diameter:1 via:4 spatially:1 visible:2 modulated:4 decrease:1 linearly:1 use:1 takes:1 working:1 acousto:3 negative:1 france:1 nucl:2 resonator:3 theoretical:2 reflects:1 zh:1 ecole:1 coating:1 curvature:2 normalized:5 excellent:2 must:1 account:1 stabilized:1 locked:2 room:1 mm:5 science:1 setup:2 vyatchanin:1 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quant-ph9903095.txt |@word represent:2 concept:9 consider:6 similarity:5 rev:7 lack:1 results:12 eds:1 writings:2 per:1 controversial:1 invariably:1 bergmann:1 follow:1 expressions:2 localized:1 particles:12 calculate:1 irrelevant:3 deterministic:1 answered:3 finally:1 under:2 ontological:3 case:4 finkelstein:1 advantage:1 outside:1 very:6 continues:1 conditions:2 every:1 jack:10 decide:1 specific:1 little:1 exact:4 condition:1 school:1 obvious:2 presented:2 issue:2 button:1 t2:7 applicable:1 t1:12 try:3 vector:3 small:2 eigenvalues:1 noted:1 added:1 tel:2 miller:1 consistent:4 outcomes:4 second:2 addition:1 even:7 index:1 what:3 plays:1 appear:1 incompatible:1 section:3 selected:10 abl:8 bergman:1 current:4 experiment:1 3n:1 above:4 new:2 consisting:1 exercise:1 paradoxical:5 evolving:2 unsure:1 never:4 component:2 equals:1 here:5 understanding:3 lev:1 indeterminism:1 concluding:1 strong:1 teaches:1 implicit:1 wait:1 box:40 root:1 allows:1 controversy:3 suggests:1 published:4 action:1 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quant-ph9903100.txt |@word secondly:1 consider:2 remarkable:1 rev:5 splitting:3 gg:1 commute:1 ga:1 expressions:2 seemed:1 compact:2 excludes:1 theorist:2 calculate:4 paris:1 description:1 tr:3 finally:3 weyl:1 those:1 th:2 under:1 hermann:1 breach:1 analogous:1 division:1 straightforward:1 very:6 account:2 wave:7 electron:2 every:4 ma:1 difference:1 matrices:1 condition:4 beginning:1 beam:1 bn:2 notes:2 t2:3 solution:1 occurs:1 solid:1 vector:1 zeitschr:1 optics:2 originally:1 smaller:2 force:1 specially:1 methodical:1 bψ:1 prediction:1 approximation:1 second:4 htr:1 growing:1 further:2 dynamics:1 odd:1 canonical:5 even:4 what:2 errors:2 plays:1 stands:1 clock:2 section:2 http:1 favour:1 expressed:1 19th:1 abs:1 goes:2 scientists:1 new:17 ever:2 method:3 contrast:1 told:1 satisfy:1 edited:1 rua:1 led:2 9th:1 ibid:1 nearer:2 respectively:1 applies:1 here:4 understanding:1 canonically:4 slow:1 address:2 consideration:2 quite:1 change:7 schiff:1 instituto:1 wesley:1 institute:1 root:1 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quant-ph9903102.txt |@word sci:1 consider:3 remarkable:1 magnetic:8 lack:1 dynamic:1 leads:1 p02:1 scalar:1 manages:1 computation:2 foundations:1 consists:1 follow:5 expressions:1 scr:1 whose:4 aligned:1 concerned:1 involve:2 containing:1 tn:1 fischer:1 tk:3 th:1 under:1 norm:3 ta:1 straightforward:3 far:2 implicitly:1 rise:1 springer:1 geometrical:7 putting:1 summarized:1 cook:2 experimentally:1 difference:3 matrices:1 condition:1 school:1 whitaker:1 level:3 evaluation:1 large:5 discrete:1 vector:7 math:2 guiding:1 small:2 setup:2 force:1 cosn:1 sin2:2 direct:1 iaσ:6 approximation:1 zero:5 perspective:1 incidentally:1 further:2 dynamics:2 scientific:1 what:1 rate:2 clock:1 deeply:1 sum:1 selected:1 cell:1 version:3 above:11 new:2 acknowledgments:1 evolving:1 full:1 eksp:1 component:4 here:2 fisica:2 mev:1 cos2:2 relaxation:1 directions:1 path:5 along:3 table:2 appears:1 change:3 obtained:2 remark:1 suitably:1 study:1 larger:2 products:1 bhandari:2 action:3 changes:3 der:1 badurek:1 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quant-ph9904014.txt |@word partial:1 virmani:2 alg:1 lack:1 results:2 entropy:3 lewenstein:2 edu:1 consists:1 sci:1 research:1 consider:1 certainly:1 byrd:5 ucsb:1 preserved:1 th:2 under:4 tf:2 stochastic:2 fax:1 orthogonal:1 choice:1 fall:1 matrices:13 condition:3 level:1 did:1 vector:1 morozova:1 eigenvalues:6 barbara:1 unaware:1 haar:3 consistent:1 further:1 calzetta:1 eigenspaces:1 ruskai:1 even:1 what:1 sud:4 appear:4 sum:1 expressed:1 uniform:4 new:4 increasing:1 acknowledgments:1 component:1 here:3 ranges:1 desired:1 plenio:2 fulfill:2 represented:1 slater:10 quark:1 logarithmic:1 obtained:1 institute:1 study:1 studied:1 leaving:1 prior:2 action:1 redundancies:1 inference:1 classification:1 apr:1 marginal:1 app:1 replace:1 conjunction:1 use:1 takes:2 would:8 negative:2 classically:1 linear:1 therefore:1 means:2 theoretical:1 more:4 naive:1 normalized:5 particular:2 cases:1 parameterize:1 springer:1 averaged:1 modified:1 obvious:1 following:1 making:2 trans:1 indicated:1 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quant-ph9904015.txt |@word gv:5 since:8 partial:1 consider:3 maximum:1 yeo:1 magnetic:1 varying:3 results:8 leads:5 future:1 scalar:2 concept:1 microwave:1 lewenstein:3 c2:16 consists:2 gm:4 gl:1 contributions:2 whose:3 calculate:4 zone:1 eˆ:3 dp:1 tp:3 presents:1 charge:1 does:5 present:2 excluded:1 tf:3 ωt2:2 worth:4 indicating:6 ingredient:1 kρ:8 evolves:2 far:10 rise:5 conditions:2 wave:4 figs:6 refractive:5 resonant:2 iǫi:1 difference:1 exact:2 condition:2 treating:1 illustrated:1 quantitatively:1 solves:1 level:3 opt:3 positions:2 list:1 solution:1 integrated:1 large:3 integro:3 vector:9 small:15 gauge:1 markov:7 referred:1 inspection:4 ρk:6 bessel:2 chew:1 milonni:1 averaged:1 ρjn:1 consistent:4 d3:4 measurable:1 approximation:8 surrounding:6 rate:71 rigorous:1 further:5 odd:1 situated:3 substitute:2 linear:5 even:2 index:5 what:5 assisted:8 expressed:2 agrees:1 current:2 3i:2 version:1 ˆf:4 ξgl:2 new:2 ˆj:5 contributes:4 ˆl:3 acknowledgments:1 contrast:2 publications:1 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quant-ph9904016.txt |@word unavoidable:1 partial:3 consider:2 global:4 results:1 eds:3 grateful:1 managed:1 expressions:1 localized:1 seemed:1 depend:1 calculate:1 deterministic:2 nonlocal:2 tn:5 program:1 tk:10 under:1 spec:2 sent:1 applied:1 g2:4 g1:3 far:2 wave:2 every:1 experimentally:1 matrices:1 condition:2 presented:2 t6:5 turns:1 solution:4 concluded:1 prevent:1 consistent:1 zz:2 dynamics:1 chem:1 haag:2 linear:4 even:3 what:1 nonlinear:31 section:4 experiment:1 new:1 method:2 clausthal:4 evolving:1 justification:1 exchange:2 here:1 ansatz:1 eikx:3 directions:1 xα:4 equations:8 interpret:1 antisymmetric:1 technical:1 involved:2 inspired:1 changed:1 allows:1 resulting:2 stimulating:1 published:1 suitable:2 changes:1 tu:2 projection:2 explained:1 integrations:1 schilling:2 derivatives:1 use:2 commun:3 probabilities:1 gruber:1 ψt:32 next:1 bialynicki:7 therefore:4 associated:1 type:2 theoretical:2 more:1 formally:1 initial:3 operators:2 odinger:13 tested:1 appendix:2 normalized:1 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quant-ph9904017.txt |@word limited:1 concept:4 partial:2 consider:4 gupta:1 rev:19 particular:3 results:8 grateful:1 follow:1 involved:1 replacements:14 calculate:1 i2:4 show:2 finally:2 compensate:1 squeezing:9 under:4 stochastic:1 td:71 include:1 worth:1 case:1 kumar:1 very:1 frequencies:7 springer:1 ηii:2 wave:1 onig:1 figs:5 condition:4 level:1 lter:2 mirror:2 solution:2 damped:6 solved:2 enhance:2 optics:2 setup:2 hasegawa:1 lˆ:2 measuring:1 employing:1 carter:2 direct:2 pulse:21 approximation:5 second:1 dissipation:1 further:3 dynamics:2 implemented:1 kitagawa:1 spectral:23 optimize:2 nonlinear:3 sub:15 section:2 selected:4 brief:1 uniform:1 ˆa:3 experiment:1 above:1 selecting:2 ˆi:6 increasing:4 method:1 contrast:1 coefficient:17 full:2 degree:1 respectively:2 component:4 here:3 agreement:3 reported:1 them:2 ansatz:1 concluding:2 strong:7 equations:2 appears:2 change:1 obtained:7 shift:2 study:2 studied:2 allows:1 periodic:2 resulting:1 fourier:1 studies:1 hn2:3 plotted:3 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quant-ph9904021.txt |@word limited:3 magnetic:13 four:7 equiprobable:2 whose:4 γp:1 γt:14 under:5 solution:1 vector:4 succession:1 enhance:1 enjoy:1 force:3 elegant:1 likely:2 even:3 established:1 errors:1 ˆb:8 above:2 new:3 evolving:2 never:4 here:5 reported:1 plenio:1 path:1 interpret:1 contraction:1 obtained:1 study:1 fourier:9 projection:1 total:5 unit:3 would:6 army:1 calt:1 arms:1 call:1 therefore:7 type:1 until:4 separated:2 expose:4 berlin:1 correspondingly:1 springer:1 characterize:1 work:2 grover:10 concepts:1 my:1 example:10 give:2 bennett:2 naturally:2 involve:2 indicates:2 point:4 end:1 thing:2 provide:1 verify:1 enk:1 feature:1 how:2 nontrivial:4 symposium:2 brassard:1 fourdimensional:2 ancilla:6 earlier:1 minimized:1 modest:1 destined:1 minimizes:2 unentangled:3 types:1 effective:2 complexity:1 nascent:1 algorithms:2 enter:1 order:6 operations:1 restriction:1 feedback:1 office:1 over:1 satisfied:1 japan:1 satisfies:1 before:1 khalili:1 exhibits:1 better:4 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quant-ph9904022.txt |@word limited:3 logarithms:1 code:5 versatile:1 consider:2 chain:4 illustrates:1 magnetic:2 global:4 shor:6 projected:1 leads:1 roy:1 concept:1 satisfactorily:1 computation:11 edu:1 obtaining:1 query:1 latorre:1 spacetime:2 payoff:1 whose:1 21st:1 tracing:1 universe:1 transferred:1 description:2 braginsky:2 factoring:1 finally:2 does:2 helps:1 th:3 under:5 must:2 resources:2 subtleties:1 applied:2 supported:1 string:1 sitting:1 very:3 intriguing:1 translationally:1 wave:1 me:3 ultraviolet:3 formula:1 classifications:1 emphasized:2 evaporation:2 manyparticle:1 founded:1 hamiltonian:8 turns:1 nucl:3 michael:1 applicable:1 large:5 discrete:1 insights:1 vector:1 fourier:5 small:2 enhance:2 shows:1 dave:1 degeneracy:8 jeff:1 measuring:2 strongly:6 smaller:2 force:3 grateful:1 disciplines:1 renormalized:1 discover:1 fusion:1 past:1 rate:1 design:1 qualitatively:2 dynamics:4 b535:1 distance:5 quite:1 even:4 established:1 what:5 errors:1 developed:1 apparatus:3 deepen:1 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