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quant-ph9909055.txt |@word gt:3 partial:1 consider:9 remarkable:1 rev:12 lack:1 results:1 acknowledgements:1 leads:2 quadrature:1 gd:2 entropy:17 whose:2 calculate:1 4ns:2 γs:3 tr:3 versity:1 quasi:4 squeezing:13 those:5 γa:1 p2:1 futhermore:1 very:1 wave:2 fan:1 resonant:1 husimi:1 difference:2 slov:1 moya:1 presented:3 tra:2 knight:3 solution:3 leave:1 au0:1 interpolating:4 small:2 eigenvalues:2 optics:3 strongly:1 smaller:2 occurrence:1 oscillation:19 sin2:8 hillery:1 approximation:1 elegant:1 second:2 tana:1 substituting:2 further:3 dynamics:1 estimated:1 what:1 nonlinear:2 sub:5 section:4 expressed:1 experiment:3 sus:1 3n:1 above:3 new:9 increasing:1 method:1 satisfy:1 lee:1 respectively:6 component:1 aσ:5 here:6 behaviour:3 desired:1 china:2 cos2:5 separation:1 ratio:10 strong:6 contraction:1 obtained:6 remark:1 exemplified:1 institute:1 involved:1 study:7 studied:2 suggests:1 amount:1 periodic:3 products:1 poisson:2 resonance:2 examining:1 buˇzek:1 useful:2 ratios:1 explained:1 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quant-ph9909068.txt |@word represent:1 partial:1 consider:1 ceases:2 gp:1 rev:10 dependence:1 results:1 existing:1 leads:2 eds:2 ge:1 generalize:1 broader:1 constants:1 gn:1 gm:1 reˇ:1 compact:2 depend:2 illustrates:1 recurrence:1 quasi:3 anharmonic:4 norm:3 g3:1 g2:4 g1:9 very:4 ginsburg:1 srivastava:1 cos2:1 wave:6 denoted:1 summarized:1 mixing:2 tridiagonal:2 difference:2 exact:4 condition:3 partitions:2 illustrated:2 plets:1 hamiltonian:12 bn:1 irreducible:1 tanh:2 solution:10 occurs:1 discrete:1 vector:2 indices:1 anal:1 terminating:2 upper:2 abbreviated:1 work:1 methodical:3 sinh2:2 sukhatme:2 oscillator:5 cosh:10 feasibility:1 dalton:1 second:4 castro:1 growing:1 further:5 chem:1 odd:8 canonical:1 even:12 index:2 adds:1 appear:3 morse:8 specification:1 while:1 gj:2 current:1 twins:1 above:4 new:11 appeal:1 method:8 exercise:2 satisfy:2 full:4 lee:1 relates:1 respectively:3 never:1 modify:1 here:2 behaviour:1 contemplate:1 asymmetry:2 ansatz:1 sinh:10 represented:1 principle:1 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quant-ph9909069.txt |@word partial:1 consider:3 rev:2 results:3 grateful:1 edu:1 consists:2 depend:1 calculate:1 analogous:1 include:1 chennai:1 straightforward:1 song:3 very:7 rise:1 stocker:1 deformations:5 b402:1 hamiltonian:4 did:1 pacs:1 large:1 small:5 pramana:1 occurrence:1 cosh:7 zero:15 canonical:2 ramachandran:1 stands:1 sum:2 expressed:1 suspect:1 above:2 new:1 method:4 contrast:1 pose:1 behavior:1 ibid:4 reported:1 sinh:19 address:1 extreme:1 institute:1 study:2 studied:1 hospitality:2 conveniently:1 involves:1 followed:1 jagannathan:2 floratos:1 summation:1 apply:1 qze:3 readily:2 narayana:3 use:1 proceed:1 would:1 next:1 nucl:1 fractions:1 introducing:1 operators:1 apparent:1 nkt:2 known:4 cases:1 eγ:2 eβ:5 me:2 deformed:13 work:3 oscillator:7 modified:1 reproduce:1 values:1 temperatures:8 following:1 my:2 stimulating:1 india:1 high:11 numbers:2 sense:1 times:2 evidently:1 end:1 rather:2 torino:2 chemical:2 how:1 pure:1 ordinary:5 parameter:2 l873:1 simplicity:1 npn:1 algebra:3 may:7 thermodynamic:3 oscillators:22 after:1 derived:1 different:2 hence:2 fh:1 verified:2 parallel:1 birman:1 order:4 typical:1 developed:2 over:1 statistical:3 derive:3 thank:2 ln:7 inclusion:2 boson:17 forms:1 systems:1 deformation:4 non:1 return:1 greiner:1 introduce:2 now:3 yu:1 colleagues:1 possess:1 eigenvalue:3 term:2 2q:2 e2β:2 thankful:1 university:1 2e:2 2a:1 2m:1 mean:2 rajasekaran:3 qz:3 primarily:1 fq:12 energy:23 journ:1 challenges:1 extended:1 ex:16 begun:1 quantum:4 eq:10 leave:1 since:2 crucial:1 cancels:1 reformulate:1 investigation:1 correct:12 theory:23 southern:1 standard:2 difficulty:1 york:1 put:1 publication:1 omit:1 βz:1 feasible:1 βe:40 int:2 expedient:1 consequence:1 βn:3 facilitate:1 first:6 ding:1 probability:4 number:6 precisely:1 electronic:1 xu:1 given:7 perturbation:2 temperature:10 lavagno:3 relations:1 their:1 scheme:1 gives:1 zeroth:2 2ak:1 part:1 x2:1 qk2:1 kind:1 unfortunately:1 iteration:6 second:1 annihilation:1 fermionic:1 future:1 powers:1 exhibit:1 function:25 rewrite:1 spectrum:1 generalization:1 mishra:2 seem:1 clearly:1 convenient:3 able:1 note:2 instance:1 nuances:1 potential:3 analog:1 play:1 shall:5 who:1 commutation:1 lee:1 consequences:1 later:1 yang:1 kt:1 swamy:3 physics:1 fact:1 quantity:1 incorporate:1 analogue:1 find:2 occupation:1 q2:1 based:1 only:2 imsc:2 goes:1 di:1 familiar:2 express:2 expectation:1 words:1 during:1 occupational:3 arxiv:1 summary:1 qa:1 qe:8 nβ:1 nγ:2 fugacity:1 set:2 sep:1 namely:4 result:5 biedenharn:1 discussions:4 nuc:1 incorporating:3 subject:2 interacting:1 phonons:1 review:1 uβ:2 various:1 closed:2 limit:17 subscript:1 terms:3 attention:1 reproduces:1 distribution:18 both:1 limits:5 many:2 against:1 hω:25 altherr:1 expression:2 arbitrarily:1 mechanics:2 point:16 corresponds:2 cd:1 described:1 basis:2 footnotes:1 due:1 been:1 eβe:8 dropping:1 interest:1 expected:3 ph:1 pn:10 abstract:1 corresponding:2 quantities:2 c2:17 c1:18 case:8 tanh:1 baskaran:1 e49:2 value:1 will:4 cast:1 replaced:2 evaluating:2 hωk:1 a22:1 a24:1 a25:2 a26:1 thus:15 herein:1 il:1 fermion:1 containing:1 develop:1 make:1 same:4 wherein:1 quant:1 grand:1 dimensionless:1 gets:1 literature:1 see:2 upon:1 effect:1 director:1 eβµ:1 partition:9 kaniadakis:3 confronted:1 well:4 quarati:3 lim:2 arising:1 drawing:1 just:1 obtain:6 valuable:2 reviewed:1 sabbatical:1 viswanathan:3 sciences:1 alternate:1 thermodynamics:1 internal:7 lett:5 mod:4 easily:1 possible:1 harmonic:5 smallness:1 occurring:1 necessary:1 like:1 follows:2 reduces:2 discarded:2 alternatively:1 replacement:1 mathematical:2 because:2 methods:1 classical:5 creation:1 some:4 begin:1 qex:2 happens:1 extensively:1 manipulations:1 does:3 journal:1 arbitrary:1 properties:1 takes:1 obeys:1 consequently:1 other:2 undeformed:10 obtaining:2 lies:1 references:1 determine:1 operator:4 deal:1 springerverlag:1 there:1 approximate:3 long:1 accordingly:5 much:1 bosons:1 low:7 was:1 lowest:1 form:9 but:2 politecnico:1 compute:3 uq:4 us:3 gratifying:1 ωk:5 simplifying:2 parthasarathy:3 demonstrate:2 problem:1 expect:1 aa:1 developing:1 computing:1 defined:3 ak:2 am:2 general:1 examine:1 aizawa:1 prevail:1 inc:1 no:2 when:3 ne:13 illinois:1 nx:6 acknowledgments:1 valid:1 role:1 papers:1 department:1 nq:1 conclude:1 briefly:1 includes:1 implies:1 longer:1 italy:1 equivalently:1
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quant-ph9909070.txt |@word limited:1 logarithms:1 sci:1 consider:1 magnetic:1 varying:1 fabricated:1 computation:7 aly:5 consists:1 4e2:1 adjustment:1 localized:3 sch:1 zone:1 lining:1 tp:5 containing:1 environment:2 under:1 td:7 supported:1 r12:2 outside:1 shifters:1 delong:1 maas:1 readout:1 electron:13 figs:1 mixing:1 laser:6 difference:2 al0:3 level:3 applicable:1 correct:1 large:5 discrete:1 small:2 der:1 epitaxially:1 employing:1 compensated:1 alx:7 ten:1 hage:1 pulse:3 approximation:2 rate:1 design:2 insertion:1 further:1 dephasing:5 expressed:1 thickness:3 current:1 designing:1 obvious:1 d1:2 consisting:1 contrast:1 fujiwara:1 satisfy:1 wavefunctions:4 l1:3 spacing:1 here:1 reported:1 asymmetry:5 cylindrical:2 free:1 others:1 ratio:2 along:6 strong:4 obtained:1 search:1 naval:1 involved:1 study:2 larger:1 through:7 prior:1 accomplished:1 simultaneous:1 resulting:3 knill:1 resonance:1 narrow:3 studies:1 plotted:2 appropriately:1 via:1 useful:2 layer:2 private:1 highly:1 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quant-ph9909073.txt |@word represent:1 concept:1 consider:2 focus:1 leads:1 commute:1 shimony:1 go:2 whose:2 deterministic:1 tr:4 γv:3 finally:1 those:1 excluded:1 under:2 hermann:1 analogous:1 worth:1 indicating:1 ta:1 p2:1 kent:2 straightforward:1 orthogonal:4 far:1 springer:3 corollary:1 every:2 interpreting:1 decide:1 difference:1 condition:1 subsets:3 presented:1 die:1 notes:1 assignments:1 irreducibly:1 section:1 path:2 unsharp:2 enforce:1 upper:2 occurrence:2 consistent:2 measurable:1 concludes:1 specker:2 theory:5 even:1 established:1 contradicts:1 sum:2 brief:1 experiment:1 above:4 infamous:1 obvious:1 journal:1 contrast:2 full:2 notions:1 degree:1 respectively:2 loose:1 discrete:1 here:4 explore:1 address:1 represented:4 consideration:1 appears:1 extreme:1 obtained:2 formalizing:1 vectors:1 credit:1 simultaneous:1 published:1 suitable:1 makes:1 uniquely:2 appropriately:1 projection:1 logical:1 objectively:1 first:1 boolean:1 aimed:1 resurrection:1 vρ2:1 vρ1:1 tools:1 unit:1 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quant-ph9909074.txt |@word represent:1 washed:1 magnetic:3 splitting:1 ds:3 leads:2 roy:1 entropy:4 computation:4 follow:1 zinn:1 whose:1 γi:5 marks:1 case:5 very:1 pichard:1 aberg:1 electron:1 stays:1 mixing:3 experimentally:1 matrices:1 condition:1 squares:2 level:8 proposals:3 vagner:2 large:5 horoi:1 eigenvalues:2 vincenzo:1 upper:2 privman:1 deutsch:1 lecture:1 blue:1 second:1 realistic:1 jacquod:1 estimated:1 odd:1 linear:1 even:4 established:1 xor:1 diamonds:1 rate:1 multiqubit:1 sum:1 near:2 access:1 errorcorrecting:1 above:3 pashkin:1 increasing:1 nakamura:1 body:4 full:2 chose:3 ibid:1 exchange:1 realizations:2 spacing:16 residual:5 here:4 hundreds:1 les:1 represented:1 ratio:2 strong:2 appears:4 change:2 institute:1 study:2 changed:1 periodic:1 poisson:2 usually:1 resonance:2 studies:2 king:1 composed:4 useful:1 technologies:1 logical:1 highly:1 scaled:1 giannoni:1 decrease:1 glance:1 total:3 linearly:1 alamitos:1 use:3 takes:3 would:4 remains:1 coupled:6 predictions:1 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quant-ph9909075.txt |@word limited:1 cπ:2 customary:2 consider:4 varying:4 focus:1 leads:2 avalanche:9 computation:1 consists:4 partial:1 remarkably:4 eη:1 issues:1 scr:1 whose:2 paris:4 including:1 finally:2 program:1 those:2 pay:1 global:1 amplitudes:5 straightforward:1 orthogonal:2 very:4 results:1 govern:1 condition:2 splitter:3 slov:2 branca:1 presented:1 transmission:2 turns:1 p01:2 large:2 small:1 enhance:1 optics:2 inserting:1 smaller:1 illustrating:1 sin4:1 sin2:37 measurable:1 pulse:3 second:9 value:7 dynamics:1 port:3 substitute:1 nonlinear:1 witnessed:1 ˆx:4 ˆy:7 section:8 expressed:1 current:3 above:5 new:3 method:2 ˆn:5 led:2 degree:1 fmax:1 respectively:2 component:2 teleportation:1 here:2 atoms:2 ionization:1 reported:3 plenio:1 nonunit:1 cos2:33 address:1 active:1 observing:1 imperfections:4 obtained:6 chumakov:1 maccone:1 incoming:4 involved:1 study:2 losses:1 allows:1 reason:1 resulting:3 walther:2 usually:2 resonance:1 implement:1 makes:1 involves:3 pxy:2 via:1 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quant-ph9909076.txt |@word consider:1 global:4 results:1 edu:1 follow:1 deterministic:1 send:1 chapt:2 under:2 stochastic:14 fax:1 orthogonal:1 condition:7 cmn:3 tre:2 eigenvalues:1 mn:1 10b:1 10a:1 direct:1 zero:1 aim:1 itˆ:1 sum:2 above:1 ρu:2 acknowledgments:1 coefficient:2 mr:4 here:1 equations:1 change:1 remark:1 institute:2 study:2 reports:1 permutation:1 verri:1 appropriately:1 extra:1 generality:1 redefining:1 use:2 takes:1 commun:1 positive:13 contains:2 noting:1 sharpen:1 operators:5 phone:1 berlin:1 excellent:1 cases:1 hold:2 iii:1 must:1 kraus:1 springer:1 ρk:1 work:1 infinitesimal:7 values:1 ρv:2 numbers:2 lρ:1 process:1 preserving:2 14b:1 14c:4 14a:1 guarantee:1 dwt:4 returning:1 maps:1 verlag:2 map:2 product:2 algebra:1 dynamical:1 davies:1 restriction:4 september:1 over:2 expects:1 london:1 diagonalized:2 rapidly:1 interesting:1 forms:1 systems:2 stephen:2 defining:1 correspondence:2 13b:3 them:1 now:4 term:3 always:2 magnitude:1 energy:1 idea:1 quantum:3 our:2 eq:31 special:1 out:1 matrix:10 itˆo:9 since:5 suffices:1 math:3 theory:2 gardiner:1 diagonal:1 completely:11 15c:2 definition:1 derivation:3 route:1 impose:1 nonnegative:2 hence:2 adjoint:5 heuristically:1 xa:1 number:1 multiplying:1 directly:1 open:1 equating:1 given:1 rewritten:1 introduction:1 eqs:4 achieved:1 ias:1 gives:2 part:4 coefficients:1 18b:2 18c:1 18a:1 determines:2 cyclic:1 normalizing:1 7c:3 7b:2 7a:2 ann:1 self:5 note:1 take:1 indexed:1 so:5 calculus:7 play:1 trace:5 index:3 trρ:1 birkh:1 most:1 phase:2 90er40542:1 observation:1 ρvn:10 iassns:1 exp:1 normally:1 supported:1 substituting:4 find:1 d1:1 basel:1 only:3 princeton:2 factor:2 dn:18 get:8 de:3 overall:1 expectation:1 dt:18 evolution:7 qr:1 intuitive:1 arxiv:1 yield:1 set:3 sep:1 differentials:5 see:3 sec:2 subject:1 exploited:1 give:3 symmetric:2 between:2 email:1 preserve:1 recently:1 vanishing:1 uρ:2 restrictions:2 taking:1 equal:1 connection:1 expression:1 conclude:1 simple:3 satisfaction:1 anti:1 respect:1 specializing:1 kossakowski:2 dropping:1 ph:2 corresponding:3 covariance:2 those:3 case:4 semidefinite:1 value:1 will:1 while:4 13c:3 unitary:1 gorini:2 refs:1 thus:3 13a:1 vn:48 ih:3 ik:1 specialization:2 grant:1 same:2 unity:2 complex:1 quant:2 physical:1 independent:1 sudarshan:2 hand:1 auser:1 idempotent:1 academic:1 olden:1 left:1 less:1 obtain:3 vρ:2 generator:5 density:6 transformed:1 c11:1 transformation:6 generalized:2 real:4 fluctuating:1 inversion:1 press:1 using:3 advanced:2 identifying:1 reduces:1 arbitrary:1 simply:1 reduced:1 right:2 methods:2 back:1 understood:1 cr:9 proofs:1 does:1 exposition:1 cnn:1 cnm:4 semigroups:1 obey:1 equivalent:1 although:1 dependence:1 o:13 important:1 frigerio:1 into:4 references:1 operator:3 hep:1 additional:1 there:1 start:1 much:1 handbook:1 was:1 form:9 construction:1 lindblad:5 fg02:1 dissipative:1 adler:3 made:2 evident:1 us:2 un:4 simplifying:1 parthasarathy:2 ue:1 called:1 abstract:1 contribute:1 general:4 peres:3 single:1 simplest:1 constructed:1 nj:2 no:4 when:1 vanishes:2 ny:1 book:1 role:1 d2n:2 department:1 nq:2 nr:6 superfluous:1 elements:1 includes:1 15a:1 generated:1 15b:1 15d:2 sides:1 structure:2 lane:1 implies:5 dρ:8 original:2
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quant-ph9909077.txt |@word ibid:1 represent:5 concept:2 consider:2 illustrates:1 magnetic:4 illustrated:1 go:1 whose:1 preserves:1 referring:1 concerned:4 technique:1 tn:3 finally:1 education:1 th:1 ti:10 tf:3 case:1 risk:1 orthogonal:1 far:2 implicitly:1 wave:26 under:1 trouble:1 condition:1 entire:1 immediately:2 hamiltonian:6 turns:1 t2:2 solution:1 t0:13 t1:7 try:1 discrete:1 vector:5 small:3 equation:6 aeronautics:1 l93:1 bacon:1 sign:1 zero:3 evaluated:2 chen:3 tierney:1 linear:1 even:1 index:1 what:1 stands:1 incompatible:2 expressed:8 uniform:2 above:5 lifshitz:1 values:1 net:1 coefficient:1 pose:1 degree:1 respectively:1 here:2 following:1 velocity:4 eikz:1 separation:1 represented:2 along:1 promptly:1 equations:4 change:1 schiff:1 increments:1 wesley:1 involved:1 study:1 larger:1 adopting:1 involves:2 uniquely:1 emerge:1 4a2:1 extra:3 plenum:1 outcomes:1 total:2 select:1 use:5 handled:1 would:2 probabilities:1 ψs:7 forcefully:1 ψk:2 ψn:10 ψl:1 εni:1 type:3 more:1 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quant-ph9909078.txt |@word represent:2 partial:1 consider:5 results:3 follow:1 expressions:1 duplicated:1 rd:1 inverse:1 equivalence:2 behave:1 under:1 include:1 applied:8 continued:2 solution:2 science:1 construed:1 consistent:1 direct:1 second:2 design:1 further:1 gm:1 linear:2 what:4 abd:1 appear:3 section:4 expressed:2 infinitesimal:2 new:2 method:4 ggu:2 notions:1 applies:1 objects:2 represented:3 b33:1 obtained:1 naval:1 rigorously:1 herrmann:16 accomplished:2 action:2 composed:3 followed:1 merely:2 summation:6 apply:1 total:1 establish:1 usa:1 remains:1 contains:2 next:1 more:2 operators:3 smirnov:1 particular:1 known:3 producing:1 must:1 md:1 word:2 r2:1 recall:1 modified:2 paragraph:1 values:2 following:1 dec:1 example:1 f0:2 stated:1 process:7 purposes:1 pieces:1 states:1 numbers:2 robinson:2 information:18 rather:4 how:1 algebra:1 may:1 mapping:1 applications:1 designed:1 waves:1 representations:1 journals:1 realized:1 imagery:1 natural:7 consequently:1 st:8 complexity:1 so:1 ultimate:1 fundamental:1 representation:1 order:2 interpretation:1 indeed:1 over:1 entity:1 course:1 including:2 mentioned:1 termed:1 matrices:2 affine:5 coordinates:10 actually:1 forms:1 production:1 injection:1 violating:1 descriptive:4 combination:5 material:1 they:3 discuss:1 nor:3 represents:1 term:2 characterizes:2 establishing:1 each:5 characterized:1 generation:3 series:1 idea:1 operator:5 books:1 measure:1 quantum:6 our:1 naming:2 shown:1 matrix:8 robert:1 since:4 content:2 hill:1 occurs:2 math:2 theory:4 mechanisms:2 standard:9 completely:1 formation:1 york:2 org:3 wanted:1 definition:1 r1:1 language:2 r3:1 times:2 hence:3 first:4 major:2 encoding:2 number:3 multiplying:1 done:2 relations:2 kobe:1 quality:1 given:1 construct:1 contra:1 intermediate:10 realization:3 typographical:1 academy:1 b22:1 part:6 somewhat:1 requisite:1 than:4 finitely:1 distance:3 holland:1 distinguishes:1 transferred:1 classes:1 solely:1 result:1 pro:1 modern:1 manner:1 need:4 any:7 viewed:2 forced:1 note:2 internal:6 transmit:1 investigations:1 measures:1 most:1 significant:1 retaining:1 class:1 especially:1 considered:1 physics:2 sum:1 b44:1 pope:1 random:1 analogue:2 translation:1 should:2 entities:3 only:5 abs:2 do:1 notation:1 means:1 dependent:2 between:1 cannot:1 combinations:1 holloway:1 hyperfinite:8 processes:1 arxiv:4 yield:4 predicted:1 through:1 fixed:1 reveals:1 set:4 exists:1 sep:1 bundling:5 relative:2 descriptions:4 nonstandard:2 consequence:1 multifaceted:1 state:10 various:3 simplest:1 approach:1 recently:1 missing:1 however:2 suppressed:1 last:1 many:1 display:1 simple:4 corresponds:1 simply:2 sequences:1 mathematically:1 considering:1 transformations:2 equivalent:1 recaptured:1 three:1 been:3 ai:4 much:1 replicate:1 basic:1 collections:1 ph:2 generating:1 describe:1 quantities:1 case:3 rueda:1 operational:1 value:1 will:2 suppose:1 behavior:4 error:1 procedure:1 vol:1 ir:1 thus:1 non:2 ii:1 characterize:1 itself:2 binary:1 things:1 annapolis:1 same:2 complex:1 quant:1 grand:2 finite:7 events:1 difficult:1 independent:4 used:9 http:3 conceived:2 upon:2 levels:1 purpose:3 infinite:1 identity:1 modeled:3 well:2 analysis:2 patterns:1 without:1 qualities:2 coordinate:12 entry:1 model:11 usual:4 less:1 being:1 obtain:4 human:1 using:2 character:1 hyperreal:2 transformed:1 transformation:6 bij:5 bii:3 read:1 sums:1 possible:1 b55:1 unification:2 world:5 unique:3 necessary:1 like:2 particle:4 follows:2 specific:21 yields:6 either:1 arbitrary:1 mcgraw:1 page:1 mathematical:5 www:3 methods:1 b1:3 b2:2 proper:1 nonzero:1 instantaneous:2 everything:1 does:2 eliminate:1 indication:1 particles:5 refer:1 object:1 scientific:1 bn:1 continuing:1 bi:2 bj:4 rudin:1 about:1 actual:2 would:4 anything:1 discussed:2 meaning:1 slightly:1 statements:1 into:3 within:3 chubykalo:1 appropriate:2 references:1 determine:1 einstein:1 elementary:8 amsterdam:1 technically:1 1999a:4 1999b:2 assumed:2 there:9 coordinatewise:2 transform:1 nova:1 quanta:1 ed:1 north:1 form:4 but:4 principles:1 astro:1 repeated:1 encoded:2 line:1 count:2 applying:1 intuitive:3 characteristic:1 operationally:2 problem:2 called:1 constant:1 separability:1 infinitesimals:1 defined:2 abstract:1 aj:3 nsp:1 general:7 single:3 physical:5 chance:1 functions:1 no:1 when:6 application:3 other:4 b11:1 department:1 mathematics:1 lend:1 models:3 symbol:1 a1:3 generated:3 suppression:1 included:1 implies:1 assume:1 notion:2 strings:1 once:1
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quant-ph9909079.txt |@word consider:8 caused:5 results:1 leads:1 scalar:1 transits:4 causes:2 scr:1 const:1 γt:2 environment:2 excluded:1 under:3 analogous:1 applied:1 supported:1 orthogonal:2 very:7 pascazio:2 wave:3 electron:1 cook:1 experimentally:1 difference:1 rotating:1 level:6 solution:2 t1:32 large:3 discrete:6 small:4 oscillation:1 direct:1 approximation:2 surrounding:1 rate:4 further:1 rivera:1 substitute:1 index:1 what:2 section:7 expressed:2 annals:3 above:1 new:2 method:3 full:4 respectively:2 never:1 chumakov:1 others:1 directions:1 consideration:3 strong:2 z0:13 change:1 deduced:2 obtained:1 institute:1 studied:1 resonance:2 makes:1 exited:1 golden:3 projection:2 mensky:2 transit:1 coinciding:1 decrease:2 apply:1 qze:10 use:2 ψi:3 fonda:1 type:1 more:2 formally:1 becomes:1 odinger:2 domination:1 particular:3 cases:3 kraus:1 account:1 eiω1:1 quantized:1 equation:5 work:1 obvious:1 following:1 spontaneous:10 example:2 process:2 chiu:1 states:8 numbers:3 sense:1 united:1 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quant-ph9909087.txt |@word gw:15 concept:4 partial:1 consider:13 remarkable:1 similarity:3 dynamic:1 results:1 four:1 scalar:5 p00:1 follow:2 gi:7 whose:1 inverse:2 depend:5 passage:1 charge:6 present:2 th:2 ti:1 applied:1 federation:1 g1:8 wave:9 electron:10 sc4:3 matrices:9 condition:2 dimensionality:1 presented:1 turns:4 t2:3 t1:3 try:1 vector:34 section:4 relation:8 upper:1 10b:1 10c:1 10a:2 sin2:5 direct:4 10d:2 cosh:5 approximation:5 second:3 pl4:1 pass:3 further:1 dsα:3 substitute:2 theory:9 index:3 g21:1 sum:2 selected:1 expressed:2 above:2 new:3 contrast:1 satisfy:1 respectively:1 component:6 here:10 l21:1 hki:16 groups:8 represented:2 consideration:2 along:2 equations:51 obtained:1 generalizing:1 glm:1 zm:20 involved:1 study:1 vectors:45 allows:2 quaternion:3 aki:2 resulting:1 action:30 changes:1 named:3 mail:1 a21:1 summation:2 apply:1 neutrino:12 operational:1 planck:1 unit:5 clifford:6 use:4 takes:2 would:1 msu:1 next:2 comparing:1 therefore:6 taken:1 themselves:1 type:5 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quant-ph9909088.txt |@word limited:3 consider:2 particular:1 results:8 leads:1 gd:7 garching:1 computation:1 crete:3 involved:1 gk:3 gj:11 gr:4 contexts:2 integral:2 does:3 those:1 amplitudes:5 without:1 far:2 frequencies:2 choice:1 resonant:4 affect:2 difference:1 exact:5 level:4 solution:5 t0:3 large:1 discrete:13 pbg:3 small:3 markov:2 optics:1 possibility:3 upper:3 employing:1 lewenstein:1 oscillation:2 dealing:2 strunz:3 approximation:4 enhancement:1 further:1 dynamics:5 estimated:1 obey:1 established:2 appear:1 sum:1 near:4 above:4 judicious:1 increasing:1 method:9 full:1 degree:1 whose:1 respectively:2 here:3 atoms:1 desired:2 explore:1 inversion:2 address:1 based:1 equations:7 change:1 box:1 institute:1 shift:1 study:1 reports:1 resonance:2 plotted:1 2gj:2 bjk:2 via:1 useful:1 figure:1 scales:1 requiring:1 semiconductors:1 replace:1 flexibility:1 apply:1 should:1 planck:1 readily:1 plot:2 handled:1 waveguides:1 prove:1 remains:2 calculation:4 vehicle:1 sought:1 theoretical:1 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quant-ph9909089.txt |@word logarithms:1 titech:2 partial:1 consider:1 global:1 results:2 leads:1 roy:1 generalize:2 computation:7 consists:1 query:2 primes:1 gh:12 compact:1 whose:1 depend:1 calculate:1 contained:1 factoring:2 containing:1 environment:4 finally:5 those:1 th:4 under:4 resources:1 applied:1 amplitudes:8 worse:1 straightforward:1 orthogonal:1 far:1 choice:4 unstructured:4 formula:2 mixing:1 affect:1 exact:2 condition:3 four:1 incoherent:1 level:1 induction:1 large:1 item:3 vector:1 small:4 enhance:1 programme:1 upper:1 periodicity:1 deutsch:1 dealing:1 sin2:6 many:1 chen:1 further:2 dynamics:2 implemented:1 gm:4 even:3 aim:1 what:1 superlattices:1 iterating:1 fine:1 section:2 lengthy:2 access:1 values:1 method:1 satisfy:1 respectively:1 mr:2 discrete:1 ansatz:2 situation:1 represented:1 const:2 standard:2 change:1 obtained:1 search:15 clarendon:1 institute:3 items:12 study:1 larger:1 subcase:1 through:1 example:4 exploitation:1 periodic:3 rf:1 usually:1 hospitality:1 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quant-ph9909093.txt |@word positions:1 concept:1 evidence:1 consider:7 pointing:1 ali:1 magnetic:13 riesenfeld:4 results:13 existing:2 leads:1 roy:2 commute:1 generalize:1 edu:1 consists:1 gn:2 whose:1 simon:6 depend:2 calculate:2 eigenbasis:1 concerned:1 similarity:1 tr:1 finally:2 γn:37 under:6 include:1 subtleties:1 belonging:1 g1:2 pressley:1 choice:1 noncyclic:33 entries:6 experimentally:1 associated:4 difference:1 matrices:5 condition:2 hamiltonian:21 zeit:1 issue:1 solution:5 large:3 discrete:2 vector:2 phase:66 eigenvalues:12 originally:1 degeneracy:11 upper:1 smaller:2 occurrence:1 kato:1 direct:1 literature:1 approximation:6 second:1 ill:1 dynamics:1 substitute:1 linear:3 even:1 stands:7 diag:4 section:11 brief:1 agrees:1 3i:1 experiment:1 subspaces:5 referees:1 nonuniversal:1 new:1 satisfy:3 christian:2 degree:2 exchange:1 respectively:4 proc:2 here:5 explore:1 inverse:1 groups:1 address:1 pati:10 path:2 along:1 equations:1 patches:1 nonunimodular:1 vba:1 antisymmetric:1 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quant-ph9910001.txt |@word limited:1 partial:1 consider:8 results:3 four:4 computation:2 latorre:2 whose:1 c0j:1 c0:1 tr:9 byrd:1 infinitesimally:1 those:1 under:1 analogous:2 applied:2 orthogonal:2 choice:2 should:1 condition:6 lucia:1 presented:1 culminating:1 deals:1 vector:10 math:1 indices:4 eigenvalues:5 upper:5 neighborhood:6 lewenstein:1 sin4:1 sin2:11 sin3:1 surrounding:3 second:2 even:1 gibbons:1 projectors:1 appear:1 giving:1 section:8 near:3 uniform:1 dχ2:2 dχ1:2 3n:7 establishes:2 overcomplete:2 new:4 acknowledgments:1 3e:1 satisfy:4 edited:1 full:1 component:1 khanna:1 here:3 understanding:1 ranges:1 met:1 explore:1 simon:1 cos2:5 concluding:1 obtained:4 antisymmetric:1 naval:1 leaves:1 larger:1 approaches:1 m3n:3 schumacher:1 pascual:2 weird:1 studies:2 uniquely:3 emerge:1 schack:1 useful:1 projection:4 9n:1 marginal:1 explained:1 a22:1 md2:2 summation:1 total:1 establish:1 unit:17 use:6 md1:2 takes:2 usa:1 prove:1 e1:1 negative:1 hilbert:7 classically:1 live:1 e3:4 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quant-ph9910002.txt |@word partial:2 consider:1 rev:11 desirable:1 results:1 entropy:11 research:1 compact:2 ohya:1 tr:12 intensive:1 finally:1 norm:2 straightforward:1 very:3 corollary:1 matrices:2 condition:2 dim:1 knight:1 cavendish:1 large:2 unproblematic:1 noted:1 vincenzo:1 programme:1 rohrlich:1 semicontinuous:2 jump:1 even:3 ˆx:1 above:1 satisfy:1 here:2 behaviour:1 plenio:2 address:2 strong:3 imperfections:1 interpret:1 obtained:1 great:1 institute:2 suggestion:1 schumacher:1 usually:1 suitable:1 madingley:1 univ:1 use:5 additive:1 asymptotic:2 prove:1 positive:2 properties:1 memoryless:1 therefore:2 taken:1 type:1 theoretical:1 operators:1 particular:2 foundations:1 must:3 logarithm:2 springer:2 permits:1 science:2 originally:1 work:1 obvious:1 cam:1 example:4 proof:4 weaker:1 attribute:1 bennett:4 distillation:2 states:13 numbers:3 simple:1 verlag:2 information:2 rather:1 s1:5 holds:2 xˆ:5 pure:3 instead:1 parameter:3 brassard:2 description:2 fe:1 cambridge:2 constants:1 complexity:1 so:4 acknowledges:1 operations:1 interpretation:1 rippin:1 over:2 course:1 paper:1 committee:1 satisfies:2 ieee:1 its:1 perfect:2 constituted:1 monotonicity:2 chosen:1 systems:1 mail:2 might:1 non:1 identically:1 now:1 vidal:1 university:1 inequality:10 each:2 entirely:1 constraints:1 related:1 society:1 expect:1 measure:8 quantum:5 laboratory:1 er:3 space:3 quantify:1 crucial:1 denotes:1 particles:2 acting:1 ref:1 math:2 shows:1 foundation:1 theory:2 free:1 standard:2 approaches:1 formation:2 jozsa:1 pairs:5 monotones:1 separable:4 symmetry:1 number:1 entanglement:32 another:2 impossible:1 given:2 approximately:1 their:1 wootters:3 gives:1 continuous:1 than:1 distance:1 wiesner:1 subsequence:1 crepeau:1 modern:1 fannes:3 final:1 border:1 any:2 conversion:1 lim:2 converges:1 note:2 coincide:1 trace:1 shall:1 measures:6 most:1 regular:1 remarks:1 acknowledgements:1 annul:1 especially:1 considered:1 clear:1 physics:2 satisfies:2 shor:1 show:2 supported:1 spaces:1 based:1 parameters:1 written:1 should:2 only:2 local:1 oct:1 continuity:10 means:1 cannot:1 sources:1 transposition:1 arxiv:1 investigate:1 requirement:1 set:6 exists:1 0he:1 bounds:1 relative:8 see:3 computer:2 result:1 close:1 satisfying:1 inequalities:1 state:10 between:2 petz:1 infinite:1 recently:2 transpose:1 however:1 suggested:1 both:1 σn:3 limits:1 contract:1 otherwise:1 confined:1 relevant:2 appeared:1 asymptotically:1 dimensional:1 sakai:1 sequences:1 speak:1 transformations:1 puts:1 lattice:1 appears:1 ph:12 algebras:2 pl:1 choose:1 general:1 quantities:1 michal:1 maximally:1 case:3 pacs:1 near:1 suppose:3 compactness:1 di:1 property:2 35th:1 chaotic:1 von:2 thus:2 ii:1 itself:1 granted:1 same:1 clearly:1 matthew:2 quant:12 european:1 closest:1 phy:1 uses:1 infinite:1 lower:2 minimize:1 poland:1 severe:1 dimension:1 entanglements:1 popescu:2 newton:1 obtain:2 gda:3 polish:1 σnk:4 density:2 thermodynamics:1 interested:2 transformed:1 lett:8 easy:1 theorem:4 guarantees:1 transformation:1 nielsen:3 possible:1 entangled:3 distillable:3 press:1 unique:1 imposed:1 particle:1 follows:2 stationary:1 essential:1 because:2 often:1 classical:1 sequence:1 some:1 donald:2 convex:1 finite:2 dimensions:1 per:3 manipulations:3 proc:1 symp:1 santa:1 includes:1 cη:1 hilbert:4 about:2 central:1 commun:2 act:1 mixed:1 other:1 road:1 op:3 converging:1 nsk:2 convergent:1 communication:3 into:2 disentangled:2 bound:3 down:1 pair:4 appropriate:1 operator:1 neumann:2 log:31 there:2 vedral:2 astrophysics:1 was:3 function:2 form:2 smolin:2 but:3 hb:2 ha:2 true:1 bures:1 made:1 horodecki:7 whether:1 characteristic:1 variations:1 up:1 limit:2 uk:1 similar:1 called:1 ex:12 ac:1 proved:2 describe:1 denote:1 peres:2 britain:1 our:2 inf:5 metric:3 regime:1 ni:1 functions:2 nm:1 no:1 rains:2 ekert:1 composing:1 tight:1 valid:1 p03b:1 prepared:1 cb3:1 important:2 scientific:1 requires:1
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quant-ph9910003.txt |@word routhian:1 consider:2 magnetic:4 lian:1 ˆj2:17 inverse:2 depend:1 calculate:2 pˆx:1 worth:1 kν:1 ˆji:1 very:3 springer:1 choice:1 ˆjz:1 matrices:2 hamiltonian:21 turns:1 solution:8 large:2 solved:2 vector:3 indices:2 eigenvalues:2 renormalized:1 direct:1 canonical:2 spectral:1 index:1 diag:1 expressed:3 reconstruction:1 new:3 body:2 ibid:1 respectively:1 component:1 here:2 along:2 equations:12 obtained:4 institute:2 study:1 eigenequation:1 minsk:1 φjm:2 conveniently:1 elaborated:1 vij:1 9p:1 total:3 unit:1 distinct:1 eφ:1 next:1 nucl:1 noting:1 ψo:1 ψm:2 taken:1 type:1 becomes:2 operators:3 odinger:9 eν:33 berlin:1 virtue:1 varying:2 known:6 reconstructed:2 account:3 equation:11 labeled:1 following:2 example:2 wang:2 give:2 states:1 axis:3 darboux:2 accordance:2 get:3 2iωt:4 how:1 instead:2 verlag:1 sin:23 may:1 after:2 data:2 realized:1 dynamical:5 effective:1 explicit:3 correspond:3 su:1 representation:1 indeed:1 soc:1 paper:1 through:1 satisfies:1 derive:1 chosen:1 exact:13 solving:2 forms:2 systems:2 belarus:2 introduce:1 they:1 rotation:2 now:1 yu:1 transparent:1 easily:1 university:1 level:1 found:1 2j:2 em:1 directly:1 ed:1 energy:1 inhomogeneous:2 frequency:1 quantum:2 our:1 matrix:6 space:1 since:1 rev:3 research:1 math:1 mπ:3 quite:1 admits:1 york:1 shun:1 dubna:2 first:1 timeindependent:1 iht:5 simplified:1 relations:2 another:1 aharonov:2 ser:1 given:1 rewritten:4 introduction:1 2ωt:4 system:1 construct:2 too:1 relationship:2 academy:1 exactly:8 part:2 anandan:2 iωt:1 cyclic:1 normalizing:1 determined:3 iˆ:19 russia:1 need:1 seek:1 built:1 note:2 sciences:1 potential:7 twochannel:2 channel:3 multiple:1 algebraic:2 phase:18 class:5 considered:2 coincides:1 exp:43 sun:1 physics:1 fact:1 v12:4 timedependent:1 v11:10 rotating:3 relation:3 solutions:14 find:1 based:1 state:4 analytic:3 employed:1 hamiltonians:6 oct:1 goes:1 notation:1 means:4 dependent:13 expectation:3 joint:1 dx:4 dt:6 evolution:2 precession:1 fields:1 arxiv:1 fixed:2 constructing:1 see:1 result:2 analog:1 eigenfunctions:3 nuclear:1 written:3 closed:1 between:2 geometric:9 approach:2 wide:3 terms:4 jm:5 wu:1 ji:1 p2x:6 suggested:1 cos:28 taking:3 energies:1 berry:2 hφ:1 allowance:2 nonadiabatic:4 simple:1 period:1 transformations:5 basis:1 been:2 ph:1 define:1 v22:9 v21:3 arises:1 corresponding:2 spin:7 case:1 value:3 heidelberg:1 nonstationary:8 procedure:5 unitary:7 vol:8 thus:2 bargmann:3 radiation:1 complex:1 quant:1 difficult:1 independent:2 used:4 hand:3 moment:1 purpose:1 potentials:3 schr:9 expression:2 obviously:1 concrete:2 components:3 model:2 chemistry:1 nd:1 vαα:3 obtain:6 using:3 scattering:2 eigenstates:1 alignment:1 preprint:1 jost:2 valid:1 lett:2 iπ:1 solvable:6 transformation:6 momentum:1 generalized:1 iθ:17 around:1 possible:1 corresponds:2 immediately:1 pertinent:1 particle:2 follows:1 adiabatic:1 δm:3 stationary:11 reduced:2 gauge:2 because:2 b1:2 b2:1 does:1 proc:1 bo:7 stone:1 pα:1 dependence:1 o:3 characterized:1 ikα:2 into:2 obtaining:1 bound:3 references:1 operator:6 jin:1 removing:1 initial:6 lond:1 jinr:1 was:1 therefore:1 function:2 form:5 hs:4 but:1 hu:1 construction:1 ho:11 atom:1 absent:1 annihilate:1 evident:3 ωt:7 us:1 limit:1 problem:8 fαα:2 examples:1 kν2:1 defined:4 abstract:1 ao:1 general:2 fizika:1 functions:1 no:2 zhong:1 when:2 detail:1 field:6 other:1 theor:1 conclusion:1 elements:4 eνα:1 models:4 problems:4 cranking:1 generated:1 important:1 variable:1 assume:1 time:20 normalized:1
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quant-ph9910004.txt |@word epeau:1 partial:1 consider:1 rev:16 roy:1 supplement:1 entropy:2 computation:1 compact:1 ahmedabad:1 technique:2 γw:2 γt:1 environment:4 th:1 tegmark:3 p2:3 zhang:1 maali:1 2γt:2 exact:10 2γr:3 solves:1 hamiltonian:6 solution:8 eigenvalues:2 shows:2 e50:1 renormalized:1 direct:1 approximation:3 rate:1 rigorous:1 further:1 linear:1 even:1 mw:2 agrees:2 annals:1 method:1 respectively:1 teleportation:1 here:2 understanding:1 behaviour:1 following:1 relaxation:1 represented:1 obtained:4 institute:1 study:3 studied:2 approaches:1 reports:1 products:1 fourier:3 ρx:1 emerge:1 via:2 hermite:1 total:1 linearly:1 readily:1 alamitos:1 use:1 dpdp:1 superpositions:1 prove:1 classically:1 m2:2 theoretical:1 today:2 rk2:1 becomes:3 savage:1 berlin:1 normalized:1 particular:2 known:2 cases:1 producing:1 high:1 springer:1 science:1 equation:11 work:2 oscillator:7 ρp:1 macroscopically:1 obvious:1 temperatures:1 freedom:1 believed:1 making:2 tune:1 example:2 give:1 bennett:1 india:2 haroche:2 states:5 distinguishable:1 verlag:1 information:1 end:1 navrangpura:1 fourth:1 brassard:1 product:1 may:2 oscillators:2 earlier:1 derived:2 constants:3 fundamental:1 representation:1 order:1 maintenance:1 wigner:2 diagonalizes:1 zeh:2 thermal:1 london:1 pointer:1 its:2 susceptible:1 interesting:1 actually:1 production:1 degrees:1 mail:2 defining:1 arguments:1 eventually:1 walls:1 they:1 bath:6 easily:1 overdamped:1 hermitian:1 orthonormal:1 inequality:1 2m:4 2i:1 wunderlich:1 differential:1 series:2 energy:7 gaussian:2 society:1 yield:3 quantum:6 laboratory:1 eq:9 out:1 emerges:1 matrix:19 rr:1 space:1 res:1 since:3 crucial:1 research:1 mγ:2 formula:1 ref:1 mλ:5 rk:1 theory:1 found:1 mω:5 diagonal:9 free:6 completely:1 pramana:1 dreyer:1 jozsa:1 interaction:3 transition:1 arbitray:1 times:4 first:1 initial:13 shapiro:3 xx:1 simplified:1 long:2 open:1 temperature:3 πd:1 introduction:1 eqs:2 tata:1 system:10 least:1 unruh:1 intermediate:2 master:8 too:1 leggett:8 final:5 shifted:1 a30:1 ryzhik:1 exactly:2 proving:1 part:2 authors:1 x2:4 edition:1 approximations:2 likely:1 limiting:1 prl:1 ann:1 anu:2 iii:1 seen:1 seek:1 any:1 zero:1 depending:1 self:1 able:1 mechanism:1 note:1 factorizable:1 8m2:1 begin:1 though:1 trρ:2 factorised:1 boltzmann:1 but:1 gradshteyn:1 kb:2 considered:1 later:2 physica:1 32m:1 feynman:2 proceedings:1 points:1 exp:12 physics:6 precise:1 shor:1 show:2 soluble:1 relation:1 solutions:9 find:3 mumbai:1 should:1 giulini:1 explicitly:1 factor:1 integrate:1 oct:1 hope:2 do:1 dk:2 cryptography:1 means:1 zurek:6 preferred:3 nearly:1 dx:1 dy:1 during:1 dt:1 dr:6 ds:2 arxiv:1 factorization:4 4πd:1 ignored:1 set:1 computed:1 habib:2 computer:2 result:1 ieee:1 caldeira:7 αy:1 αx:1 αz:2 eigenstates:2 state:4 conceptual:1 geometric:1 conditions:4 brune:1 venugopalan:4 terms:1 tables:1 weak:3 p2k:1 vernon:2 answers:1 eipy:1 both:1 taking:1 uncertainty:1 equal:1 hω:2 raimond:1 expression:1 ck:1 co:2 ca:1 harmonic:1 121a:1 lagrange:1 respect:2 basis:13 addition:1 three:1 been:5 interest:2 ph:2 corresponding:2 commutes:1 suppress:1 coherence:2 c3:2 denote:1 present:1 case:6 pacs:1 kupsch:1 appearance:1 near:1 replaced:1 behavior:1 property:1 35th:1 coupled:1 characteristics:1 thus:1 ii:1 ernet:1 technology:1 agarwal:2 different:1 verified:1 paz:5 same:1 tr:1 stimulated:1 quant:2 wavepacket:1 φn:7 development:1 independent:5 used:1 hand:2 driven:1 purpose:1 normalization:1 recent:1 joos:2 off:1 modeled:1 academic:1 without:1 coordinate:4 position:5 model:1 quoted:1 being:2 obtain:3 questions:2 world:1 λn:4 16m2:4 density:20 except:1 other:1 lett:4 theorem:6 diagonalization:2 heidelberg:1 momentum:4 tests:1 b59:1 increased:1 advances:1 iγ:1 press:2 using:3 loss:1 particle:6 success:1 4mw:1 reduces:1 wooters:1 yields:4 either:1 integrals:2 arbitrary:3 become:1 reduced:7 because:1 classical:2 some:3 cr:1 pioneered:1 lead:1 integration:1 maitre:1 prog:1 agreement:1 symp:1 substitution:1 bz:1 tracing:1 dependence:3 o:2 side:1 convergent:1 h2:6 into:1 functional:1 due:3 appropriate:1 right:1 references:1 operator:2 tifr:2 uncertainties:1 there:1 transform:3 u3:2 ordinate:1 los:1 function:3 complete:1 form:4 hr:3 hw:5 ht:3 hu:1 heat:1 hn:4 hagley:1 factorized:1 kumar:2 limit:1 2mγ:2 constant:1 defined:1 abstract:1 influence:1 general:2 peres:1 single:1 our:2 physical:1 eventual:1 detail:1 valid:1 department:1 interpretable:1 theor:1 conclusion:2 elements:2 provided:1 models:2 polynomials:1 implies:1 coupling:8 ghosh:1 curve:2 factorizes:1 4m:1 time:3 decoherence:8 starting:1
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quant-ph9910005.txt |@word limited:1 concept:1 consider:8 pointing:1 represent:1 both:1 four:7 obstruction:1 scalar:2 commute:1 computation:1 consists:1 follow:1 gl:5 whose:4 depend:1 aug:1 producing:1 equivalence:8 ρs:3 environment:14 finally:3 asking:1 those:2 under:3 analogous:1 worth:1 norm:1 applied:1 belonging:6 amplitudes:1 orthogonal:1 far:2 rise:6 iτ2:2 connects:1 seemingly:1 choice:1 every:1 affect:1 matrices:3 arrange:1 leads:1 hamiltonian:12 irreducible:10 guo:1 involution:1 vector:2 phase:1 eigenvalues:1 possibility:1 unexpected:1 b23:4 direct:2 second:1 perspective:1 pass:1 manipulating:1 dynamics:1 even:4 index:1 what:4 errors:1 apparatus:1 giving:3 d2:1 sum:3 foregoing:1 expressed:1 uniform:3 subspaces:1 new:4 unrestricted:1 consisting:2 evolving:1 simultaneously:1 exchange:1 respectively:6 realizations:2 here:3 bi:2 experimentalist:2 objects:1 bj:2 groups:1 address:1 active:2 consideration:1 enveloping:3 appears:2 b31:2 scienze:1 antisymmetric:1 involved:2 vectors:1 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quant-ph9910006.txt |@word sci:1 chain:1 similarity:2 rev:5 magnetic:4 particular:1 none:10 scalar:5 commute:1 computation:5 edu:1 reˆ:1 whose:3 inverse:1 leung:4 knill:3 technique:2 supported:1 glaser:1 swap:2 under:4 case:1 updated:1 methyl:1 amplitudes:1 returned:1 advantage:1 frequencies:1 springer:1 maas:1 readout:16 orientations:1 fall:1 difference:4 entire:4 solves:1 presented:1 suffices:1 t2:4 solution:5 t1:3 admissible:8 vector:1 noted:1 lloyd:2 application:3 ten:1 deutsch:27 miller:1 grover:1 demonstrations:1 imply:1 displays:1 j21:1 j20:1 further:1 implemented:5 index:1 errors:2 appear:3 giving:1 ˆy:1 ˆz:2 selected:1 remain:1 version:2 ˆf:7 collins:2 method:2 contrast:1 respectively:1 realizations:3 residual:1 here:2 behaviour:1 selective:12 inversion:1 relaxation:1 represented:2 equations:1 appears:1 box:3 drx:1 shift:1 larger:3 allows:1 prior:1 accomplished:4 resulting:1 permutation:1 resonance:2 suitable:1 via:15 followed:1 requiring:1 merely:1 addressed:2 apply:1 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quant-ph9910007.txt |@word limited:1 gt:51 consider:11 remarkable:1 illustrates:1 interference:3 magnetic:2 global:5 amplifier:3 results:6 perelman:1 leads:2 eds:2 quadrature:4 entropy:4 intricate:1 expressions:5 a45:1 establishment:1 optical:4 compact:4 amplification:5 depend:1 calculate:2 pb2:1 technique:1 squeezing:11 those:1 under:2 stochastic:1 indicating:1 ingredient:1 division:1 supported:1 amplitudes:9 straightforward:3 very:6 frequencies:3 2re:2 account:1 atoms:1 choice:2 subpoissonian:1 reordering:1 fronsdal:1 resonant:2 ln:3 difference:4 exact:7 electronics:1 condition:3 cmn:5 impressive:1 hamiltonian:12 evaluation:1 solution:6 large:12 discrete:2 convenience:1 lorentz:2 phase:8 progress:1 extrema:3 variances:2 indices:1 eigenvalues:1 rk:1 optics:13 upper:1 strongly:2 approximately:2 2k0:1 periodicity:1 foundation:1 za:1 literature:2 cosh:5 past:1 second:3 design:1 value:26 further:1 dynamics:4 odd:3 substitute:1 canonical:4 even:3 will:15 what:3 nonlinear:2 detuned:3 rate:1 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quant-ph9910009.txt |@word represent:1 partial:2 consider:2 global:1 focus:1 four:2 inverse:1 technique:1 spain:4 th:1 under:2 te:2 applied:1 co2:1 very:2 springer:1 wishes:1 every:1 nieto:2 difference:5 deformations:1 condition:1 leads:3 hussin:2 solution:5 eigenvalues:1 csch2:2 za:1 second:2 odd:1 auspices:1 subscripts:1 nonlinear:6 plays:1 appear:1 iterating:1 sum:1 henceforth:1 wxxx:1 new:6 method:5 here:1 water:1 reported:1 departamento:3 fulfill:1 equations:4 implicit:2 change:1 remark:1 institute:1 studied:1 allows:1 superpotential:2 resulting:2 hospitality:1 studies:1 named:1 classification:1 marginal:1 ipn:1 coinciding:1 modulated:1 derivatives:1 would:1 h0:3 physics:1 ψn:1 therefore:3 type:2 theoretical:1 introducing:1 chabanov:1 solitons:1 odinger:3 validity:1 berlin:1 particular:1 known:5 must:1 keeping:1 equation:13 work:2 modified:1 values:4 making:1 example:3 performed:1 links:1 give:1 process:1 states:1 numbers:1 verlag:1 information:2 darboux:1 get:1 df:1 criterion:1 parameter:2 de:9 blocks:1 singular:5 transforming:1 singularities:1 dx2:1 gardner:1 applications:2 waves:1 constants:1 stress:1 andez:4 natural:1 explicit:1 βk:9 order:15 βk2:1 paper:1 committee:1 satisfies:1 its:3 le:1 acknowledge:2 energies:1 interesting:1 solving:1 offers:1 main:1 easier:1 supersymmetry:2 them:1 acklund:4 singularity:1 now:5 handy:1 easily:1 term:3 castilla:1 university:1 each:4 found:1 glasser:1 differential:1 energy:5 w12:1 related:1 our:1 out:1 rev:3 looking:1 shows:1 theory:2 barrier:1 derived:2 ısica:3 possibility:1 quite:1 oro:2 generate:1 starts:1 could:1 times:1 universidad:3 hence:1 first:5 miura:1 number:1 given:11 adopted:1 sech2:3 master:1 denominators:1 free:4 relationship:3 tool:2 wide:1 kind:1 iteration:2 see:2 project:1 gives:2 intertwining:4 null:2 any:5 warsaw:2 generalizes:1 depending:3 general:7 able:1 instance:1 potential:14 salle:1 even:1 multiple:1 shall:2 wells:2 riccati:5 algebraic:2 beta:3 regular:2 iterate:1 exico:1 soliton:4 constructed:2 physica:1 principle:4 typically:1 fact:1 quantity:1 solutions:9 wahlquist:2 d2:1 partners:11 mielnik:2 parameters:2 only:3 explicitly:1 writen:1 hamiltonians:4 oct:1 notation:1 means:2 v1r:1 superpotentials:4 v1n:1 dx:2 coth:2 continuum:1 approach:1 arxiv:1 factorization:8 greene:1 worrying:1 set:1 constructing:1 depends:1 cultura:1 w1:1 satisfying:1 eigenfunctions:1 educaci:1 affecting:1 conditions:1 available:1 notice:1 terms:1 cinvestav:1 matveev:1 wt:1 providing:1 acquiring:1 cot:2 many:2 taking:1 expression:3 periodic:4 simple:2 coincidence:1 applicability:1 wider:1 table:4 considering:1 transformations:1 been:4 much:2 interest:1 ph:1 abstract:1 generating:1 supersymmetric:1 sufficient:1 estabrook:2 last:1 denote:1 present:1 case:7 dges:1 tanh:2 ǫk:15 ǫn:2 will:1 while:1 suppose:1 orica:2 procedure:1 mexico:2 vk:4 thus:2 vn:3 canceled:1 susy:19 partner:3 different:6 same:3 complex:1 quant:1 finite:5 higher:7 used:7 keys:1 effect:1 hand:1 v0:11 v1:7 v2:5 potentials:9 changing:1 recent:1 schr:3 poland:1 well:5 without:1 just:1 previous:2 preprint:1 seems:1 transparent:1 conacyt:1 lett:4 iπ:1 solvable:3 transformation:2 real:2 iκ:2 valladolid:4 vacuum:1 mod:1 necessary:1 particle:4 intertwiner:1 korteweg:1 arbitrary:3 become:1 parity:1 sketch:1 some:3 moreover:1 kdv:5 organizing:1 provided:2 confirm:1 integration:5 does:1 steps:1 bm:1 kruskal:1 rosas:3 expansion:1 bt:1 step:2 deriving:1 about:1 most:1 discussed:1 dependence:2 o:3 multisoliton:3 introduced:1 into:1 h1:3 bound:1 fern:4 en:2 references:1 operator:1 reducing:1 additional:1 ortiz:2 support:1 initial:3 was:1 function:4 simplifications:1 construction:3 link:1 ho:1 encoded:1 adler:1 ministerio:1 embedded:1 us:4 demonstrate:1 problem:1 similar:1 taylor:1 constant:3 int:1 certain:1 universal:1 comming:1 ap:1 a1a:1 corresponding:3 check:1 physical:2 again:1 extending:1 when:1 junta:1 application:1 other:2 role:1 concerning:1 conclusion:1 kinds:1 superposition:6 separate:2 symbol:1 problems:1 a1:5 building:1 factorized:1 algorithm:7 assume:1 vries:1 observe:1 presenting:1
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