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quant-ph9910010.txt |@word consider:1 illustrated:1 quadrature:3 entropy:3 computation:1 inverse:2 program:1 squeezing:7 under:1 worth:1 sent:5 applied:2 amplitudes:3 worse:1 straightforward:1 orthogonal:1 choice:1 every:1 difference:2 timely:1 splitter:2 presented:1 transmission:6 large:4 discrete:1 bangor:1 small:1 unconditioned:1 optics:1 lloyd:2 says:1 foundation:1 α2i:1 cosh:1 past:1 second:3 cost:2 substituting:1 implemented:1 even:6 established:1 nonlinear:1 sum:2 beaten:2 decoding:2 shared:7 net:1 consisting:1 contrast:3 slotine:1 αin:6 simultaneously:1 exchange:1 respectively:3 component:7 teleportation:4 here:4 explore:1 sinh:3 situation:1 along:3 strong:1 implicit:1 obtained:1 sending:2 sender:2 suitably:2 institute:2 larger:1 allows:2 significantly:1 prior:1 amount:2 resulting:4 schumacher:1 advantages:1 bob:20 ipb:3 ipa:2 extra:1 requiring:1 yuen:2 private:1 outcomes:1 modulated:3 pβ1:1 achievable:1 pβ2:3 rarely:1 circumvent:1 asymptotic:1 would:1 distributing:1 going:1 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quant-ph9910011.txt |@word represent:1 consider:1 rev:4 leads:2 scalar:1 entropy:1 go:1 calculate:3 aug:1 ts:8 under:1 include:1 norm:1 frequencies:1 ously:1 bratislava:3 valued:2 mixing:2 difference:9 matrices:14 conserved:1 hamiltonian:10 proposals:1 discrete:1 vector:8 dealing:1 second:1 further:1 dynamics:15 canonical:2 spectral:1 index:2 what:3 nonlinear:24 invertible:1 incompatible:1 section:1 expressed:2 mycielski:1 version:5 above:4 new:2 method:1 full:1 led:1 dψj:1 degree:1 κk:4 here:12 tangent:1 represented:1 b33:1 observing:1 change:1 obtained:2 remark:8 generalizing:1 inspired:1 allows:1 poisson:2 pick:1 usually:2 conveniently:2 heslot:1 criticism:1 formulated:3 transformations:4 family:1 unit:2 derivatives:2 use:1 proceed:1 would:1 prove:1 probabilities:1 positive:1 contains:1 ψt:6 next:2 ψj:5 ψk:1 linear:11 bialynicki:1 centre:1 characteristics:1 taken:1 theoretical:2 more:3 duality:1 becomes:1 operators:8 odinger:4 berlin:2 everywhere:1 known:1 foundations:1 cases:4 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quant-ph9910012.txt |@word represent:1 concept:1 sci:1 consider:2 leads:1 hennig:1 generalize:1 consists:1 gr:1 aug:1 ts:5 under:1 bratislava:2 matrices:5 condition:2 hamiltonian:9 natl:1 solution:1 concise:1 jump:1 second:1 dynamics:1 canonical:1 what:3 nonlinear:13 brackets:2 expressed:2 version:1 above:3 new:1 acknowledgments:1 edited:1 here:1 tangent:1 groups:3 represented:1 equations:1 obtained:3 simultaneous:1 products:1 poisson:2 usually:1 makes:1 quotient:1 uniquely:1 formulated:3 useful:1 schilling:1 additive:1 probabilities:6 contains:1 ψt:3 call:1 type:1 theoretical:2 more:1 duality:1 operators:3 odinger:3 known:1 projective:1 insights:1 valued:6 defines:1 anything:1 equation:2 fock:1 concepts:1 koopman:3 lφ:1 references:1 process:1 accept:1 states:9 sense:1 looses:1 information:1 rays:1 requirements:1 rather:1 how:2 pure:1 ordinary:1 parameter:3 map:1 fr:1 algebra:4 different:2 hence:2 4th:1 geometrical:1 transposed:3 realized:1 natural:3 dynamical:1 imply:1 grant:2 cannot:1 so:1 restriction:1 wigner:1 help:1 ith:1 developed:1 satisfied:1 paper:1 banach:1 mentioned:3 its:2 group:3 probability:2 chosen:3 exact:1 expectations:1 forms:1 derivative:1 correspondence:2 evolution:3 introduce:1 framework:1 hamilton:1 they:1 now:1 eigenvalue:1 february:1 several:1 dirac:2 university:2 traced:1 backgrounds:1 identified:2 theory:7 l2:2 done:1 2n:1 mean:1 subset:1 differential:3 formulate:1 elementary:2 obtains:1 measurement:1 quantum:17 our:1 shown:1 space:10 restricted:1 reformulate:1 contained:1 induced:1 math:1 reformulation:1 linear:17 possibility:1 besides:1 definition:1 transition:6 consequence:1 first:1 symmetry:6 bijection:1 ona:4 restrict:1 simplified:1 another:1 hartree:1 given:6 rewritten:1 barycentre:1 system:4 their:1 echet:1 eqm:1 pavel:1 postulate:1 scheme:1 gives:1 ashtekar:1 continuous:2 quasiclassical:1 july:1 representing:1 approximations:2 zero:2 determined:2 subtheory:1 result:1 symmetries:5 say:1 any:6 genuine:1 convenient:1 agency:1 note:3 generalized:1 analogy:1 heisenberg:2 trace:2 shall:4 measures:3 algebraic:2 connected:2 automorphism:3 phase:1 measured:1 class:2 nonlinearity:1 considered:5 flow:5 traditional:1 proceedings:2 points:2 exp:1 physics:1 supported:1 relation:3 solutions:1 interpretation:3 proposed:1 implementation:1 state:3 should:1 only:1 various:1 hamiltonians:1 oct:1 continuity:1 subspaces:1 dependent:1 express:1 straightforwardly:1 ones:1 processes:2 qt:2 arxiv:1 summary:1 qc:1 contain:1 qm:8 requirement:4 set:5 dobrev:1 reference:1 frame:1 differentials:1 see:1 projections:2 doebner:1 symmetric:2 written:3 identification:1 between:1 geometric:1 terms:2 attention:1 however:3 uφ:10 topology:1 observable:2 interpretations:1 according:3 conference:2 fulfilled:1 symplectic:2 cm:1 cb:1 corresponds:2 dimensional:5 respect:4 considering:1 described:2 transformations:6 reduction:1 ph:2 define:1 corresponding:6 robability:1 extendable:1 present:1 case:3 subsets:1 value:1 will:2 unitary:4 almost:1 endowed:1 von:1 wkb:1 equal:1 cocycle:2 dual:1 comenius:2 containing:3 φt:29 author:1 perhaps:1 same:1 clearly:1 complex:1 quant:1 mixtures:2 finite:1 extended:3 reinterpretation:1 trivially:1 numerical:2 flows:2 hand:1 uses:2 necessity:1 infinite:1 invariance:2 eith:1 schr:3 well:2 usual:3 manifold:1 φtt:10 just:2 being:1 resp:1 thanks:1 world:2 eigenstates:1 density:5 other:1 theorem:1 transformation:6 real:3 possible:1 cf:3 using:1 unique:2 modifications:1 like:2 automorphisms:1 informative:1 evolutions:1 acad:1 neumann:1 classical:2 pϕ:4 some:3 back:1 pψ:18 specific:2 dense:1 remind:1 does:1 exposition:1 proc:1 selfadjoint:3 scientific:2 jumps:1 although:1 hilbert:4 submanifold:2 about:1 trivialization:1 extension:2 discussed:1 dependence:1 o:1 mutually:2 sept:1 organizers:1 conserving:1 into:3 functional:1 slovak:2 operator:7 topologies:1 support:1 conservation:3 way:3 was:1 function:4 form:10 sketched:1 but:2 hh:1 hi:1 hb:1 ha:2 he:1 versions:1 up:3 us:8 liouville:2 similar:1 called:1 mechanics:12 constant:1 conserves:1 defined:5 abstract:1 measure:4 general:2 formulation:3 physical:2 functions:5 no:1 rewriting:1 field:1 valid:2 republic:1 department:1 picture:2 expressible:1 vega:1 problems:1 bounded:2 luecke:1 implies:1 dψ:1 assume:1 equivalently:1 time:2 observables:6 requires:1
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quant-ph9910013.txt |@word neighbors:1 limited:1 partial:1 consider:9 dynamic:2 results:3 four:1 continual:1 scalar:1 commute:1 amplified:1 centers:1 localized:3 dimentional:1 amplification:2 zone:1 re:1 white:1 nonlocal:4 passage:1 finally:1 under:1 presentation:2 random:7 amplitudes:1 δa:6 very:1 frequencies:3 harmonics:1 wave:5 kittel:1 fall:1 iǫk:1 associated:1 difference:3 condition:1 manyparticle:1 ωm3:2 illustrated:1 cmk:3 progression:1 presented:5 positions:1 solution:3 large:1 ǫk:3 vector:3 small:1 referred:1 optics:3 noted:1 upper:3 bessel:1 force:2 consistent:1 direct:1 approximation:9 second:1 enhancement:1 correlator:5 dynamics:1 expressions:1 linear:8 even:1 index:1 nonlinear:2 plays:1 appear:1 sum:2 expressed:1 cell:6 above:2 susceptibility:2 new:4 contrast:1 coefficient:4 crouch:1 fiz:5 eksp:5 here:11 atoms:10 iωτ:1 phoenix:3 replacements:3 ωk1:1 relaxation:1 represented:1 consideration:1 along:3 equations:18 appears:3 change:5 obtained:10 property:1 items:1 vectors:1 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quant-ph9910014.txt |@word consider:2 fabricated:2 leads:1 quadrature:3 generalize:1 29a:2 finally:3 squeezing:11 p2:2 zhang:1 fan:1 experimentally:2 condition:1 presented:1 large:2 convenience:1 interpolating:2 small:1 eigenvalues:2 optics:1 smaller:1 oscillator:1 consistent:1 further:1 plays:1 sub:5 section:2 above:1 obvious:1 increasing:1 method:1 funtion:1 satisfy:1 lee:1 ibid:1 multinomial:2 respectively:2 keynes:1 here:3 ranges:1 reported:2 china:2 concluding:1 strong:1 equations:1 contraction:1 obtained:2 remark:2 involved:1 larger:1 periodic:1 via:1 9b:1 lima:2 plot:2 use:2 dnm:4 eφ:4 negative:1 next:2 therefore:1 torre:1 until:3 reflects:3 becomes:5 controlling:1 cases:1 must:1 keeping:1 science:1 equation:5 work:1 ρm:3 ρn:1 fock:2 subpoissonian:1 learn:1 following:6 making:1 arrive:1 example:1 control:1 weaker:4 figure:2 states:44 minimum:1 degenerate:1 sense:1 end:2 discussion:1 write:1 how:1 acta:1 iθ0:2 parameter:4 sin:1 fu:8 algebra:2 replacing:1 ladder:5 changchun:1 faculty:1 natural:1 correspond:2 su:3 so:6 fundamental:1 suggest:1 paper:2 through:1 barnet:1 statistical:1 eiθm:3 its:3 puri:1 interesting:1 fig:2 mail:2 deformation:1 them:1 pegg:5 they:1 discuss:1 eigenvalue:4 hereafter:1 university:3 hamiltonian:1 into:2 mode:1 2b:1 each:1 ei:3 barnett:4 reduce:6 allan:1 related:1 investigated:3 quantum:1 our:2 eq:1 out:1 ηc0:2 shown:1 matrix:1 51a:1 since:2 rev:6 increase:2 attracted:1 acting:1 formula:1 math:2 shows:1 foundation:1 linear:2 state:11 e2:1 domokos:1 first:3 xn:1 probability:1 number:5 iht:1 proposing:1 reached:1 open:3 similarly:1 introduction:1 relations:1 their:3 intermediate:13 normalization:1 gives:1 interests:1 part:3 authors:1 x2:2 than:1 milton:1 namely:2 limiting:1 solomon:2 determined:2 expm:2 tion:1 exhibit:1 motivation:1 say:1 seen:1 lie:1 lim:3 note:5 generalized:2 shall:4 gallardo:1 letter:1 phase:16 considered:1 clear:1 later:1 dattoli:1 points:1 principle:2 exp:3 holstein:1 notion:1 drastically:1 supported:1 relation:2 substituting:1 find:3 symmetric:2 northeast:2 knowledge:1 parameters:2 written:2 jap:1 only:2 generators:1 factor:4 oct:1 dn:7 do:1 get:1 de:2 ρcm:1 da:1 evolution:1 fields:4 arxiv:1 acknowledgments:1 europhys:1 fixed:2 national:1 ωt:1 depends:2 sec:3 recently:2 satisfying:1 αa:1 enough:2 between:2 barranco:1 approach:5 joshi:1 ends:1 terms:1 amplitude:2 attention:1 interpolate:1 jm:5 31a:1 essentially:1 2θm:4 limits:6 figures:1 expand:1 variance:1 disappears:2 cn:3 point:4 poissonian:11 narrower:2 corresponds:2 dimensional:1 wider:2 respect:2 due:1 pb:13 much:1 ph:4 define:1 corresponding:1 θm:33 subspace:1 cos:3 coherent:20 c0:9 case:3 exponential:2 variances:1 50a:3 will:1 squeezed:4 characterizing:1 stoler:2 opt:3 studied:1 szabo:1 different:8 pay:1 radiation:3 same:2 quant:4 finite:4 development:1 independent:1 literature:1 see:4 effect:2 identity:1 primakoff:1 well:1 solve:2 coordinate:1 teich:1 proposed:1 obtain:2 eigenstates:1 previous:1 olya:1 except:3 lett:3 easy:1 momentum:1 real:6 l83:1 easily:1 vacuum:3 using:3 mod:3 separately:1 marques:1 right:1 βnm:2 30a:1 sharma:1 normal:2 inserting:1 silva:1 binomial:2 bs:12 plots:1 imaginary:1 super:5 properties:6 6aa:1 dependence:1 distinct:1 range:4 introduced:2 ηf:8 soc:2 ηn:1 ηm:4 references:1 operator:9 jing:1 statistics:7 mandel:2 was:1 function:4 hypergeometric:1 form:2 displacement:1 considerable:1 raising:1 2πm:1 maximum:1 us:2 mk7:1 limit:12 uk:2 distribution:2 called:1 ac:2 constant:5 computing:1 defined:2 abstract:1 am:1 single:1 saleh:1 formalism:1 sasaki:5 physical:1 nm:1 when:2 detail:2 field:4 other:1 role:1 department:1 mathematics:2 conclusion:1 superposition:3 photon:3 nonclassical:4 meaning:1 values:1 adam:1 time:2 starting:1
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quant-ph9910015.txt |@word yamaguchi:1 represent:1 concept:1 magnetic:4 results:8 four:4 computation:2 leung:2 knill:1 technique:1 tr:1 glaser:1 under:2 arranged:1 applied:2 belonging:1 far:1 ρth:6 worst:2 difference:1 notations:1 hamiltonian:6 irreducible:1 convenience:1 team:1 small:1 deutsch:5 direct:2 pulse:21 second:3 j23:18 implemented:8 index:1 plays:1 d2:1 axes:2 expressed:1 kup:2 experiment:2 superposed:3 increasing:2 method:1 body:4 margolus:1 lee:4 respectively:6 never:1 component:1 reported:1 free:1 along:1 imperfections:1 change:4 obtained:2 convert:1 weinstein:1 institute:2 shift:1 study:1 studied:1 simultaneous:1 usually:1 resonance:4 suitable:1 involves:1 divide:1 turchette:1 total:3 univ:1 exciting:1 distinct:3 positive:1 predictions:2 few:2 call:1 therefore:8 type:9 theoretical:3 more:4 linden:3 successful:3 outputs:2 operators:10 iiy:1 iix:1 iiz:4 tested:1 cases:1 iii:3 science:3 work:1 protons:1 ρp:3 labeled:1 ch3:1 obvious:1 ms:2 following:2 hansen:1 example:2 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quant-ph9910016.txt |@word code:7 consider:9 remarkable:1 rev:21 global:1 results:4 leads:1 proposition:7 computation:7 follow:1 compact:2 whose:1 knill:6 arbitary:1 acting:1 environment:13 finally:2 under:3 stabilizing:2 norm:1 belonging:2 straightforward:1 far:3 permutation:1 induce:1 mixing:1 condition:5 dim:2 eccs:1 swapping:1 hamiltonian:5 irreducible:2 notes:1 guo:2 noiseless:10 irreducibly:2 recall:1 eigenvalues:1 viola:4 ρj:2 villa:1 bacon:2 direct:1 suffices:1 fold:1 likely:4 bitstring:1 manner:1 dynamics:13 odd:1 eigenspaces:3 linear:2 even:2 index:1 what:1 errors:4 appear:1 sum:1 analogously:1 above:4 new:4 satisfy:1 supporting:8 processing:4 led:1 notions:1 exchange:2 here:4 desired:2 address:1 appears:1 obtained:3 remark:1 property:1 exemplified:1 commutant:6 institute:1 study:1 allows:4 amount:1 products:1 stressed:1 action:3 opinion:1 therein:1 suitable:3 mutual:1 via:2 stabilization:4 family:2 inducing:2 logical:1 modifying:1 addressed:1 bra:1 projector:1 would:1 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quant-ph9910017.txt |@word represent:1 vila:1 sci:1 consider:5 remarkable:4 results:18 illustrated:1 roy:1 ge:1 expressions:3 cases:6 whose:1 inverse:3 essentials:1 paris:1 hump:2 technique:4 containing:1 presents:1 finally:4 monotonically:1 present:4 excluded:1 under:1 analogous:1 te:2 worth:1 divergent:2 case:24 g3:1 g2:1 very:6 keeping:1 wave:4 implicit:1 witten:2 every:1 wich:2 socorro:1 specific:2 nieto:5 difference:3 exact:1 condition:4 look:1 annihilated:2 hussin:1 level:6 turns:3 tanh:10 solution:12 leave:1 solved:2 differential:5 eigenvalues:2 possibility:1 strongly:1 force:1 dealing:3 direct:3 literature:1 cosh:19 jump:1 elegant:2 zero:5 evaluated:1 ıaz:1 odd:2 substitute:1 linear:1 even:3 established:2 what:1 nonlinear:1 plays:1 letts:1 morse:2 giving:1 d2:4 section:6 while:2 expressed:1 thicker:2 henceforth:1 version:2 above:1 lifshitz:1 new:16 increasing:1 method:1 contrast:1 coefficient:1 limα:1 divergence:1 here:4 agreement:2 behaviour:8 desired:1 tangent:1 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quant-ph9910018.txt |@word epeau:1 consider:5 remarkable:1 global:1 four:2 proposition:2 computation:3 edu:3 whose:1 violate:1 tr:1 send:1 environment:2 thapliyal:1 infinitesimally:1 tk:2 under:1 supported:1 zhang:1 vla:3 vlb:2 condition:4 tra:1 trb:3 guo:3 eigenvalues:1 rohrlich:1 direct:2 hillery:1 zero:2 µe2:1 spectral:1 will:3 what:1 plays:1 contemp:1 diag:3 above:6 shared:3 κn:1 κi:2 respectively:2 never:1 teleportation:2 here:1 ulb:2 iσy:1 plenio:2 china:3 address:3 represented:5 equations:2 obtained:1 search:1 institute:1 popescu:5 resulting:1 schumacher:2 bob:24 involves:1 useful:1 projection:2 marginal:7 hardy:1 apply:1 unit:2 use:2 prove:2 remains:1 positive:1 negative:1 properties:1 ψi:3 jonathan:3 more:1 linden:3 successful:1 operators:9 needed:1 degrade:1 known:1 must:4 ρa:8 states:36 ρb:6 science:2 equation:3 work:1 obvious:1 following:5 ula:2 example:1 proof:8 f1:2 f2:3 process:1 uap:12 bennett:6 share:7 involve:1 indicates:1 minimum:1 numbers:2 occur:1 clair:1 information:5 respective:1 quantph:1 rather:1 εe1:1 orthogonal:1 machine:1 far:1 pure:14 optimal:1 brassard:2 map:1 product:2 may:5 clone:1 after:3 mixed:6 fi:1 concentrating:5 types:2 transposed:1 realized:1 attempt:1 purify:2 purification:2 so:6 fundamental:2 increase:1 bipartite:7 operations:7 help:1 zek:1 paper:1 differs:1 fidelity:1 still:3 its:1 perfect:3 write:1 derive:1 chosen:3 lo:2 li:1 mail:1 schmidt:5 non:1 greater:1 combination:1 introduce:2 they:3 now:2 discuss:1 easily:1 execute:1 finite:2 opera:1 characterizes:1 university:1 orthonormal:1 each:5 side:4 subsystem:8 ei:1 expect:1 measurement:8 quantum:16 laboratory:1 operation:4 eq:9 hlb:2 hla:3 secretly:3 shown:5 decreasingly:1 matrix:5 space:3 quality:1 furthermore:1 since:4 rev:18 optimally:1 particles:3 acting:4 eprint:5 kent:1 denoted:1 get:1 foundation:1 theory:1 interactions:1 standard:4 completely:1 california:1 term:1 e1:1 e2:1 definition:1 pairs:7 applications:1 could:3 δij:1 consequence:2 first:2 there:4 probability:6 succeeds:1 coding:4 done:1 impossible:5 electronic:3 interchange:3 given:2 rewritten:1 similarly:1 unitarity:1 system:9 indicate:1 assumption:1 scheme:1 final:2 gives:1 γmax:1 manipulation:2 natural:2 than:2 coefficients:5 wootters:3 unfortunately:1 showed:2 wiesner:1 require:1 transferred:2 tion:1 outcome:1 remained:1 need:3 concentration:3 any:5 subsystems:1 general:4 note:1 high:1 absorbed:1 generalized:4 destroy:1 even:1 most:1 eisert:1 involving:1 letter:1 pair:1 probabilistic:12 observation:2 surprising:1 considered:1 implications:1 kl:2 physics:1 fact:1 laws:1 show:2 probe:4 bring:1 attempts:1 pkl:3 feng:1 proposed:1 parameters:1 should:4 jan:1 only:14 bernstein:1 local:14 his:4 cryptography:1 means:8 cannot:3 evolution:4 resource:1 κf2:2 arxiv:1 summary:1 fuchs:1 investigate:1 protocols:3 contain:1 uncover:1 set:8 exists:1 national:1 identify:1 collectively:2 individual:8 result:5 particle:1 phases:1 satisfying:3 ways:1 µl:1 state:34 µn:1 µi:4 µk:3 between:2 invariant:1 conditions:1 preserve:2 barenco:1 importance:1 transpose:1 hefei:1 residual:2 efficiency:1 concentrate:7 key:1 concentrated:8 both:6 many:3 etc:1 σx:1 gisin:1 cn:3 simple:1 dimensional:4 κt:1 werner:1 constant:1 singlets:1 described:1 transformations:4 basis:1 been:3 reduction:1 ph:5 pi:4 define:1 arises:1 corresponding:1 influence:1 sufficient:3 observers:3 proven:3 demand:2 maximally:18 present:1 p0:6 p1:5 pacs:1 choices:1 aim:1 ail:1 while:2 suppose:3 aik:2 aij:1 situation:3 property:4 unitary:14 thus:3 probabilistically:1 ik:1 duan:2 ia:3 ib:10 technology:2 different:7 jozsa:1 σz:1 perform:1 make:2 same:17 quant:5 wilkens:1 several:1 φn:8 uses:1 supposing:1 entanglement:13 task:3 obviously:2 know:1 entanglements:1 guang:1 just:2 when:1 obtain:1 actions:2 distant:3 λi:14 λn:4 previous:1 density:9 wei:1 had:1 transformed:1 lett:12 theorem:7 republic:1 transformation:1 real:1 nielsen:2 possible:1 department:1 vidal:3 entangled:33 using:6 projects:1 mod:3 necessary:3 like:2 success:2 follows:3 alice:25 communications:1 yields:2 always:5 output:4 because:2 deal:1 people:1 some:3 cr:1 measurements:1 manipulations:3 does:3 decomposition:6 manipulate:1 bl:22 problems:1 equivalent:3 arbitrary:1 cλ:1 bu:1 although:1 hilbert:3 bz:1 chuan:2 massar:3 probabilities:1 act:1 concentrations:1 consequently:1 individually:2 communication:5 into:5 obtaining:1 determine:1 parties:1 operator:12 matrixes:1 classical:5 her:3 transfer:1 initial:2 question:1 inner:1 way:1 was:1 function:1 complete:3 form:4 smolin:4 but:2 he:1 made:1 applying:2 whether:2 maximum:1 those:2 problem:2 ua:25 called:1 ub:20 mechanics:1 ab:50 ordered:2 defined:1 certain:1 ak:13 measure:1 linearity:1 deep:1 denote:3 peres:1 exist:2 our:2 physical:3 performed:4 no:3 ekert:2 generally:3 composite:3 role:1 np:2 superdense:4 divincenzo:2 describe:1 meaning:1 important:1 sides:2 fundamentally:1 together:2 ustc:3 requires:1 original:1
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quant-ph9910020.txt |@word secondly:3 concept:1 partial:4 consider:7 represent:5 directions:1 commute:5 entropy:2 contradict:1 consists:2 follow:2 expressions:2 saved:1 reasoning:2 whose:1 inverse:1 depend:4 eigenbasis:6 concerned:1 equivalence:1 tr:1 including:1 simplify:1 finally:1 indicate:1 present:2 th:1 under:1 norm:3 started:1 case:14 amplitudes:1 boucher:1 very:1 increase:2 choice:4 every:1 mixing:1 difference:5 condition:6 look:3 treating:1 nonselective:4 anarchical:1 hamiltonian:9 solution:12 occurs:1 try:1 solved:3 unrelated:1 indices:4 eigenvalues:6 shows:2 der:1 concluded:2 strongly:1 says:1 occurrence:1 direct:4 go:2 second:5 design:1 substituting:2 further:3 dynamics:7 belief:2 even:2 established:1 what:7 appear:3 apparatus:14 expressed:7 below:1 above:6 new:6 consisting:2 contrast:2 satisfy:7 agreement:1 simultaneously:1 prescriptions:1 αij:4 qm1:10 respectively:3 proper:3 realizations:1 prescribe:1 here:9 diagonal:7 behaviour:1 desired:2 ansatz:1 situation:1 alone:1 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quant-ph9910021.txt |@word partial:1 consider:2 caused:1 four:3 entropy:2 computation:1 edu:1 contributions:2 concerned:1 send:2 under:2 aux:12 sent:1 orthogonal:1 very:1 exact:4 partially:3 guo:1 lˇ:1 α2k:1 theory:1 even:1 what:3 expressed:3 above:5 utkenhaus:1 new:1 method:1 coefficient:1 degree:6 never:1 teleportation:28 here:1 china:3 represented:2 obtained:1 sending:6 sender:2 reason:2 amount:2 schumacher:2 adopting:2 via:2 bounds:1 explained:1 prefer:1 apply:1 total:1 massar:1 αbb:1 therefore:1 taken:2 more:2 linden:1 successful:10 chuan:1 cases:2 science:2 originally:1 work:1 obvious:1 concepts:1 following:3 example:1 give:2 process:2 bennett:4 states:8 performed:1 absolute:1 information:11 provide:1 means:1 varies:1 pure:2 optimal:10 reestablish:3 brassard:3 product:1 may:12 after:1 informs:1 natural:1 so:2 operate:1 operations:2 help:1 satisfied:2 experiments:1 through:3 mentioned:1 fidelity:1 lo:1 li:3 degrees:2 schmidt:2 maximal:1 they:1 hereafter:1 always:2 university:1 inequality:1 transmitted:3 calsamiglia:1 each:1 qubit:6 side:1 2k:1 lished:1 deterministically:1 measurement:20 quantum:31 laboratory:1 operation:1 extract:2 out:2 shown:5 rev:7 particles:1 performs:2 mattle:1 foundation:1 linear:1 difficulty:1 completely:1 disposition:2 jozsa:2 pairs:2 could:12 βy:2 βa:3 βb:5 first:1 initial:3 probability:22 number:1 channels:2 directly:2 blank:1 carry:2 unknown:2 eqs:1 system:2 adopted:1 their:2 wootters:3 gives:2 scheme:1 preparation:1 determined:3 crepeau:2 amplitude:1 accessed:4 distinguished:1 extracting:2 generality:1 need:1 seen:1 any:3 min:2 efficient:1 generalized:1 smolin:1 channel:17 though:1 pair:4 probabilistic:2 considered:4 calculated:1 physics:1 show:2 supported:1 feng:1 popescu:4 state:23 should:2 αba:1 only:3 eibl:1 bernstein:1 local:2 oct:1 get:3 cannot:1 shared:1 report:3 evolution:6 arxiv:1 2b2:1 investigate:1 satisfy:1 exists:1 national:1 operates:4 result:9 fails:1 draws:1 αx:2 αa:5 written:4 αb:3 between:2 invariant:1 c2i:1 email:1 βab:1 ability:4 nature:1 hefei:1 unnormalized:3 concentrated:2 received:1 mono:1 equal:1 povm:1 receiver:2 contribution:2 whole:2 ci:1 cn:1 bell:10 corresponds:1 werner:1 considering:2 basis:2 been:1 strategy:1 ai:16 pk:3 ph:2 pi:8 corresponding:5 zeilinger:1 maximally:1 case:5 multi:2 p1:3 pacs:1 value:1 will:5 while:4 unitary:1 endowed:1 von:4 thus:2 site:4 technology:1 same:5 clearly:1 quant:2 pan:1 difficult:1 independent:1 used:1 entanglement:17 bob:13 lower:1 task:1 analysis:1 vaidman:1 without:2 left:1 guang:1 just:4 less:4 being:1 transforms:1 purified:1 eigenstates:3 adding:1 kluwer:1 regarded:4 transformed:2 lett:2 suominen:1 transformation:1 possible:1 entangled:7 using:4 loss:1 necessary:1 particle:11 follows:1 collective:2 alice:22 either:1 fully:1 evolutions:1 page:1 because:2 neumann:4 classical:1 successfully:1 some:3 b2:3 proper:2 matching:10 provided:1 measurements:3 mined:1 ba:5 bb:5 bi:11 bz:1 about:1 discussed:1 essential:2 αaa:1 αab:1 mixed:2 introduced:1 previously:1 communication:1 methods:2 wan:1 her:2 extraction:1 there:1 width:3 way:1 was:1 collapsed:2 he:2 waste:1 transmits:1 up:1 devices:1 similar:2 aa:1 ab:6 defined:2 certain:2 measure:1 general:9 peres:3 bouwmeester:1 no:2 eq:6 when:1 other:2 department:1 picture:2 meaning:1 a2:2 auxiliary:2 assume:1 lanl:1 ustc:1 original:3
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quant-ph9910022.txt |@word represent:1 partial:22 consider:9 neglected:1 results:9 generalize:1 lewenstein:2 managed:1 fmrx:1 massar:1 preserves:3 29d:1 equivalence:1 tr:31 29c:1 29a:2 environment:1 thapliyal:1 finally:7 infinitesimally:1 those:4 under:5 tr1:2 tr2:1 swap:2 ingredient:1 p2:1 conjecture:1 supported:1 kent:1 straightforward:1 ρta:6 very:1 continues:2 differently:1 every:1 ρts:2 mixing:11 condition:18 indicate:1 basics:1 immediately:2 level:7 turns:1 solution:2 large:2 convenience:1 vector:3 phase:1 der:1 lloyd:1 deutsch:2 haar:1 10a:1 sign:1 second:8 equal:2 further:1 implemented:2 odd:4 even:3 aim:1 what:1 plays:1 invertible:1 section:7 analogously:1 expressed:1 3i:1 3n:4 above:7 shared:1 ˆl:2 acknowledgments:1 ρad:1 chose:1 respectively:3 never:1 here:6 desired:2 erb:1 others:1 strong:1 equations:1 obtained:3 convert:2 antisymmetric:12 institute:1 study:8 vectors:4 allows:2 completely:4 leaving:1 resulting:1 permutation:1 hospitality:1 bob:11 proof:1 via:1 useful:2 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quant-ph9910023.txt |@word neighbors:1 now:5 concept:2 sci:1 illustrates:1 surrounding:1 caused:2 invariable:1 activated:1 results:5 p20:1 continual:1 supplement:1 grateful:1 consists:1 expressions:2 adjustment:1 relationships:1 whose:3 certainly:1 dimensionality:1 const:7 ıv:1 graph:2 undistorted:1 deterministic:2 father:1 passage:1 charge:2 does:3 those:1 under:2 analogous:1 novikov:1 applied:1 adiabatic:3 last:2 dynamic:1 connects:1 wave:11 electron:3 reflects:1 condition:1 induced:1 obvious:2 presented:1 ref:7 t2:1 solution:8 large:1 discrete:5 vector:5 indices:6 frolov:1 markov:1 noted:4 effective:3 neighborhood:5 oscillation:5 haar:1 direct:1 approximation:1 go:1 rate:3 enclosed:1 further:1 dynamics:6 chem:1 substitute:1 canonical:2 index:1 deeply:1 axes:4 uniform:1 cell:6 new:2 pictorially:1 condensed:1 relates:1 respectively:4 mr:1 fields:3 here:11 atoms:1 2m:4 possibility:2 separation:1 represented:1 path:3 along:6 equations:5 change:1 ukraine:1 substance:2 hamiltonian:3 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quant-ph9910024.txt |@word magnetic:2 results:3 gg:1 garching:1 contributions:1 alamos:1 technique:6 passage:1 presents:6 charge:6 σu:2 far:1 continues:1 wave:4 electron:2 resonant:1 experimentally:2 difference:1 presented:6 ref:1 proposals:1 leave:1 sang:2 differential:1 small:2 optics:2 force:1 dutra:1 direct:1 feasibility:1 second:4 evaluated:1 errors:1 wijnands:1 selected:2 current:2 experiment:4 above:1 new:1 net:2 increasing:1 method:2 leeuwen:1 exchange:1 respectively:1 component:1 teleportation:1 here:1 atoms:8 separation:1 address:1 directions:3 path:1 along:3 change:2 obtained:3 undeflected:2 parameters:10 losses:3 allows:2 suggestion:1 resonance:1 suitable:3 changes:1 via:2 followed:1 scales:1 highly:2 stern:1 p45:2 total:2 planck:1 linearly:1 plot:3 conventional:1 superpositions:1 probabilities:1 contains:1 calculation:1 measureable:1 taken:2 associated:2 populations:4 becomes:2 apparent:1 visibility:1 virtue:1 known:1 resemblance:1 states:7 mf:4 setup:2 work:4 ρn:6 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quant-ph9910025.txt |@word concept:1 partial:1 consider:4 maximum:3 focus:1 illustrated:2 go:2 follow:1 denotes:2 gk:11 localized:1 devoted:1 whose:2 amplification:3 concerned:1 deterministic:1 kentaro:1 environment:11 tail:1 critical:1 stable:3 stochastic:16 must:1 meetings:1 case:26 supported:1 hibbs:1 very:1 modes:1 conditions:1 choice:8 umezawa:1 ichiro:1 figs:1 experimentally:2 emphasized:2 difference:2 condition:2 level:2 ref:3 trb:5 large:2 phase:1 splitted:1 small:5 trs:2 attracting:1 upper:1 work:3 force:4 occurrence:1 periodicity:2 renormalized:1 10a:2 profs:2 feasibility:1 second:1 realistic:2 ill:1 dynamics:10 volovich:3 canonical:2 bilinear:1 appear:1 deeply:1 specification:1 brief:1 experiment:2 above:2 new:6 contributes:1 antiresonance:1 method:2 contrast:1 satisfy:3 27a:2 27b:2 kicked:1 respectively:5 here:14 understanding:1 iωτ:2 relaxation:1 concluding:1 based:1 along:2 strong:2 equations:3 obtained:7 waseda:7 technical:1 shift:15 study:2 studied:5 denominator:1 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quant-ph9910027.txt |@word represent:1 concept:1 partial:1 consider:4 maximum:3 interference:1 focus:1 leads:4 scalar:2 entropy:7 comments:1 grateful:1 consists:1 follow:2 ror:1 faster:1 issues:1 reynaud:4 whose:1 depend:2 calculate:2 alamos:2 environment:6 finally:1 behave:1 under:2 td:4 division:1 straightforward:1 zhang:1 very:1 frequencies:5 peaks:1 results:2 frequencydependent:1 dispersions:1 experimentally:1 condition:4 hamiltonian:8 transmission:2 positions:1 solution:1 large:3 small:2 enforce:1 smaller:2 neighborhood:1 oscillation:3 ρm:3 sin2:2 prediction:1 sign:2 approximation:2 rate:12 value:2 dynamics:1 remarkably:1 linear:5 spectral:4 plays:1 perf:3 selected:1 goes:1 satisfy:1 edited:1 full:1 ms:1 degree:3 dissipates:1 here:5 understanding:1 q2:3 illustration:1 relaxation:2 alone:1 ratio:1 along:3 sine:1 respect:2 obtained:7 instituto:1 davidovich:1 shift:3 larger:1 contradiction:1 resulting:1 action:1 hospitality:1 fourier:2 via:3 replace:2 decrease:1 linearly:1 plot:2 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quant-ph9910028.txt |@word limited:1 consider:5 priori:4 helstrom:1 global:3 reversibility:1 results:3 four:1 entropy:2 per:2 computation:1 research:2 particles:4 preserves:1 depend:3 calculate:1 tr:1 topic:1 ny:1 under:2 characterised:1 sent:1 henderson:2 rb:1 advantage:1 orthogonal:16 fav:1 plausibility:1 choice:1 every:1 telling:1 difference:1 exact:3 condition:1 swapping:1 transmission:5 turns:2 steeply:1 eve:3 large:4 upper:1 employing:1 sin4:3 sin2:13 direct:9 zero:1 further:3 port:2 theory:1 even:4 employ:3 what:4 errors:1 giving:3 section:4 goes:1 shared:5 method:12 contrast:1 coefficient:1 full:9 degree:1 ρab:2 respectively:1 teleportation:49 understanding:1 cos4:3 cos2:11 making:1 directions:1 obtained:1 sending:6 convert:1 sender:2 receive:2 popescu:3 vectors:1 allows:1 approaches:1 lo:1 prior:3 accomplished:1 extremes:1 schumacher:3 symmetrical:1 bob:34 makes:6 plotted:2 being:1 via:1 projection:1 bounds:1 outcomes:3 hardy:2 apply:1 total:1 unit:9 use:6 feb:1 asymptotic:3 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quant-ph9910029.txt |@word consider:4 trigonometric:2 whose:1 feeding:1 depend:1 paris:1 tr:5 tl:1 behave:1 yˆ1:10 yˆ2:10 breach:1 worth:1 ın:1 overlaps:17 applied:1 advantage:1 far:5 electron:1 mixing:4 splitter:12 smithey:2 presented:1 transmission:1 yˆm:1 yˆn:1 yˆi:3 large:2 solved:1 small:2 optics:4 equation:1 employing:1 prudnikov:1 2max:3 direct:6 approximation:2 zero:1 chopping:1 traveling:2 insertion:1 further:2 click:3 canonical:9 ˆt:1 section:3 expressed:1 d3:2 homodyning:3 new:1 increasing:4 method:10 outgoing:1 simultaneously:2 behavior:1 degree:1 respectively:3 desired:7 ei:1 cos2:2 concluding:1 sine:2 obtained:1 suitably:1 involved:2 allows:1 yˆ:39 fourier:1 plotted:2 transmittance:4 appropriately:1 being:3 projection:1 f2:2 replace:1 plots:1 use:1 superpositions:2 commun:1 sake:1 positive:1 poizat:1 next:1 few:2 noting:1 ψn:13 therefore:3 ψl:3 th:2 out1:1 becomes:3 operators:4 odinger:6 berlin:1 particular:5 known:1 conditioned:2 must:4 valued:1 r2:1 rβ:1 setup:2 work:2 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quant-ph9910030.txt |@word jason:1 consider:9 chain:1 similarity:7 canonical:2 magnetic:1 suggests:1 focus:3 invent:1 existing:1 illustrated:1 computation:1 consists:3 denotes:1 minuscule:2 issues:1 gr:1 devoted:1 whose:4 theorist:1 fellowship:1 arthurs:2 striving:1 concerned:2 tr:1 send:1 spirit:1 finally:1 efficiencies:2 squeezing:2 protocols:1 whatsoever:4 under:1 breach:1 resources:2 ingredient:1 applied:1 lack:1 presently:2 orthogonal:6 far:3 2re:3 rise:1 fav:6 misunderstanding:1 wave:2 wishes:1 every:3 hewlett:1 experimentally:1 variance:2 lam:2 branca:1 immediately:1 presented:1 did:1 positions:1 venue:1 threat:1 bangor:2 phase:1 assurance:2 recall:1 small:3 gauge:2 optics:4 ρout:3 upper:1 replicates:1 assure:1 likely:1 noise:2 dried:1 further:1 toolbox:1 goes:3 even:4 nothing:4 what:13 plays:1 appear:3 brackets:1 giving:1 section:4 http:1 supplied:1 uniform:3 experiment:16 above:4 pristine:1 new:5 ever:5 acknowledgments:1 edited:2 full:3 transportation:1 lee:1 degree:1 fmax:3 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quant-ph9910035.txt |@word consider:4 magnetic:1 global:1 results:7 hσν:1 leads:1 eds:2 proposition:4 expressions:2 research:1 reˇ:1 localized:3 seemed:1 layers:7 inverse:2 depend:2 hµρ:2 technique:1 tr:1 trivial:1 manifolds:1 th:1 under:5 geom:1 analogous:2 dramatically:1 kν:1 conjecture:1 supported:4 orthogonal:2 springer:2 geometrical:1 electron:2 sons:1 schmit:1 formula:1 hµν:4 deformations:1 condition:3 beginning:1 hamiltonian:7 notes:1 tubes:1 large:2 discrete:4 vector:1 announced:1 recall:3 small:7 hνµ:5 upper:1 employing:1 renormalized:1 ρm:3 estimates:1 modified:1 second:7 pass:1 further:2 dynamics:1 estimated:1 odd:1 theory:2 spectral:2 aim:2 what:1 g22:1 trapping:1 cast:1 diag:1 section:3 while:2 expressed:2 gj:5 above:4 replaced:1 construction:2 order:1 waveguide:1 satisfy:1 compact:3 κn:2 encircled:1 relates:1 respectively:3 l1:1 modify:2 here:1 behaviour:1 desired:1 objects:1 decay:1 directions:1 change:2 obtained:6 remark:3 sobolev:1 rigorously:1 technical:1 vectors:1 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quant-ph9910036.txt |@word limited:2 concept:3 evidence:1 consider:4 springer:1 illustrates:1 interference:3 magnetic:23 lack:1 dynamic:3 gz:1 existing:3 four:1 eds:2 ge:1 proposition:1 polarizers:1 c2:4 consists:1 sci:2 clarified:1 contributions:1 reasoning:1 causes:1 gh:1 excludes:1 careful:1 depend:2 calculate:2 paris:1 subjected:1 deterministic:1 aggregations:1 created:1 environment:4 charge:9 av:2 under:2 presumed:1 spec:2 amplitudes:1 presently:1 returning:1 far:5 frequencies:1 implicitly:1 none:1 seemingly:1 results:6 electron:67 sons:1 every:7 interpreting:1 prof:1 experimentally:2 ln:1 difference:6 exact:7 condition:1 trigger:1 leads:3 annihilated:1 obvious:1 immediately:2 hamiltonian:4 diverging:1 unusual:3 solution:4 try:1 discrete:2 settle:1 elsewhere:1 wst:2 evanston:1 speculation:2 cms:3 noted:5 concluded:1 smaller:1 insignificant:2 dealing:2 consistent:3 sign:1 approximation:2 go:1 second:6 plenum:1 enhancement:4 insertion:1 realistic:1 ueu:1 further:3 copenhagen:2 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quant-ph9910042.txt |@word represent:3 alm:6 consider:1 particular:2 desirable:1 leads:1 eds:4 concept:1 entropy:7 foundations:1 constants:8 expressions:3 contributions:1 devoted:1 increase:2 inverse:1 depend:2 referring:2 advantage:1 irrelevant:1 concerned:2 eˆ:2 tr:53 environment:3 γj:10 preserved:1 under:3 indicating:2 ingredient:1 case:6 conjecture:1 probe:1 ˆjn:39 straightforward:3 orthogonal:2 very:9 dell:1 choice:6 hove:1 affect:1 difference:3 condition:2 induced:1 exponential:3 hamiltonian:5 did:1 turns:1 notes:2 solution:3 t0:72 large:2 surements:1 differential:3 fourier:1 small:4 div:5 optics:1 strongly:1 dealing:1 maximization:1 direct:1 past:1 second:6 qualitatively:1 dynamics:12 linear:2 established:2 what:2 plays:2 appear:3 apparatus:1 ˆw:1 section:1 expressed:1 consistently:2 ˆf:2 new:3 ˆj:10 method:1 justification:1 respectively:1 component:1 asymmetry:1 separation:1 philipps:1 represented:5 equations:10 appears:3 obtained:1 remark:1 barchielli:2 study:1 allows:1 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quant-ph9910047.txt |@word dimentional:1 maximum:14 global:1 gx:9 leads:7 facilities:1 ge:1 ga:19 go:2 follow:3 expressions:3 denotes:2 consider:5 dsn:1 const:2 ac02:1 concerned:1 groundstate:10 quasi:4 does:2 th:1 under:1 cm0:1 g2:4 very:1 wave:17 decide:1 li:1 difference:5 exact:9 encounter:1 cmn:8 unlike:1 hamiltonian:7 bn:6 2κl:2 solution:19 c30:2 large:4 vector:1 recall:1 small:2 eigenvalues:3 infinities:1 degeneracy:1 upper:1 smaller:4 sturm:1 consistent:1 sign:12 approximation:5 fold:1 zero:6 evaluated:1 ψeven:57 further:4 odd:8 even:6 gl:30 fine:1 section:15 while:2 expressed:1 above:5 new:3 3a:2 ground:3 method:3 3e:1 body:1 polyakov:1 systematic:4 convergences:2 whose:1 respectively:3 modify:1 here:1 59b:1 china:3 illustration:1 others:1 directions:1 along:3 equations:5 appears:1 change:5 differential:2 box:1 g2r:2 institute:1 study:3 larger:1 gle:2 trial:3 periodic:1 resulting:2 permit:1 action:1 conveniently:1 makes:1 uniquely:2 being:1 useful:3 family:1 defer:1 requiring:3 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quant-ph9910048.txt |@word limited:1 consider:4 maximum:3 results:1 leads:3 overlap:3 whose:2 simon:2 calculate:1 alamos:3 γt:3 quasi:1 those:1 under:6 sent:1 supported:1 amplitudes:1 already:1 orthogonal:1 far:2 wave:2 denoted:3 every:1 should:3 experimentally:1 exact:1 splitter:1 level:6 dif:1 make:1 herbert:1 large:3 brukner:1 phase:2 small:1 optics:1 setup:4 upper:2 hillery:4 approximation:1 zero:1 machines:2 even:1 index:1 trapping:1 anton:1 sum:1 current:2 version:1 3n:1 3m:1 new:1 method:1 simultaneously:1 respectively:2 component:1 here:1 atoms:9 behaviour:1 represented:1 path:1 along:3 strong:1 transformation:2 change:1 incoming:7 fwf:1 studied:2 simultaneous:1 symmetrical:1 makes:1 buˇzek:5 via:3 namely:1 austria:1 achievable:1 total:2 wang:1 use:4 would:2 massar:2 probabilities:2 gregor:1 scenarios:1 few:4 ψi:3 therefore:5 type:2 until:1 decomposable:1 more:2 mm:1 emission:20 berlin:1 particular:1 cases:1 producing:2 fly:1 springer:1 ρi:1 science:1 originally:1 work:2 cat:1 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quant-ph9910049.txt |@word chingangbam:2 sundermeyer:1 since:1 consider:2 show:1 definite:1 over:1 obtain:1 rest:1 disc:3 gauge:2 hyperboloid:1 follow:1 momenta:1 research:1 line:2 reduced:13 q1:1 q2:2 thank:1 chosen:2 interesting:1 equal:1 april:1 minus:1 coordinates:2 appropriate:1 parts:1 only:1 setting:1 degrees:1 systems:6 ambiguity:1 pair:1 integrable:2 quantise:1 go:1 oct:1 momentum:1 real:1 do:2 non:1 teitelboim:2 university:1 straightforward:2 get:3 henneaux:1 similar:1 showing:1 delhi:1 term:1 corresponds:1 cannot:1 lecture:1 press:1 using:2 singularity:2 boundary:2 condition:1 secondary:1 generated:2 restrict:1 evolution:4 dirac:7 2q:5 excluding:2 hamiltonian:8 turns:1 notes:1 arxiv:1 eigenvalues:1 acknowledgments:1 paper:2 index:1 follows:1 relation:1 reveals:1 essential:1 constraints:17 satisfy:1 requirement:1 set:2 financial:1 classical:6 map:1 imposing:1 some:1 springer:1 sign:3 consists:2 namely:1 p21:8 interval:2 choosing:1 p22:2 quantum:4 further:3 dynamics:1 regge:1 canonical:3 even:1 will:2 matrix:1 space:19 restricted:1 singular:5 lagrangian:8 include:1 find:1 looking:1 case:2 pankaj:1 eliminate:1 above:1 between:1 without:2 new:1 geometric:1 reading:1 conditions:1 method:4 math:1 choose:1 evolving:1 earlier:1 chose:1 dropped:1 respectively:1 each:2 points:1 however:2 here:1 residual:1 completely:2 would:1 multiplier:1 put:1 rigorous:2 configuration:3 equations:2 hilbert:5 proceed:1 obtained:1 restrictions:3 essentially:1 her:1 r2:13 constraint:9 lincei:1 freedom:2 study:1 discussed:1 reproduces:1 quantization:8 motion:1 introduction:1 r1:1 poisson:1 assumed:1 discussions:1 support:1 south:1 first:4 arbitrarily:1 contains:1 useful:1 manuscript:1 extra:1 ca:1 qˆ:4 obtaining:1 primary:1 due:1 dimensional:7 phase:14 pole:1 inequality:1 done:1 solve:1 lagrange:1 operator:2 next:2 open:2 positive:4 lect:1 given:2 arbitrariness:1 second:6 hyperbolic:1 quantisation:1 unknown:1 adjoint:2 there:2 system:8 been:1 reanalyse:1 start:1 appears:1 therefore:2 under:1 basic:1 ph:1 gives:3 pˆ2:3 corresponding:1 grant:1 both:1 started:1 reduce:1 operators:3 eqn:1 eliminates:1 but:2 jamia:1 industrial:1 lectures:1 hole:3 removed:3 iii:1 present:1 must:4 p2:8 ii:1 level:2 p1:10 determines:1 disconnected:1 quantized:1 pacs:1 whether:1 cij:1 equation:1 nazionale:1 up:2 us:2 transformation:1 annihilation:1 dei:1 manifestations:1 critical:1 starts:1 canonically:3 radius:5 derived:1 example:1 manner:1 mechanics:1 unitary:1 yeshiva:1 defined:1 india:2 them:1 qˆ2:3 sharan:1 states:1 sphere:2 examine:1 ij:1 pˆ:3 numbers:1 council:1 conjugate:1 unphysical:1 qureshi:1 constrained:2 apparently:1 any:4 spaces:3 again:1 functions:2 roma:1 zero:4 no:2 amounts:1 things:1 self:3 same:1 princeton:1 field:1 nontrivial:1 priori:1 quant:1 department:1 φi:2 φj:2 out:1 conclusion:1 wave:1 square:2 centre:2 may:2 after:1 upon:1 definiteness:1 inherently:1 v2:4 plane:3 position:1 infinite:2 hanson:1 lagrangians:1 choice:3 class:4 commutation:1 scientific:1 branches:1 dynamical:1 emr:1 considered:1 adjointness:1 brackets:1 center:1 analysis:6 4q:2 quantize:1 bracket:2 so:1 principle:2 fixing:1 coordinate:2 observables:2 academia:1 acknowledges:1 physics:2 fact:1 consisted:1
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quant-ph9910050.txt |@word consider:1 broaden:1 particular:5 grateful:1 expressions:2 relationships:3 inverse:2 const:2 technique:1 γj:1 finally:1 program:1 under:2 analogous:1 case:1 springer:1 choice:2 matrices:5 condition:2 notes:1 solution:8 wronskian:2 second:2 further:2 linear:2 spectral:1 stands:1 diag:1 dr2:16 expressed:1 above:1 international:1 method:1 coefficient:1 respectively:2 here:2 represented:2 along:1 marchenko:1 equations:10 obtained:3 search:1 institute:2 vectors:1 allows:1 minsk:1 resulting:1 identity:1 makes:1 useful:1 coinciding:1 summation:1 establish:1 linearly:1 use:2 remains:1 ψj:2 nucl:2 humi:1 cαβ:1 themselves:1 type:2 until:1 more:4 company:1 odinger:6 carrying:1 geophysics:1 virtue:1 varying:2 known:5 cases:4 rudyak:1 account:1 equation:3 work:1 det:1 values:5 following:2 making:1 performed:1 allowed:1 sought:1 verlag:1 end:1 darboux:14 transforming:1 after:2 applications:1 plane:1 studies:1 waves:1 multiplication:1 requirements:1 lines:1 correspond:1 perform:1 so:1 order:1 developed:1 over:2 paper:1 spheroidal:1 y1:1 satisfies:1 its:2 derive:1 ln:7 forms:1 systems:1 derivative:1 belarus:1 combination:1 introduce:1 functional:2 now:5 represents:1 inversion:1 equality:1 2h:2 side:5 ed:1 energy:7 related:1 owing:1 quantum:2 eq:18 matrix:6 twice:1 research:1 pνµ:2 lecture:1 independence:1 foundation:1 theory:3 favored:1 standard:1 dubna:1 definition:6 derivation:1 turn:1 obey:2 multiplying:1 construct:3 another:1 angular:3 given:4 rewritten:2 introduction:1 unknown:2 eqs:6 system:5 relations:4 their:3 normalization:1 using:4 academy:1 exactly:3 part:2 differentiate:1 x1:1 than:1 wide:1 γj2:1 double:1 zero:1 determined:1 russia:1 rewrite:1 modern:1 generalization:4 any:1 latter:2 instance:1 potential:14 take:2 forces:1 channel:2 heisenberg:1 formulas:1 continuous:1 scripta:3 shall:1 algebraic:9 regular:1 formulae:2 acknowledgements:1 class:2 appear:1 clear:2 physica:3 physics:4 quantity:1 show:1 supported:1 relation:3 solutions:21 substituting:1 d2:17 find:1 subtracting:1 multichannel:3 parameters:1 state:2 should:1 vαβ:12 explicitly:2 oct:1 dh:8 get:1 dependent:1 familiar:1 express:1 joint:1 ones:2 words:1 dy:4 dw:1 dr:38 approach:4 arxiv:1 imposed:1 analytical:5 fixed:8 satisfy:4 set:1 constructing:1 dyµ:3 see:2 result:1 discussions:1 eigenfunctions:1 nuclear:1 symmetric:1 written:1 closed:3 between:3 boundary:1 conditions:3 multiplied:1 terms:5 initially:1 key:1 suggested:3 both:3 essentially:1 limits:2 taking:2 conclusions:1 propagation:1 connection:1 expression:6 allowance:1 cy:1 respect:1 levitan:1 publishing:1 basis:1 three:1 been:3 int:1 ph:1 corresponding:3 received:1 body:1 expounded:1 those:2 applied:1 look:1 straight:1 value:1 heidelberg:1 will:3 procedure:2 coupled:1 vol:1 characteristics:1 refs:1 conf:1 bargmann:14 orbital:1 different:5 righthand:1 author:1 journal:1 radiation:1 same:3 quant:1 independent:1 hand:4 v1:1 potentials:7 landau:1 cµ:3 schr:6 acoustics:1 well:1 coordinate:1 chemistry:1 gelfand:1 being:2 when:1 vαα:1 obtain:4 atomic:1 summed:1 differentiation:1 scattering:2 sciences:1 jost:1 transformed:1 easy:2 solvable:3 transformation:2 momentum:4 generalized:10 real:1 easily:1 world:1 pertinent:3 follows:2 either:1 arbitrary:5 reduced:1 because:1 some:2 specified:1 provided:1 electromagnetic:1 investigations:1 integration:3 does:2 proc:1 scientific:1 equivalent:4 conventional:1 cν:2 cβ:6 cα:2 von:2 transformations:21 central:1 dependence:2 obeys:1 consequently:2 statements:1 into:3 within:1 integral:2 bound:2 jβ:2 appropriate:3 right:4 references:1 determine:5 sov:1 additional:1 transform:2 was:2 function:7 form:11 simplifications:1 regard:1 pµν:1 october:1 versions:1 us:6 problem:3 professor:1 mechanics:1 required:1 constant:1 defined:1 certain:2 general:5 single:2 constructed:3 functions:6 compared:1 completeness:1 no:2 yµ:10 whereas:2 generally:1 vanishes:2 papers:1 elements:1 may:3 superposition:2 models:2 problems:2 a18:1 variable:6 coupling:1 coulomb:2 dφ:1 interval:1 time:1 restored:1
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quant-ph9910051.txt |@word 51b:1 partial:1 consider:4 similarity:1 results:12 edu:2 follow:1 expressions:3 contributions:1 calculate:1 technique:2 those:1 under:1 applied:1 amplitudes:1 very:2 wave:24 continued:1 condition:12 entire:1 basics:1 presented:1 transmission:10 ref:2 solution:3 large:1 rj:1 hospitality:2 zh:1 f21:1 sukhatme:7 10a:2 diffuseness:1 cosh:6 approximation:2 elegant:1 integrability:1 anggi:1 chem:1 substitute:1 even:2 panigrahi:1 morse:3 section:1 expressed:1 find:1 goes:2 new:1 method:3 satisfy:1 27a:1 27b:1 mω:1 explore:1 them:2 pub:1 sinh:4 address:4 concluding:1 equations:5 obtained:12 instituto:2 suitably:1 institute:1 oman:4 study:2 studied:1 suggests:1 amount:1 superpotential:8 complicated:1 suitable:1 emerge:1 via:1 useful:1 borkovec:1 9a:2 9b:2 55c:1 readily:1 150b:1 use:7 takes:1 usa:2 prove:1 remains:2 coordena:1 few:1 nucl:3 therefore:6 taken:3 nagarajan:1 simpler:1 theoretical:1 more:1 introducing:2 l195:1 operators:13 starting:1 odinger:8 2w1:2 2ex:1 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quant-ph9910052.txt |@word fleury:1 logarithms:1 measurements:1 sci:1 consider:3 magnetic:8 particular:4 dynamic:7 results:3 roy:2 computation:14 reson:3 follow:1 fellows:1 contributions:1 issues:1 increase:1 preserves:1 depend:4 knill:1 environment:1 under:1 include:1 indicating:1 applied:11 probe:1 advantage:1 very:2 frequencies:1 rise:1 geometrical:1 fall:1 experimentally:1 difference:1 matrices:1 hamiltonian:9 induction:1 t2:2 t1:1 large:1 discrete:1 phase:47 science:1 small:1 slower:1 deutsch:2 pulse:10 feasibility:1 second:2 further:3 dynamics:2 implemented:3 machines:1 theory:2 errors:3 giving:1 rectangles:2 interactions:1 while:7 experiment:2 resilient:2 new:3 systematic:1 placing:1 partly:1 here:4 ranges:1 desired:1 inversion:1 relaxation:5 path:7 along:3 change:1 magnetisation:1 unidentified:1 shift:8 leaves:2 permit:1 resonance:15 conveniently:1 narrow:1 changes:2 cancellation:1 examining:1 via:1 visible:1 addressed:1 castagnoli:1 apply:2 total:4 use:4 working:1 commun:1 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quant-ph9910058.txt |@word represent:1 managed:1 limited:1 rev:13 results:10 four:1 computation:1 go:1 follow:4 contributions:1 particles:2 simon:1 nonlocal:2 finally:1 critical:5 those:6 excluded:1 stabilizing:1 case:12 conjecture:3 supported:2 returned:3 returning:2 very:3 choice:1 novel:1 every:1 orientations:1 entries:2 experimentally:2 difference:1 matrices:7 condition:2 randomness:1 magic:1 swapping:3 level:1 solution:2 discrete:1 vector:3 verdict:1 math:1 michler:2 limitations:1 10o:1 farkas:2 prediction:7 approximation:2 carefully:1 second:1 further:3 αi1:1 αi2:1 even:6 established:1 what:5 hide:1 stands:1 apparatus:1 distance:1 fine:1 mlp:1 experiment:13 above:3 mlv:1 increasing:1 method:7 satisfy:3 full:3 chose:1 respectively:1 never:1 here:5 ranges:2 directions:1 based:1 along:1 strong:1 equations:1 imperfections:1 obtained:5 search:1 property:2 incoming:2 study:1 vectors:2 suggests:1 resulting:1 usually:1 sinusoidal:16 makes:1 ake:1 formulated:1 spatially:1 projection:2 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quant-ph9910059.txt |@word logarithms:1 code:18 consider:1 results:4 gf:2 computation:2 inverse:1 knill:1 tr:1 factoring:1 th:2 advantage:2 very:2 otteler:1 summarized:1 matrices:1 condition:1 school:1 presented:5 discrete:4 erasures:1 small:1 fold:1 canonical:1 spectral:2 established:1 errors:13 brief:1 decoding:6 version:1 new:2 contrast:1 full:2 degree:1 here:1 operating:1 expansion:3 groups:1 represented:2 november:2 obtained:3 great:1 shift:1 products:1 resonance:1 fourier:5 via:1 useful:1 addressed:1 boolean:1 sloane:1 apply:1 unit:1 usa:1 prove:1 cory:1 ψj:1 linear:8 encode:1 theoretical:1 michaelis:1 normalized:1 known:1 foundations:1 iii:1 grassl:3 science:1 focs:1 grover:1 following:4 dec:1 stimulating:1 ions:1 f2:2 figure:2 abelian:1 process:1 suggestions:1 states:3 minimum:2 acm:2 occur:1 information:3 syndrome:3 provide:1 how:5 subroutines:1 magdeburg:1 symposium:2 ensemble:1 product:1 mar:1 derived:2 diagram:1 types:1 short:1 fahmy:1 register:3 algorithms:4 order:1 office:1 over:18 years:1 paper:3 london:1 cold:1 ieee:2 its:1 massey:1 systeme:1 thank:1 encoding:5 writing:1 systems:1 main:2 might:1 syndromes:1 pu:1 them:1 combination:3 introduce:1 holub:1 steane:1 they:2 nov:1 realize:1 φk:3 dirac:1 stabilize:1 fully:1 orthonormal:2 outperform:1 2n:2 2k:10 domain:2 en:1 ei:2 weight:1 series:1 principles:1 society:2 frequency:2 measurement:1 quantum:51 eq:1 shown:1 matrix:1 rs:8 furthermore:1 since:1 interference:1 denoted:1 ro:1 theory:5 given:4 york:1 detecting:1 e1:1 definition:8 computers:3 length:4 disturbed:1 circuit:2 hence:1 informations:1 already:1 enlarges:1 probability:1 striking:1 coding:1 number:2 set:2 several:1 differ:1 introduction:2 dft:5 system:3 least:1 their:2 assumption:1 normalization:1 uka:1 cope:1 honolulu:1 authors:1 havel:1 distance:2 cyclic:5 modelled:1 solomon:12 determined:1 berlekamp:1 extracting:1 pre:1 rainer:1 boston:1 correction:3 exchanging:1 any:2 vulnerable:1 mappings:1 efficient:2 self:6 trapped:1 able:1 generalized:1 concatenated:2 finding:1 so:1 towards:1 multiple:1 cosets:3 most:2 germany:1 but:1 phase:5 beth:3 class:2 kk:7 medical:2 kn:4 proceedings:2 construction:4 tech:1 mechanical:3 fact:1 thomas:1 show:1 registers:2 based:7 parameters:1 implementation:2 written:1 only:4 local:3 oct:1 do:1 notation:1 de:1 during:2 stoc:1 prime:1 fields:8 arxiv:1 factorization:1 common:1 characteristic:1 erroneous:1 computed:1 physically:1 ary:1 flip:8 relative:1 see:10 computer:3 discussions:1 techniques:3 detect:1 tensor:2 nuclear:1 review:2 currently:1 representatives:1 f22:1 state:4 ira:1 numerous:1 email:1 nature:1 qubits:15 harvard:1 last:1 f2k:7 many:1 taking:1 annual:2 according:1 σz:2 σy:2 σx:2 und:3 context:1 qubit:5 cb:3 corresponds:1 polynomial:2 respect:3 pp:6 commutative:1 capable:2 addition:1 been:3 basic:2 ph:1 hardly:1 fig:2 corresponding:1 sufficient:1 search:1 stems:1 c2:2 general:1 present:1 euclidean:1 error:18 35th:1 laflamme:1 non:1 iv:1 ii:1 dual:12 ready:1 id:1 binary:10 different:1 same:1 complex:1 quant:1 pauli:2 finite:5 higher:1 used:5 eds:1 changing:1 identity:2 weakly:5 database:1 nevertheless:1 markus:1 no:1 dimension:1 calderbank:1 transmitting:1 resp:1 obtain:1 transforms:3 using:3 followed:2 yet:1 zoller:1 royal:1 transformed:1 theorem:6 input:1 transformation:1 possible:1 press:1 integer:1 bit:5 correcting:12 necessary:1 like:1 particle:1 martin:1 translated:1 shor:2 classical:6 some:1 searching:1 b1:3 28th:1 images:1 transactions:1 proc:2 demonstrated:1 bn:2 bi:1 bj:1 bk:1 universit:1 about:1 would:1 extension:4 basis:10 o:1 letters:1 into:2 references:1 acknowledgements:1 institut:1 there:1 transform:3 fast:2 decode:1 start:1 way:1 function:1 phenomena:1 encodes:1 encoder:1 hi:1 reed:12 encoded:1 true:1 versions:1 circuits:2 cij:2 up:3 ur:1 spectroscopy:1 problem:2 define:1 examples:1 storing:1 cirac:1 computing:3 defined:1 abstract:1 combining:1 denote:1 exist:1 physical:2 codes:35 variety:1 rains:1 when:2 field:5 karlsruhe:2 conclusion:1 superposition:1 important:1 building:1 bch:1 algorithm:3 together:1 equivalently:1 investigated:1 time:3 far:1 rep:1
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quant-ph9910060.txt |@word logarithms:1 code:52 saturating:1 consider:2 focus:1 four:1 gf:2 computation:6 aug:1 technique:3 editors:1 environment:9 finally:3 those:1 th:1 under:1 norm:1 ingredient:1 case:4 supported:1 orthogonal:10 frequencies:1 otteler:1 results:1 electron:1 matrices:3 condition:1 siam:1 level:1 transmission:1 positions:3 july:3 large:1 discrete:2 vector:2 erasures:1 fourier:1 small:2 der:1 upper:2 zc:19 sign:1 likely:2 replicated:1 implemented:1 odd:2 theory:5 spectral:2 errors:25 plays:1 appear:1 w5:2 section:3 brief:1 expressed:1 decoding:11 errorcorrecting:2 fortschritte:1 above:1 new:2 acknowledgments:1 contrast:1 margolus:1 simultaneously:1 respectively:1 promising:1 here:4 iσx:1 them:1 expansion:4 represented:4 auxiliary:1 z0:2 change:1 obtained:3 search:1 sender:1 shift:1 larger:3 allows:1 prior:1 products:2 usually:1 hamming:2 implement:1 suitable:1 changes:2 via:1 addressed:1 sloane:2 unit:1 remaining:1 use:6 additive:1 takes:2 would:2 codewords:4 contains:1 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