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quant-ph9712005.txt |@word code:1 consider:1 remarkable:1 caused:1 results:1 four:2 computation:3 edu:1 consists:1 whose:1 knill:2 technique:2 tr:1 environment:2 under:4 suffered:1 include:1 resources:4 advantage:1 evolves:1 far:1 denoted:4 every:2 difference:1 condition:5 hamiltonian:8 fhe:2 knight:1 guo:2 applicable:1 t0:17 occurs:1 large:6 succession:1 small:1 eigenvalues:1 tru:1 limitations:1 approximately:1 deutsch:1 approximation:3 zero:1 eigenspace:5 further:1 implemented:2 linear:1 rewritten:1 nonlinear:1 sub:1 rate:7 sum:1 near:1 expressed:4 decoding:3 above:4 coefficient:1 respectively:1 equals:1 protection:1 china:3 2kb:3 address:1 represented:1 ratio:1 aω2:5 obtained:1 involved:2 vectors:2 suggests:2 implement:1 ηmax:3 sloane:1 apply:2 circumvent:1 unit:1 use:4 working:2 remains:1 h0:3 few:2 bz:1 encode:1 simpler:1 type:3 tell:1 more:4 beyond:1 bennett:1 successful:1 operators:2 corrected:1 berlin:1 known:1 states:7 springer:1 science:7 equation:1 when:3 ρr:3 norm:1 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quant-ph9712006.txt |@word childs:1 rev:6 thomas:1 leads:1 roy:1 grateful:1 causes:3 whose:1 preserves:1 concerned:1 young:3 interactions:2 vigier:2 present:3 ti:3 must:3 cm3:1 ta:10 division:2 fax:1 supported:1 advantage:1 very:8 wave:2 berkowitz:1 nuttall:2 every:1 affect:1 encounter:1 induced:3 transmission:1 positions:1 proposals:1 solution:1 fewer:1 large:1 small:4 smaller:2 prediction:3 pulse:1 approximation:3 likely:1 cost:1 pass:1 further:1 estimated:1 even:2 aim:1 what:1 appear:2 apparatus:5 chicago:2 selected:1 near:2 uniform:1 experiment:14 method:1 filled:1 raising:1 lee:1 desorption:1 commercial:1 heller:1 here:2 atoms:25 ionization:1 believed:1 objects:4 free:1 address:1 directions:1 standard:1 appears:2 great:1 technical:1 involved:2 settles:1 experience:1 suggests:1 products:1 surely:1 narrow:4 diameter:1 useful:3 danger:1 visible:2 apply:1 obligation:1 cloud:1 use:4 proceed:1 would:20 lose:2 predictions:2 process:2 scheer:3 chu:2 m2:1 taken:3 sharpen:1 until:1 today:1 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quant-ph9712007.txt |@word magnetically:1 magnetic:21 fabricated:1 roy:1 per:1 gn:5 whose:1 mcr:2 charge:14 rei:1 analogous:2 worth:1 string:2 g0:2 far:1 rise:1 account:3 wave:1 etal:1 electron:2 putting:1 experimentally:1 amaldi:1 convenience:1 vector:1 gauge:1 noted:1 degeneracy:1 sin2:1 second:1 odd:1 what:1 appear:1 expressed:1 uniform:5 reminiscent:1 experiment:2 3n:2 new:2 consisting:1 body:1 here:1 atoms:2 cos2:1 directions:1 along:2 equations:2 logarithmic:1 bhubaneswar:1 obtained:2 institute:1 resulting:1 usually:1 makes:1 rρ:1 conventional:1 takes:2 would:2 remains:1 positive:1 eφ:1 negative:1 nucl:2 noting:1 ψn:3 ψo:1 means:1 type:1 today:1 separated:1 introducing:1 becomes:2 charged:4 me:1 none:1 mc:1 equation:5 theories:1 bent:1 do:1 india:1 states:15 degenerate:2 doubling:1 hydrogen:11 axis:2 get:1 feature:1 sin:2 may:1 b79:1 so:3 polyakov:1 order:2 d18:1 produced:1 paper:1 through:2 differs:1 existence:1 its:1 2e2:3 d35:1 absence:1 permanent:4 h0:3 them:1 contention:1 combination:1 singularity:3 term:2 dirac:5 magnitude:1 electrically:1 found:1 ei:2 ej:3 ed:1 eg:6 hara:1 elementary:1 frequency:2 static:3 quantum:5 our:1 shown:1 superscripts:1 res:1 rep:1 since:5 rev:9 particles:2 magnetostatic:1 equate:1 a133:1 ri:2 rj:3 shows:1 linear:1 standard:1 zwanziger:1 york:1 e0:6 definition:2 interaction:2 saha:3 transition:2 motion:1 instrum:1 exponentially:1 incorporated:1 first:1 singleton:1 number:2 angular:2 given:2 1r:1 similarly:1 system:1 their:2 passed:1 eqn:4 gives:3 acquire:1 showed:1 cimento:1 gentile:1 orger:1 sec:1 function:1 hagen:1 electrodynamics:1 wilson:1 strength:1 latter:1 note:1 causing:1 take:2 electric:16 opposite:2 collaboration:1 extending:2 ordinates:1 device:1 pradhan:1 considered:1 flow:1 ferrari:1 left:1 physics:2 fact:2 show:1 definite:2 relation:6 d3:13 ground:3 current:5 just:1 written:4 factor:1 parabolic:2 ieg:2 abelian:1 di:2 beams:1 expectation:1 beam:3 dye:1 densities:1 numerous:1 arxiv:1 view:2 multiplying:1 physically:1 violated:1 electrostatic:3 radius:1 result:1 quantizing:1 closer:1 detect:3 rings:1 dipole:10 state:5 between:3 approach:1 terms:1 cabrera:2 however:2 vanishing:1 selectively:1 jetp:1 both:1 cos:2 taking:1 compton:1 equal:1 passing:1 schroedinger:2 experimental:1 co:2 point:2 simple:1 corresponds:1 dimensional:1 radiative:1 due:2 been:2 ph:1 excite:1 external:2 former:1 those:1 case:1 laser:2 pacs:1 value:1 will:2 region:1 squid:1 non:2 surface:3 superconducting:2 im:1 vanish:3 orbital:1 radiation:2 quant:1 infinity:2 numerical:1 action:1 moment:10 fabrication:1 identity:1 charges:1 macro:1 analysis:1 bohr:1 solve:1 undertaken:1 posses:1 bending:1 proposed:1 obtain:1 identify:1 λe:2 absorption:1 smith:1 potential:1 lett:4 excited:7 momentum:2 real:1 possible:1 press:1 particle:1 follows:1 either:1 integrals:1 therein:1 parity:4 right:1 old:1 methods:1 specified:1 2c2:1 prog:1 proc:1 cabibbo:1 equivalent:1 hansch:1 use:1 although:1 2m:9 intense:1 discussed:1 dependence:1 posess:1 stand:1 considerations:1 soc:1 h2:2 maxwell:2 into:1 integral:2 acad:1 references:1 operator:2 graziani:1 log:2 there:1 stark:1 ordinate:1 conservation:1 hooft:1 was:1 energy:1 therefore:2 hz:1 form:6 hv:1 jul:1 volume:1 hi:4 atom:14 hc:10 hg:1 fabricate:2 placed:2 below:1 converted:1 limit:1 ωn:7 distribution:1 monopole:1 mechanics:1 constant:1 defined:1 certain:1 abstract:1 am:2 general:1 dξ:1 exist:1 wavelength:1 ind:1 no:1 when:3 vanishes:1 field:10 detected:1 problems:1 a0:3 generated:2 sides:1 searches:1 independently:1 baker:1 time:1 n1:4 n2:4 nuovo:1
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quant-ph9712008.txt |@word secondly:1 customary:1 consider:1 chinese:1 represent:1 forbidden:2 leads:3 partial:2 inverse:1 remarkable:1 dp:2 finally:1 th:1 divergent:3 emphasizes:1 choice:2 hamiltonian:1 convenience:2 noted:3 coordinate:8 approximation:6 second:2 value:2 further:1 chem:1 canonical:1 index:5 near:2 uniform:5 above:2 new:2 method:3 satisfy:2 respectively:1 china:1 path:6 along:6 quite:1 calculate:2 box:1 institute:1 amount:1 action:3 suitable:4 emerge:1 integrations:1 summation:3 total:1 propagators:1 derivatives:3 use:1 feb:1 sake:1 contains:1 classically:4 therefore:1 introducing:1 becomes:3 robbins:1 pairs:1 qdp:1 cases:1 1th:2 must:1 springer:1 mf:2 ndimensional:1 equation:1 work:3 foci:3 following:3 example:1 beijing:1 dropped:1 want:1 allowed:2 yα:4 spa:8 yβ:4 conversely:2 verlag:1 regions:8 how:1 simplicity:1 singular:4 after:7 orbits:1 representations:2 wave:1 sq:1 sp:4 explicit:1 so:1 representation:3 over:4 stability:2 paper:1 mentioned:1 satisfies:1 its:5 before:2 chosen:1 fix:1 coordinates:5 choose:3 decades:1 overcome:1 them:2 landau:1 they:2 now:2 2t:5 represents:1 february:1 2s:19 always:2 by5:1 traj:3 found:1 2n:8 repaired:1 ed:1 energy:6 related:2 inhomogeneous:1 used:2 quantum:7 laboratory:1 eq:16 special:1 shown:3 matrix:2 space:26 rev:2 chaos:1 denotes:1 contained:1 formula:4 math:2 shows:1 theory:2 standard:1 reason:1 york:2 creagh:1 enormous:1 counterpart:3 first:4 initial:1 approximate:1 temporarily:1 done:1 relations:2 given:6 rewritten:1 similarly:1 eqs:1 system:1 construct:4 molecular:1 final:3 centered:2 academy:1 helpful:1 transverse:4 optical:1 differentiate:1 dqα:5 holland:1 rewrite:1 boston:1 say:1 conjugate:1 need:1 recover:1 any:4 ray:1 depending:1 convenient:1 sciences:1 causing:1 absorbed:1 analogy:2 green:23 formulas:1 added:1 trace:2 though:1 sewing:1 simplify:1 regular:1 phase:2 preexponential:2 intrinsic:1 class:3 constructed:1 calculated:2 adopt:1 points:2 exp:7 physics:3 fact:2 qα0:15 spaces:5 based:1 topological:3 should:1 terminal:1 explicitly:2 factor:5 local:5 achieve:2 get:2 simplified:2 ones:1 dt:4 du:2 ds:17 differentiating:1 runs:1 textbooks:1 arxiv:1 gutzwiller:1 contain:1 thanks:1 sew:1 set:3 exists:1 achieved:1 acquired:3 ary:1 discussions:1 exponent:2 boundaries:1 written:2 between:3 boundary:1 approach:1 available:1 however:1 analyzed:1 configuration:13 both:2 last:1 according:1 pdq:1 connection:1 expression:3 finds:1 among:1 point:2 2nd:1 dimensional:5 respect:3 pq:1 pz:2 trajectory:6 py:1 three:1 been:10 ph:1 determinant:5 adopted:1 diversity:2 restrictions:1 general:1 spin:1 case:1 multi:2 pacs:1 evaluated:2 will:5 while:1 replaced:3 evaluating:1 property:2 almost:2 refs:1 wkb:1 ik:1 itself:1 different:1 author:1 divergences:3 same:1 quant:1 emphasize:1 littlejohn:4 finite:2 development:1 independent:1 arrives:1 trajectories:8 usually:4 fourier:2 qa0:2 messiah:1 without:1 firstly:2 position:9 unified:1 maslov:8 accurate:1 obtain:1 press:1 atomic:1 adv:1 transformation:2 momentum:18 term:1 confined:1 immediately:2 apart:1 semiclassical:23 necessary:1 success:1 particle:1 steps:2 works:1 replacement:2 specifies:1 reidel:1 because:1 old:1 methods:1 deal:1 smoothly:2 some:2 back:1 choosing:1 vol:1 does:1 propagating:1 inserting:3 caustics:4 disjoints:1 properties:4 pβ:2 pα:10 most:2 column:1 discussed:1 o:1 mixed:16 primitive:3 locally:1 pergamon:1 into:4 integral:6 references:1 amsterdam:1 classical:13 delos:3 there:2 transform:3 long:2 way:2 theory2:1 propagator:5 function:19 considerably:1 north:1 form:2 but:4 line:1 applying:1 2πi:11 attached:1 2πik:5 problem:1 similar:1 professor:1 mechanics:7 constant:1 defined:3 abstract:1 denote:2 single:3 physical:1 qα:27 again:2 functions:6 qβ:58 dpα:1 no:1 detail:2 field:2 yang:1 symbol:2 problems:2 includes:1 important:1 lifschitz:1 geometrical:2 time:2
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quant-ph9712009.txt |@word evidence:1 consider:3 remarkable:1 funct:7 alg:4 blanchard:2 gz:2 produce:1 lr1:2 berezin:3 lr2:2 grateful:1 projective:2 talks:1 query:1 mill:1 disk:4 c1:2 compact:14 whose:4 preserves:4 inverse:1 gˆ:1 concerned:1 equivalence:4 canonical:4 uniqueness:2 asking:1 manifolds:16 th:2 under:4 dartmouth:1 norm:6 conjecture:1 charles:1 expressing:1 r10:2 zhang:1 very:8 desirable:2 conditions:1 choice:2 isomorphism:2 every:3 promise:1 microlocal:1 li:1 associated:5 nagy:8 matrices:1 deformations:5 condition:1 partitions:1 riemann:6 level:6 induction:2 notes:4 t0:1 ri:2 involution:6 suµ:8 vector:2 gauge:1 speculation:1 added:1 neighborhood:1 dealing:2 edu:1 bialgebra:1 boca:1 consists:1 zero:1 tangential:5 go:3 follow:1 further:4 dynamics:2 linear:5 even:3 dissertation:2 what:12 gl:1 appear:7 brackets:1 giving:1 specification:1 brief:2 find:1 version:2 above:14 new:4 learned:1 rd:2 method:1 contrast:2 told:1 completion:1 rosenberg:1 full:1 simultaneously:1 herb:1 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quant-ph9712013.txt |@word limited:1 concept:1 consider:2 similarity:2 magnetic:6 four:5 eds:1 broader:1 bergmann:1 reasoning:1 issues:1 restrictions:2 aligned:1 depend:1 switched:1 excluded:1 under:1 nodes:2 must:1 broaden:1 alternating:1 b185:1 very:1 exception:1 wave:8 normalizability:1 electron:3 witten:1 experimentally:1 nieto:4 exact:3 condition:2 treating:1 entire:2 presented:1 leave:1 truax:1 small:1 eigenvalues:1 noted:1 upper:1 tel:1 sukhatme:1 consistent:2 zero:6 further:4 chem:1 theory:2 even:2 established:2 trapping:1 chicago:1 giving:1 fact:1 selected:1 expressed:3 above:2 new:4 ground:2 method:2 filled:3 full:4 degree:1 spacing:1 here:3 atoms:3 desired:1 others:1 active:1 quite:1 equations:1 appears:1 interpret:1 obtained:5 shift:4 study:1 allows:1 ignoring:1 accomplished:1 adopting:1 suitable:1 involves:2 appropriately:1 via:5 extra:1 requiring:1 vii:1 plenum:1 highly:1 names:1 circumvent:1 select:1 conventional:1 takes:2 would:5 objectives:1 suppl:1 e0:2 occupying:1 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quant-ph9712014.txt |@word villeurbanne:1 transitions:1 consider:4 results:1 leads:2 commute:1 tricomi:1 consists:1 research:1 devoted:1 inverse:1 concerned:1 lnr:1 mials:1 finally:1 ρdρ:2 decomposition:1 hill:1 p2:4 orthogonal:1 mn3:3 wave:1 putting:2 varshalovich:1 condition:3 four:2 level:1 irreducible:1 solution:9 deals:1 discrete:4 eigenvalues:1 degeneracy:3 ij0:1 2k1:1 2k2:1 miller:1 sin2:7 direct:1 sign:4 evans:1 ter:4 l2z:2 odd:2 scientific:1 even:1 will:2 zhedanov:1 appear:1 section:1 expressed:1 new:2 journal:1 coefficient:1 wavefunctions:5 fiz:2 respectively:1 here:2 cylindrical:6 cos2:7 separation:4 november:1 equations:1 change:1 obtained:1 search:1 arrive:1 institute:1 published:1 orthonormality:2 va:2 hermite:1 vols:1 viz:1 asymptotic:1 would:1 bernard:1 positive:1 give:1 france:1 hakobyan:1 nucl:1 going:1 ψn:9 m2:4 taken:2 associated:2 theoretical:1 grosche:1 separated:1 introducing:1 hahn:2 operators:4 odinger:2 normalized:1 particular:1 hold:1 θdθ:2 monopoles:1 ma:9 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quant-ph9712015.txt |@word limited:2 consider:4 magnetic:5 results:2 leads:1 consists:2 gn:3 localized:7 whose:1 2n0:1 depend:2 charge:1 present:1 th:2 under:3 stochastic:2 quasienergy:4 p2:4 conjecture:1 frequencies:1 springer:2 wave:17 electron:2 figs:2 formula:1 resonant:8 husimi:5 difference:3 exact:5 condition:8 illustrated:1 randomness:1 level:10 positions:1 solution:1 t0:5 large:4 vector:1 minimal:2 small:9 eigenvalues:8 degeneracy:1 upper:2 employing:1 oscillation:1 excited:1 penetrates:1 approximation:6 located:1 second:8 equal:1 dynamics:6 situated:2 linear:1 even:1 nonlinear:2 appear:1 section:1 http:6 expressed:1 uniform:2 cell:23 above:4 suppose:1 increasing:2 coefficient:3 kicked:2 gif:12 here:2 geisel:1 behaviour:2 wild:1 δωn:2 consideration:1 along:4 strong:1 equations:1 appears:1 logarithmic:3 extreme:1 remark:1 involved:1 studied:1 suggests:1 periodic:1 stressed:1 action:1 resonance:31 changes:2 relation:1 plotted:2 via:2 explained:2 marked:1 decrease:1 use:1 takes:3 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quant-ph9712016.txt |@word logarithms:1 measurements:1 partial:1 gr:8 chain:2 reversibility:1 results:5 roy:1 proposition:4 legal:2 computation:5 consists:2 query:6 depend:1 passage:2 presents:2 γi:1 presentation:1 case:4 amplitudes:5 string:1 advantage:1 construction:2 continues:1 print:5 corollary:2 every:5 cellular:3 mixing:4 exact:1 condition:1 notations:1 gov:1 notes:1 list:2 solution:1 correct:3 discrete:2 spaces:1 phase:3 small:2 deleting:2 proof:2 zm:1 focs:1 grateful:1 deutsch:2 zero:1 noise:1 ecc:2 estimated:1 machines:1 linear:1 even:3 aim:3 what:1 errors:5 plays:1 bb:3 section:4 remain:1 lexicographic:1 sequential:1 above:2 deal:1 new:2 3a:1 method:1 contrast:1 notions:1 tapp:1 respectively:3 here:5 bi:1 protection:4 inversion:1 address:1 represented:1 along:2 z0:2 z1:3 z2:1 obtained:2 rdt:8 search:1 receive:2 my:1 step:8 p2:3 action:2 automaton:1 makes:3 uniquely:1 divide:1 boolean:1 apply:1 establish:1 readily:1 use:2 takes:4 would:2 remains:2 jozsa:1 give:2 chooses:1 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quant-ph9712018.txt |@word partial:1 similarity:1 focus:1 ge:1 commute:1 edu:1 follow:1 finally:1 th:1 under:2 nodes:1 b185:1 far:1 translations:1 choice:1 witten:1 nieto:1 condition:8 hamiltonian:4 list:1 large:1 eigenvalues:1 superalgebras:1 2k0:2 sukhatme:2 diffuseness:1 sign:1 integrability:3 chem:1 linear:1 plays:1 morse:6 section:1 new:2 method:3 ˆn:1 satisfy:4 here:3 ginocchio:1 explore:1 address:2 november:1 equations:2 box:2 institute:2 study:2 suggests:1 superpotential:4 resulting:2 hospitality:1 via:1 elaborated:1 establish:1 readily:1 usa:3 prove:1 distinct:1 definiteness:1 nucl:2 ψn:1 taken:1 introducing:4 operators:12 odinger:1 normalized:1 cases:1 balantekin:3 iii:1 must:2 account:1 deformed:1 science:1 originally:2 work:4 oscillator:5 remain:1 obvious:1 following:1 dec:1 barclay:1 give:1 share:1 states:1 indicates:2 provide:1 discussion:1 utilize:2 write:1 classify:1 algebra:17 replacing:1 ladder:1 derived:1 constraint:1 catalog:1 explored:1 fd:1 realized:1 dynamical:2 imply:1 spectra:3 explicit:1 yielding:1 su:5 so:3 representation:1 developed:1 expects:1 paper:1 committee:1 during:1 satisfies:2 its:2 thank:1 interesting:1 permanent:1 systems:2 2λx:1 non:1 amenable:1 finitedimensional:2 introduce:2 scaling:2 they:4 oxford:1 eigenvalue:2 gets:2 publication:1 university:7 identified:2 2m:12 2n:1 subset:1 weyl:1 series:2 energy:5 related:4 investigated:1 quantum:3 relates:2 eq:17 out:2 shown:6 space:1 rep:1 since:2 rev:3 research:2 may:1 b284:1 oscillators:1 foundation:2 wisconsin:5 theory:3 hull:1 nth:1 khare:3 york:1 remainder:2 e0:4 care:1 definition:1 phy:1 turn:1 generalizations:1 scarf:3 first:4 pairing:2 symmetry:1 omitted:1 number:1 utilized:1 relations:6 electronic:1 illustrate:1 given:8 rewritten:1 introduction:1 eqs:6 system:1 construct:1 their:4 identity:1 gives:1 commutativity:1 2an:1 exactly:3 draayer:1 part:2 schr:1 translation:1 alhassid:1 specify:1 second:1 annihilation:3 classes:1 symmetries:1 rewrite:1 ann:2 spectrum:1 generalization:1 sv:1 seem:1 any:2 lie:8 strength:3 zero:2 depending:1 note:1 k0:7 generalized:2 finding:1 heisenberg:1 mˆ:1 depths:2 most:2 involving:1 class:4 later:1 alumni:1 typeset:1 exp:4 physics:2 fact:1 fukui:1 madison:1 show:5 supported:1 relation:1 solutions:3 ground:6 completion:1 parameters:6 commutators:1 state:8 should:2 only:1 explicitly:1 molecules:1 indeed:2 2be:1 hamiltonians:3 do:1 df:1 dg:1 superpotentials:1 dx:6 dw:3 approach:3 arxiv:1 factorization:1 acknowledgments:1 body:1 set:2 reference:1 achieved:1 national:1 ursey:1 depends:1 result:1 βa1:1 techniques:1 2mv0:4 commutation:6 nuclear:2 review:1 written:1 invariant:9 conditions:4 terms:2 wa:2 iachello:2 however:2 jr:1 would:1 article:3 jetp:1 both:1 many:1 etc:1 connection:2 context:1 finds:1 detailed:1 harmonic:5 dimensional:8 exploit:1 simply:1 associated:5 along:1 reflectionless:1 described:1 aˆ:13 addition:1 been:3 ph:1 algebras:16 define:1 generating:1 supersymmetric:2 coherent:1 spin:1 those:5 tanh:2 eigenstate:1 will:1 deferred:1 couplings:1 2βn:1 unitary:1 a24:1 a26:1 thus:1 iv:1 ii:1 confining:1 partner:2 seattle:2 different:2 grant:1 granted:1 belong:1 lett:4 same:1 complex:1 quant:1 emphasize:1 dimensionless:2 finite:8 pan:1 independent:3 used:3 see:2 v0:4 v1:2 v2:2 purpose:1 potentials:25 infinite:5 invariance:27 normalization:1 recent:1 qa1:1 without:1 position:1 usual:1 spherical:1 cosh2:1 λx:4 obtain:1 infeld:1 shape:36 underlying:3 identify:2 alternative:1 previous:1 conjugates:1 conclusions:1 except:1 potential:13 treatment:1 solvable:3 transformation:2 easily:3 results:1 possible:2 simmons:1 press:1 using:7 moshinsky:1 mod:1 like:1 follows:1 δn:1 either:3 become:2 creation:4 some:1 examples:2 nonzero:1 provided:1 scale:1 cooper:2 lead:2 extensively:1 does:2 revtex:1 found:1 βn2:1 properties:3 chuan:1 carried:1 commutator:1 levine:2 o:3 range:3 important:1 obeys:1 introduced:2 consequently:2 ηf:1 h2:1 into:1 washington:3 bound:2 down:1 appropriate:1 en:6 references:1 operator:2 proportional:2 additional:1 support:1 there:1 transform:2 infinitedimensional:1 was:4 naturally:1 function:3 complete:1 form:3 funds:1 extended:1 extend:1 wisc:1 problem:1 called:3 mechanics:2 constant:4 defined:2 abstract:1 am:1 textbook:1 general:7 tˆ:10 pˆ:2 aizawa:1 corresponding:3 again:3 functions:1 no:3 wavefunction:3 when:1 application:1 role:1 department:4 problems:1 a1:39 a0:9 a2:15 astronomy:2 nuclei:2 structure:4 algebraic:9 implies:1 factorized:1 assume:1 orbit:1 ormand:1 n2:1 requires:1 once:1
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quant-ph9712019.txt |@word saturating:1 consider:1 global:1 leads:2 depend:2 similar:1 tr:3 environment:1 company:1 finally:1 present:1 characterised:2 kraus:1 could:2 geometrical:1 hewlett:1 erp:1 generalised:1 trm:3 trl:2 trn:1 leave:1 vector:4 challenge:1 upper:4 smaller:2 villa:1 direct:1 hillery:2 second:2 notwithstanding:1 machines:5 established:1 what:1 giving:1 version:1 reconstruction:1 here:1 address:1 concluding:1 equations:1 obtained:1 elaborate:1 larger:1 contradiction:2 caf:1 amount:1 products:2 buˇzek:3 via:1 explained:1 outcomes:1 total:1 use:3 would:5 prove:3 positive:4 contains:1 properties:1 ψi:12 popescu:2 therefore:1 taken:1 candidates:1 type:1 qcm:2 more:2 relax:1 outputs:2 operators:6 validity:3 berlin:1 particular:3 known:1 must:1 evolves:1 springer:1 sheds:1 equation:1 work:2 values:1 following:4 arrive:1 example:2 proof:2 process:2 bennett:1 states:11 sphere:1 application:1 performed:2 want:2 allowed:2 verlag:1 end:1 goal:1 provide:2 discussion:1 acts:1 length:1 write:4 maps:1 pure:10 torino:1 optimal:35 map:2 blanks:1 may:4 clone:2 after:2 derived:3 produce:2 stress:1 light:1 explicit:1 allow:2 pleasure:1 subsequently:1 operate:1 order:2 operations:2 restriction:1 holds:1 indeed:1 paper:3 london:1 fidelity:17 volta:1 its:4 before:1 perfect:1 machine:10 derive:2 thank:1 how:1 actually:2 better:5 estimating:3 pavia:1 main:1 them:2 good:1 combination:1 universality:1 mention:1 effects:1 oxford:2 now:6 nor:1 february:1 vidal:1 equality:2 always:1 university:1 presented:1 inequality:1 realise:1 each:5 found:1 2n:1 european:1 macchiavello:1 inputs:6 society:1 extended:2 measurement:16 quantum:21 laboratory:1 operation:4 eq:5 special:1 out:4 divincenzo:2 shown:4 matrix:3 factors:2 furthermore:1 since:1 rev:5 research:1 performs:2 formula:1 ref:4 math:1 shows:1 linear:1 written:2 fisica:1 quite:1 clarify:1 completely:3 ask:1 beginning:1 definition:1 derivation:1 chiara:1 bassi:1 creates:1 isi:1 consequence:2 first:5 there:1 probability:1 number:2 directly:1 blank:1 impossible:1 quality:1 given:5 unknown:3 dipartimento:1 system:1 their:2 intermediate:1 statement:4 wootters:1 1l:9 gives:1 excellent:1 proving:1 assumption:1 part:1 constituent:1 copy:1 uhlmann:3 than:6 albeit:1 kind:1 showed:1 fuchs:1 require:3 see:4 were:3 outcome:2 result:4 shrinks:1 argument:2 already:1 any:13 viewed:2 constructions:1 angle:1 cloners:9 ideas:1 parks:1 note:1 instance:1 finding:2 trace:1 who:2 letter:1 multiply:2 class:3 calculated:1 saturate:1 principle:1 subsequent:1 realised:1 fact:1 show:1 buzek:1 supported:5 find:3 based:2 just:1 specified:1 ox1:1 only:1 black:2 factor:11 meas:16 oct:1 do:1 above:3 means:1 zurek:1 express:1 overall:1 colleagues:1 generalise:1 cannot:3 packard:1 numerous:1 arxiv:1 fixed:1 view:1 set:1 exists:1 achieved:1 namely:2 cloning:18 discussions:2 best:2 still:1 ways:2 factorisation:1 symmetric:12 qubits:21 state:27 rephrase:1 disprove:1 between:3 αi:9 neither:1 reading:1 approach:2 concatenate:3 notice:1 terms:2 extend:5 nature:1 initially:1 combining:1 however:2 received:1 cow:2 many:3 taking:1 infinitely:2 connection:3 qubit:10 estimation:11 otherwise:1 comment:1 cn:2 conclude:3 overview:1 corresponds:2 dimensional:1 cirac:1 maximize:2 moreover:1 described:4 transformations:1 due:3 been:1 defined:2 ph:3 corresponding:1 relaxing:1 both:3 subspace:9 optimality:2 those:1 case:4 will:3 suppose:1 applies:1 exist:1 di:1 property:1 procedure:8 identical:3 unitary:1 orientation:1 thus:6 concatenation:3 helped:1 different:1 italy:2 perform:2 belong:3 indistinguishable:1 same:7 clearly:1 reconstructed:1 quant:3 avoids:1 finite:1 higher:1 independent:1 literature:1 numerical:1 possible:1 changing:1 passing:2 prescribed:2 lower:1 task:1 pµ:8 acknowledge:1 well:1 know:2 without:1 convenient:1 severo:1 justify:1 proposed:1 obtain:1 devise:1 thanks:1 rotates:1 candidate:1 density:19 royal:1 other:1 extends:1 lett:3 input:14 guarantees:1 transformation:3 opt:22 3pu:1 bailey:1 entangled:4 sanpera:1 using:3 helpful:1 like:1 particle:1 specific:1 werner:2 steps:1 either:1 output:10 reduced:10 because:3 methods:3 sequence:2 some:2 respect:1 provided:2 tmr:1 describing:1 lead:2 measurements:1 does:3 provides:1 assuming:1 refer:2 rep:1 clarendon:1 step:1 viale:1 hilbert:1 bz:1 central:1 working:1 massar:4 mixed:7 bloch:5 road:1 statements:2 into:5 bound:7 down:1 device:1 artur:1 operator:12 shrinking:12 realisation:1 existed:1 prepare:1 support:2 initial:4 way:2 was:5 lowest:1 form:6 concatenated:2 smolin:1 tarrach:1 but:1 construction:1 clones:9 cloner:27 applying:2 originals:4 intuitive:1 shrunk:1 us:9 below:1 uk:1 problem:3 optimisation:1 average:1 gisin:4 bruß:2 unfolding:1 required:1 proved:1 povm:1 certain:1 universal:22 describe:2 linearity:1 general:4 single:4 associating:1 our:7 constructed:2 nm:1 ekert:2 generally:1 tight:1 valid:1 becomes:2 shrink:1 conclusion:1 generates:1 meaning:2 palma:1 network:1 auxiliary:3 space:1 together:1 equivalently:1 impossibility:1 original:7
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quant-ph9712020.txt |@word produces:1 when:1 vacuum:3 cosh:1 obtain:5 press:1 quadrature:1 paper:2 distant:1 meekhof:1 using:2 find:3 postulates:1 mathematics:1 feng:2 derive:1 ratio:13 lc:1 4ns:2 density:1 photons:2 except:1 decreases:3 improvement:1 only:2 complex:1 squeezing:3 fig:1 under:1 he:1 transformation:1 hope:1 iφ:2 opt:2 his:1 therefore:1 means:1 far:1 familiar:1 de:3 moller:1 results:1 za:1 they:1 performance:2 dv:1 experimentally:1 nieto:2 possess:1 easily:1 february:1 necessary:1 concerned:1 knight:2 signal:11 arxiv:1 λa:2 niels:1 large:1 bad:1 arbitrary:1 small:1 relation:1 2n:31 fixed:1 optics:1 university:2 mean:2 deal:1 energy:4 some:1 allan:2 modified:1 observed:1 operator:6 depends:1 frequency:3 result:4 quantum:13 our:1 optimum:2 shown:1 lead:2 electromagnetic:1 section:1 rev:6 ρs:1 per:2 αa:1 state:11 µa:1 email:2 available:1 letting:1 noise:11 recently:2 power:2 slight:1 derived:1 applies:1 conventional:1 squeezed:14 comm:1 extent:1 yuen:5 put:1 group:1 equations:2 properties:4 mod:1 obtained:2 both:3 great:1 constraint:1 6aa:1 henriksen:1 so:4 addition:1 whence:2 must:1 wolf:1 expression:1 finds:1 2ns:5 plotted:1 matos:1 there:3 additionally:1 number:27 alone:1 references:1 specifically:1 elementary:1 open:3 unit:2 unusual:1 transformations:1 introduction:1 eqs:4 classic:1 question:1 system:2 been:2 optimize:1 their:1 too:1 interest:1 basic:1 taken:1 ph:1 analyze:1 was:1 a2:1 naturally:1 arises:1 imperfect:1 form:1 kim:2 reduce:1 operators:2 photon:4 displacement:3 coherent:12 optical:3 sharply:1 particular:1 attainable:2 cases:1 given:5 present:1 milton:1 case:2 king:1 maximised:1 showed:1 pacs:1 deformed:1 equation:1 reα:1 maximum:2 value:5 ρn:1 mk7:1 solomon:3 future:1 values:3 uk:3 keynes:1 following:3 dec:1 mechanics:1 ac:2 unitary:1 proved:1 ad:1 vogel:1 computing:1 defined:4 abstract:1 thus:1 general:2 states:25 minimum:1 mandel:1 allocating:1 element:1 any:1 physical:1 oliveira:2 functions:1 uncertainty:2 no:1 eq:3 discussion:1 radiation:1 lett:7 same:1 note:3 field:1 other:1 quant:1 becomes:1 optimal:7 ordinary:1 ns:18 parameter:1 deviation:1 extended:1 see:1 may:2 max:4 use:2 nonclassical:4 what:1 most:1 generated:1 important:1 significant:1 faculty:1 cambridge:1 summarize:1 sinh:1 reduces:1 su:1 ωns:2 more:1 leibfried:1 ratios:1 exp:4 paradigm:1 diminution:1 buzek:1 terms:2 usual:3
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quant-ph9712021.txt |@word limited:3 gt:1 consider:5 exponentiation:2 caused:1 alternatives:1 results:3 noisy:4 leads:2 roy:1 commute:1 entropy:3 computation:26 consists:1 gl:3 whose:1 rosen:1 dimensionality:1 depend:1 calculate:3 knill:6 technique:1 tr:3 extraneous:2 preprint:2 environment:2 finally:1 those:3 under:2 stochastic:1 include:1 sent:1 p2:2 digit:1 presently:1 advantage:1 orthogonal:1 very:3 memories:2 choice:4 manipulated:1 stays:1 experimentally:1 ln:3 ending:1 condition:1 arrange:1 generalised:2 severely:1 incoherent:1 solves:1 hamiltonian:5 transmission:2 knight:19 who:2 having:2 solution:2 damped:1 large:5 solved:1 minimal:1 small:3 possibilities:1 optics:2 noted:2 relative:2 prevent:1 strongly:1 smaller:2 ensemble:1 periodicity:1 deutsch:9 estimates:1 murao:8 l3:1 approximation:3 rate:13 lines:4 invariant:1 dynamics:5 ǫl:1 among:1 linear:6 even:7 will:19 what:5 errors:3 trapping:1 church:1 calcium:1 section:2 selected:2 while:1 find:5 experiment:7 attractive:1 above:7 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quant-ph9712023.txt |@word since:3 partial:1 consider:6 global:1 concern:1 results:2 four:2 manages:1 montr:5 computation:8 edu:1 consists:1 reasoning:1 inverse:2 depend:3 alamos:3 description:3 rf:5 send:5 shall:4 finally:1 india:1 permanently:3 under:2 include:1 sent:5 ingredient:1 string:4 advantage:1 outside:1 very:2 conditions:2 choice:4 wishes:1 every:9 decide:2 fall:1 trouble:2 difference:2 matrices:6 condition:1 entire:5 beginning:1 immediately:2 level:7 did:1 louis:1 having:1 bright:1 try:1 spaces:1 form:2 math:1 recall:3 small:2 enhance:1 optics:2 equation:1 ville:1 des:1 says:3 zi:4 purifications:1 direct:3 second:2 picked:1 pass:2 defines:1 implemented:1 even:2 nothing:2 what:10 stands:1 section:7 disentangle:3 contributed:1 brief:3 expressed:1 henceforth:1 version:3 goes:1 new:5 ever:2 public:2 revealing:1 freely:1 focuses:1 tapp:1 respectively:7 applies:2 gilles:2 understanding:1 desired:1 test:3 ignore:2 november:4 strong:2 respect:1 change:5 knowledge:2 obtained:6 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quant-ph9712024.txt |@word limited:1 extrapolated:2 dynamik:1 forget:1 caused:1 truncated:2 results:4 leads:1 code:1 computation:6 consists:1 gillespie:2 whose:2 theorist:1 flannery:1 depend:1 iii:1 tn:1 finally:1 those:1 under:1 hermann:1 anharmonic:1 include:1 spec:1 henderson:1 case:1 random:3 amplitudes:1 orthogonal:3 far:1 supercomputer:1 straße:1 wharton:1 wishes:2 mixing:1 vlp:2 difference:2 fakult:1 ibm:1 four:3 prize:1 vibrational:5 hamiltonian:5 ref:13 having:1 list:2 correct:1 large:4 discrete:1 vector:2 small:5 eigenvalues:5 leonardi:4 hospitality:1 smaller:3 grateful:1 10m:1 smalley:1 miller:2 consistent:2 direct:3 approximation:1 second:2 further:1 dynamics:3 chem:27 odd:8 even:11 interatomic:1 errors:6 morse:1 fact:1 near:3 experiment:1 above:6 vetterling:1 values:6 rigidity:3 method:7 3d:1 pioneering:1 chaotic:2 full:1 led:1 respectively:2 error:4 here:4 diagonal:1 ranges:3 desired:3 groups:1 congestion:1 auxiliary:1 sinc:1 change:1 great:1 transition:1 involved:1 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quant-ph9712032.txt |@word discards:2 foug:8 lack:1 results:4 four:7 entropy:1 garching:1 broader:1 consists:1 follow:2 expressions:4 research:1 contributions:1 causes:1 consider:4 c0:3 calculate:2 supported:1 uniqueness:3 tm:9 indicate:1 those:1 excluded:1 include:1 resources:4 p2:1 photocount:1 amplitudes:1 spreading:1 very:6 wave:1 d5:4 electron:2 interpreting:1 decide:1 summarized:2 nieto:1 difference:18 exact:1 entire:1 obvious:2 retaining:1 issue:2 ri:3 large:3 bangor:1 harry:1 small:2 refer:1 optics:1 setup:1 consistent:3 d3:5 direct:15 hillery:1 mh:1 go:4 second:2 cost:1 dϕ1:1 notwithstanding:1 further:1 port:15 canonical:1 what:9 cˆm:5 plays:1 appear:1 apparatus:1 giving:1 trivial:1 section:8 dr2:2 expressed:1 debate:1 version:4 ˆd:5 above:5 new:2 scr:1 method:1 contrast:3 edited:2 led:1 behavior:2 respectively:2 component:2 here:3 reported:1 address:2 ratio:2 along:1 sine:2 teaches:1 change:2 obtained:5 arrive:1 incoming:2 institute:1 shift:9 study:1 allows:1 approaches:1 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quant-ph9712034.txt |@word consider:3 helstrom:1 results:6 ρaµ:1 quadrature:8 entropy:2 amplified:1 2r2:2 2r1:2 devoted:1 calculate:1 ohya:2 tr:8 γt:10 environment:3 kβ:5 kα:5 monotonically:1 squeezing:6 under:1 orthogonal:1 very:3 frequencies:1 at1:2 wave:3 matrices:5 obvious:1 hamiltonian:1 transmission:4 solution:1 noiseless:1 solved:1 vector:3 reγ:3 small:1 upper:2 oscillation:1 sin2:1 kodai:1 approximation:1 second:8 zz:1 theory:12 decoding:2 access:4 homodyning:1 above:1 new:1 method:2 simultaneously:2 degree:1 component:7 here:4 understanding:1 cos4:1 cos2:3 address:1 represented:6 consideration:1 equations:3 obtained:4 institute:1 shift:1 vectors:1 products:1 schumacher:1 action:2 narrow:1 useful:1 use:4 additive:1 commun:1 probabilities:3 positive:2 contains:1 therefore:1 type:5 theoretical:1 more:6 nauka:1 decoders:1 eiφ1:2 operators:2 factor:1 particular:1 known:2 cases:1 eγ:8 must:2 kraus:1 mc:2 recall:1 equation:1 work:2 det:3 measures:1 values:3 following:6 dec:1 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quant-ph9712035.txt |@word represent:2 logarithms:1 allowed:1 consider:4 desirable:1 results:4 p02:1 p01:1 proposition:3 entropy:31 overlap:1 grateful:1 consists:1 partial:6 research:1 increase:5 compose:1 depend:2 calculate:1 ohya:1 iii:2 tr:3 acting:8 ascribing:1 finally:6 present:2 fidelity:3 kwong:1 sent:1 inform:1 overlaps:1 applied:5 conjecture:2 provides:2 kraus:1 far:2 p0i:3 p1:2 additional:1 difference:1 matrices:1 dim:6 induced:1 obvious:1 level:2 transmission:14 ref:4 noiseless:5 solved:1 convenience:1 small:4 eigenvalues:4 economically:2 upper:1 says:3 kodai:1 rate:2 further:3 implemented:1 peredachi:1 even:3 established:2 stands:1 apparatus:2 sum:1 decoding:4 establishes:1 dieks:1 replaced:2 increasing:1 acknowledgments:1 westmoreland:1 compresses:1 full:1 notions:1 degree:2 respectively:2 here:12 desired:2 compressed:3 justifies:1 consideration:1 knowledge:2 obtained:8 sending:1 convert:1 spite:1 institute:1 larger:3 allows:1 lo:1 p2:4 amount:2 resulting:1 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quant-ph9712036.txt |@word results:1 leads:1 reasoning:2 depend:1 deterministic:1 tween:1 under:14 virtue:2 very:1 implicitly:1 choice:5 wishes:1 difference:2 condition:14 entire:2 level:1 did:3 cause:1 says:2 dealing:1 prediction:1 past:1 second:1 further:1 even:1 established:2 what:4 giving:1 consistently:1 experiment:3 goes:1 reply:1 exchange:2 here:1 contemplate:1 explore:1 separation:1 consideration:1 implicit:2 change:1 ascribing:1 involved:1 allows:2 action:2 provable:1 narrow:1 changes:1 involves:1 formulated:2 useful:1 extra:1 requiring:1 merely:1 outcomes:4 apply:2 use:2 spoke:1 would:6 predictions:1 diaphragm:1 noting:1 taken:1 theoretical:2 more:2 separated:1 validity:2 rigid:1 basically:1 actual:1 hold:2 must:2 me:1 word:1 science:1 challenge:3 remain:2 renders:1 meet:1 dec:1 my:7 example:1 proof:1 claim:4 accept:1 involve:1 something:1 sense:1 occur:1 rather:4 s2:1 s1:1 how:1 criterion:7 significance:1 instead:4 ordinary:1 redefining:1 description:2 may:1 earlier:2 derived:1 consequence:2 tack:1 parallel:1 natural:6 consequently:1 provide:1 so:1 specifying:1 allow:1 things:2 subsequently:1 order:1 talk:2 closely:1 developed:2 held:1 experiments:3 through:2 argued:1 exclusion:1 decay:2 actually:5 detected:2 relate:1 happened:5 thereby:1 framework:1 they:2 now:2 nor:2 worlds:2 term:1 identified:1 possibilities:6 l2:7 reasonable:1 each:2 found:1 referred:1 hard:1 measurement:2 quantum:3 relates:1 beyond:2 out:4 since:1 adhere:2 investigation:1 forth:1 shows:1 after:1 theory:1 given:3 free:6 differing:1 completely:1 definition:1 pairs:2 r1:2 r2:2 ata:1 could:4 place:1 hence:1 precepts:1 first:3 already:1 clause:1 directly:2 passes:1 inapplicable:1 exists:1 system:1 their:2 assumption:1 statement:9 toe:1 exploring:1 collapse:1 discussion:3 took:1 part:1 authors:1 than:3 distance:2 kind:1 require:1 project:1 matter:1 future:2 supposed:1 prone:1 false:3 argument:7 subordinate:1 apparently:1 any:3 relationship:1 mermin:11 once:1 latter:1 responsible:1 able:1 oriented:1 stapp:3 formulas:1 sure:1 opposite:1 who:1 significant:1 claims:1 nothing:1 why:1 radioactive:1 later:5 differ:1 points:2 normally:1 notion:1 affirmed:1 show:2 detection:1 based:2 knowledge:1 situations:1 specified:2 assertion:2 should:4 only:3 ambiguity:1 do:3 his:4 establishes:2 between:3 countered:1 cannot:1 words:4 adhered:1 conjunction:1 procedures:1 hinges:1 arxiv:1 view:2 conform:1 set:3 reference:2 violated:1 connections:1 see:1 result:2 fail:1 disturbing:1 fails:1 various:2 correctly:2 simplest:2 neither:1 conditions:4 terms:3 parallels:1 nature:8 importance:1 ascribed:1 key:1 observable:1 outcome:1 region:2 against:1 connection:5 context:4 logic:3 whole:1 experimental:1 among:1 premise:1 point:2 simple:2 meaningfulness:5 simply:2 applicability:2 asserted:1 throughout:1 described:1 basis:1 create:1 been:3 appears:2 validating:1 extends:1 ph:1 wants:1 both:1 influence:3 sufficient:1 gap:1 worked:1 former:1 those:2 applied:1 myself:1 choices:1 will:3 error:2 determinism:1 situation:4 property:2 procedure:1 almost:1 thus:2 itself:1 perform:1 counterfactuals:4 make:4 same:2 quant:1 events:3 entitled:1 independent:1 used:1 upon:1 effect:1 experimenter:2 purpose:1 changing:1 makes:3 no:2 epr:7 bohr:6 thought:1 without:3 comes:1 position:1 usual:1 just:3 sentence:1 being:1 proposes:1 spatially:1 alternative:3 captured:1 regarded:1 conclude:1 had:2 except:1 slits:1 easy:1 spooky:1 momentum:2 gave:1 real:2 aspects:1 rules:5 big:1 breaks:1 possible:10 confined:1 world:1 occurring:1 necessary:1 particle:4 performing:1 continue:1 either:3 translated:1 become:1 essential:3 mathematical:1 because:6 deal:1 obliged:1 plausible:1 some:8 examples:1 escape:1 happens:2 describing:1 nondeterministic:1 normal:2 counterfactual:9 conservative:3 everything:1 leap:1 does:4 assuming:1 meanings:1 truth:2 performed:7 l1:5 substitution:1 refers:2 properties:1 about:4 asserting:1 central:1 modal:3 constraints:1 slightly:1 automatically:1 statements:1 into:1 within:3 down:2 lies:1 appropriate:1 einstein:1 argumentation:2 verbal:1 conceivably:1 strictly:1 there:8 question:1 strict:1 physicists:1 way:6 was:6 himself:1 elsewhere:1 regard:1 but:6 philosophers:3 contradictory:1 true:6 he:8 made:4 wholesale:1 bounds:1 until:1 limit:1 problem:1 sometimes:1 proved:1 defined:1 measure:1 am:3 meaningless:5 deep:9 single:1 our:4 denying:1 physical:4 compared:1 locality:1 whereas:1 when:3 invalid:1 reality:3 other:5 conclusion:1 meaning:13 important:1 nucleus:1 structure:10 independently:1 rule:4 fact:1 experimenters:1 time:3 backward:1 having:1 classical:1 augmented:1
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quant-ph9712037.txt |@word secondly:1 similarity:1 interference:91 idealised:1 entropy:1 consists:1 forget:1 whose:1 calculate:11 aug:1 presents:1 whatsoever:1 under:5 rise:4 every:10 experimentally:3 vast:3 vibrational:3 solution:1 succession:1 favoured:1 consistent:14 direct:1 pulse:1 approximation:3 surrounding:2 likely:2 rigorous:3 even:9 errors:1 selected:10 above:13 new:15 net:1 ever:3 consisting:2 evolving:8 notions:1 never:5 here:12 atoms:5 governing:3 path:13 violate:1 obtained:2 leaves:3 completely:5 ignoring:3 permit:2 suitable:1 spacetime:1 divide:1 slices:4 2δt:3 total:3 linearly:1 would:46 dnt:1 call:2 therefore:7 type:2 tell:5 separated:2 successful:1 odinger:1 aware:1 aligned:1 blocking:6 circumstances:3 word:1 mc:1 setup:1 work:3 theories:8 mv:1 dn0:1 concepts:1 example:22 indicated:1 give:6 relativistic:16 involve:3 want:5 end:13 travel:5 feature:3 recovers:1 far:8 adjacent:2 significance:1 answer:1 ordinary:1 description:1 after:17 diagram:4 wrong:1 law:6 parallel:1 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quant-ph9712045.txt |@word consider:2 similarity:1 lack:1 results:2 four:4 entropy:1 computation:4 consists:2 causes:1 whose:2 irrelevant:1 environment:3 finally:1 critical:1 those:3 under:4 resources:1 p2:13 belonging:2 supported:1 worse:1 straightforward:2 very:1 rise:1 choice:2 hewlett:1 affect:1 difference:2 matrices:2 condition:4 transmission:1 knight:1 convenience:2 small:4 optics:1 upper:1 smaller:1 deutsch:2 direct:11 zero:2 greenberger:1 even:5 will:3 3x:1 plays:1 sub:6 advantageous:1 section:1 expressed:1 new:1 method:2 teleportation:1 understanding:3 plenio:1 operating:1 others:2 directions:1 ratio:1 ensembles:1 obtained:6 institute:1 popescu:3 larger:1 completely:1 suggests:2 amount:2 resulting:2 procedure:3 action:1 bob:9 makes:1 involves:1 via:15 useful:2 divide:1 classification:1 apply:2 use:1 would:1 remains:1 next:2 call:2 therefore:1 m2:3 type:18 theoretical:3 more:11 linden:1 successful:2 initial:17 high:2 science:1 rohrlich:2 ρn:1 ρr:1 ρw:4 following:3 dec:1 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quant-ph9712046.txt |@word departement:2 preparation:1 leaking:1 developed:1 over:2 pitaevskii:5 results:1 lemmens:4 interpreted:1 stability:2 radii:1 paper:2 including:1 jetp:1 alkali:1 scattering:1 d3:1 ground:6 rev:7 based:2 conclusions:2 seems:1 boson:1 should:3 potential:6 degrees:1 attractive:7 stable:1 role:1 bradley:1 local:4 into:1 hope:1 details:1 his:1 jensen:1 thereby:1 reveal:1 bound:3 instance:1 confined:2 using:1 singularity:3 poses:1 leads:2 gov:1 documented:1 like:1 particle:2 introduced:1 approach:3 anisotropy:1 arxiv:1 ri:2 large:1 realistic:2 inequality:1 unstable:2 trap:1 fully:1 analytical:1 instability:5 path:1 view:1 mathematical:1 upper:3 interest:1 functional:3 exists:1 energy:7 sov:1 some:1 gaussian:1 lett:2 approximation:1 zero:8 frequency:2 our:2 bose:3 ev:5 out:2 even:1 pronounced:2 length:1 stands:1 collapses:2 confirm:1 leak:1 nuovo:1 associate:1 vlaanderen:1 near:1 research:1 particles:2 state:9 does:1 above:1 between:1 progress:1 before:1 ref:1 checks:1 rj:2 shows:1 considering:1 object:1 barrier:1 interactions:3 applies:1 jp:1 however:3 standard:1 step:1 forthcoming:1 wr:1 situation:1 put:1 preprint:2 devreese:4 extreme:1 earlier:1 temperature:2 interaction:13 derivation:1 rv2:1 freedom:1 study:1 density:1 discussed:1 dependence:1 voor:1 repulsive:1 trial:2 range:12 describing:1 resulting:1 isotropic:1 consequence:1 mean:1 disappears:1 finds:1 wetenschappelijk:1 comment:1 detailed:1 artefact:2 overlook:1 point:1 wave:5 integral:1 harmonic:7 separated:1 signifies:1 determine:1 einstein:2 respect:1 tempere:1 throughout:1 natuurkunde:2 readily:1 clustering:1 given:1 long:1 takes:1 might:2 fwo:1 found:3 assumed:2 condensate:4 there:1 question:1 system:6 groenenborgerlaan:1 eindhoven:1 few:2 describes:1 bosons:5 allows:2 calculations:1 forward:1 onderzoek:1 ph:2 variational:3 hardly:2 hulet:1 more:3 function:9 interparticle:6 corresponding:2 collapse:2 form:1 metastable:2 quantities:1 collapsed:1 xxx:1 gas:1 but:3 confinement:1 generalization:1 number:5 presented:1 than:1 present:1 case:7 distance:1 houbiers:1 made:2 applying:1 specific:1 pacs:1 tunnel:1 bec:4 equation:1 width:1 cimento:1 maximum:3 submitted:1 rb:1 will:1 below:1 replaced:2 burnett:2 following:1 demonstrate:1 dec:1 bohr:1 uia:1 antwerpen:5 would:1 december:1 metals:1 reads:1 minimum:8 confining:1 numbers:1 limit:1 li:1 fonds:1 occur:1 disappear:1 dalfovo:2 huge:1 strength:1 thermodynamical:1 tollett:1 rather:1 edwards:2 technische:1 note:1 how:1 narrowing:1 lifts:1 quant:3 take:1 units:1 global:1 finite:2 parameter:4 stringari:2 conclusion:1 deviation:1 used:1 gross:5 replacing:1 max:1 class:1 numerical:2 derived:1 minimized:1 action:1 v2:3 internal:1 preliminary:1 pair:3 fi:1 analytically:2 senior:1 single:1 recent:1 short:1 stoof:1 nevertheless:1 lanl:1 analysis:3 universiteit:3 feynman:1 depth:1 without:1 fact:1 correlation:3 claims:1 model:5 salasnich:3 requires:1 order:4 incomplete:1
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quant-ph9712047.txt |@word consider:1 caused:1 magnetic:2 results:2 edu:1 ionized:1 depend:4 technique:1 environment:7 finally:2 asking:1 swap:1 under:5 hill:1 division:1 belonging:1 rel:3 misinterpretation:3 very:5 diatomic:1 implicitly:1 plausibility:1 2ra:1 choice:2 electron:5 sons:1 every:1 condition:2 quantitatively:1 progression:1 presented:1 turns:1 solution:5 occurs:1 leave:1 solved:2 vector:17 manifestly:2 eigenvalues:1 version:1 consistent:1 mirage:1 approximation:1 imply:2 qualitatively:1 dynamics:4 hopefully:2 linear:29 even:3 what:3 sub:8 d2:1 sum:1 brief:1 negates:1 experiment:1 above:4 new:5 3a:1 ever:1 satisfy:1 simultaneously:2 drill:1 respectively:2 never:1 prescribe:1 here:2 understanding:2 following:1 represented:3 quite:1 observing:2 implicit:5 interpret:1 box:2 remark:1 exemplified:1 technical:3 involved:3 vectors:3 completely:1 contradiction:2 ri:1 simply:2 uncharted:1 usually:3 makes:1 options:1 projection:3 claim:2 discontinuous:4 merely:4 cosmetic:1 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quant-ph9712048.txt |@word limited:1 saturating:1 systematic:8 magnetic:15 desirable:1 four:26 circuitry:1 entropy:2 transversally:3 assembled:1 localized:6 whose:3 feeding:2 under:10 recycle:1 digit:1 shielding:1 rise:1 intriguing:1 every:4 summarized:1 experimentally:2 dominate:1 succession:1 enhance:2 infancy:1 estimates:3 direct:1 second:12 rigorous:1 implemented:8 seth:1 machines:1 even:32 established:1 errors:144 organisms:1 selected:3 decoding:1 errorcorrecting:2 above:6 designing:1 resilient:1 new:11 ˆj:1 deemed:1 simultaneously:4 reliably:8 never:3 here:5 met:1 fairly:1 protection:2 represented:5 path:6 quark:1 obtained:9 balance:1 suitably:2 study:4 approaches:1 procedure:43 california:2 suitable:6 changes:3 secure:1 classification:3 highly:6 turchette:1 sloane:3 achievable:1 total:6 linearly:4 charge:31 would:37 codewords:20 m5:2 m4:2 noting:1 call:3 therefore:15 m3:4 m2:4 strike:1 type:7 until:4 separated:4 tolerated:2 successful:1 expose:1 curvature:1 correspondingly:1 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