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quant-ph9803002.txt |@word emch:6 skip:1 magnetic:10 splitting:2 leads:1 scalar:1 concept:7 computation:1 consists:2 gh:1 depend:1 removal:1 finally:1 infinitesimally:1 th:1 under:3 norm:1 ta:1 string:1 advantage:1 orthogonal:1 very:2 rise:1 translations:2 results:1 monopoles:1 every:8 exact:1 level:1 involution:2 vector:5 indices:1 shows:1 force:1 relativit:1 direct:2 matrices:1 zero:1 summer:1 perspective:1 eo:8 further:1 dynamics:3 implemented:1 quite:1 linear:7 spectral:3 what:1 appear:2 euclidean:1 section:2 find:1 henceforth:1 en:1 sur:1 3c:1 3b:1 ˆj:1 contrast:1 satisfy:2 full:2 component:1 vol:1 here:2 gge:1 ei:5 les:1 illustration:1 groups:1 sym:1 path:1 strong:1 equations:1 differential:4 obtained:1 antisymmetric:1 thirty:2 commutant:1 institute:1 leaves:1 studied:1 allows:1 manifold:1 controversy:1 porteous:1 permutation:1 action:2 hospitality:1 involves:1 inherits:3 classification:1 brought:1 addressed:1 translational:1 apply:1 etries:1 tools:1 unit:4 clifford:2 ψz:1 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quant-ph9803004.txt |@word iǫ2:2 consider:5 qian:1 rev:8 particular:6 dynamic:1 roy:1 grateful:1 expressions:2 whose:2 calculate:2 presents:2 squeezing:2 include:1 kumar:2 far:2 choice:1 every:2 condition:4 hamiltonian:10 solution:8 solved:1 pˆ2:1 small:1 optics:2 smaller:1 force:1 lewenstein:1 det:2 direct:3 surrounding:1 second:7 bold:2 expressed:2 new:2 method:9 satisfy:1 full:1 chose:1 degree:1 respectively:6 equals:1 here:5 behaviour:2 equations:2 change:1 obtained:3 solid:2 institute:1 study:3 studied:2 plotted:1 via:1 extra:1 qˆ:20 scaled:1 ipv:1 apply:1 establish:1 plot:1 use:3 projector:1 properties:1 vol:1 more:1 bulgarian:1 operators:8 factor:1 appendix:3 varying:1 evolves:2 recall:1 equation:12 work:1 oscillator:41 values:2 following:3 example:4 proof:1 figure:6 calculation:4 states:17 minimum:2 numbers:1 sense:1 blvd:1 axis:1 information:1 reuter:1 regions:1 very:1 influences:1 instead:1 sin:5 mar:1 description:1 oscillators:1 space:3 diagram:2 horizontal:1 constants:3 branches:1 third:1 grant:1 explicit:3 quadrant:1 so:2 specifying:1 representation:3 wigner:8 help:1 developed:1 over:1 london:1 differs:1 satisfies:1 its:1 derive:1 solving:1 boson:1 forms:1 parts:3 systems:2 mail:1 pure:1 effects:1 they:1 front:1 possess:1 eigenvalue:2 february:1 equality:2 invariants:10 university:1 presented:4 trap:1 each:1 found:8 2i:2 mean:6 ei:1 series:1 idea:1 related:1 frequency:26 quantum:43 our:3 beyond:1 eq:1 special:1 shown:8 matrix:3 pˆ0:10 lagrangian:1 re:3 contained:1 hill:1 math:3 shows:2 foundation:1 linear:8 southern:1 mω:2 completely:4 base:2 california:1 york:1 besides:1 geometry:1 used:3 keep:1 motion:13 isotropic:1 first:7 there:3 malkin:2 number:2 nonnegativity:1 wronskian:1 done:2 compensated:1 precisely:1 xu:1 given:1 their:6 system:10 construct:1 glauber:5 too:2 1g:1 molecular:1 dutta:1 ictp:1 simulate:1 than:1 coefficients:2 toronto:1 kind:1 determines:1 cyclic:1 depends:1 annihilation:1 determined:2 were:3 ann:1 qˆ2:1 conjugate:2 need:1 convenient:1 ideal:4 switching:12 heisenberg:2 formulas:2 investigations:1 twodimensional:1 letter:1 pair:2 deviations:1 especially:1 later:1 physica:1 possesses:2 traditional:1 exp:2 mechanical:1 mre:1 physics:3 show:4 lewis:1 supported:1 relation:5 solutions:2 find:1 q0:1 based:2 parameters:2 should:1 1hz:1 only:1 going:1 corresponds:4 indeed:1 density:6 means:1 dependent:5 express:1 despite:1 dv:1 dw:3 dt:14 evolution:6 yuen:1 arxiv:1 bulgaria:1 achieved:1 undergoes:1 see:4 discussions:1 analog:2 concern:1 satisfying:1 commutation:3 ways:1 state:9 various:1 invariant:2 caves:2 conditions:2 preserve:1 terms:7 manko:2 σq2:7 distribution:1 suggested:2 both:1 essentially:1 many:1 taking:1 uncertainty:4 according:2 connection:2 berry:1 σq:3 σp:3 expression:4 detailed:2 point:3 sweep:1 dimensional:5 bose:1 proved:1 pp:1 described:2 aˆ:9 three:2 been:9 describes:1 ph:1 cqp:8 define:1 determinant:6 corresponding:3 sufficient:1 cos:9 gao:1 coherent:5 observe:1 derivative:2 bulg:1 present:2 case:8 ǫk:1 variances:1 value:5 will:5 receive:2 replaced:1 owns:1 squeezed:9 situation:2 nonstationary:9 property:1 region:5 procedure:1 tn:3 thus:1 equal:1 im:5 ic:1 agarwal:2 different:2 inc:1 author:1 same:3 complex:5 quant:1 widely:3 dimensionless:1 finite:2 hermiticity:1 independent:1 phi:1 literature:1 dǫ:3 i0:1 possible:1 ion:1 moment:5 uˆ:1 2mω0:1 normalization:1 schr:6 analysis:3 obviously:1 solve:1 coordinate:5 position:1 parametric:1 dimension:1 usual:1 moments:7 accurate:1 sofia:1 obtain:1 valuable:1 shape:1 intervals:1 atomic:1 paul:2 eigenstates:2 preprint:1 vibration:3 except:1 5s:1 book:1 lett:3 easy:2 theorem:1 trifonov:7 transformation:1 momentum:4 real:3 term:1 harmonic:23 know:1 vacuum:1 using:5 accepted:1 mod:1 necessary:1 specific:1 either:1 integrals:5 arbitrary:2 evolutions:4 reduced:1 therein:1 acad:1 classical:17 lectures:1 creation:1 some:1 examples:1 proper:1 nonzero:1 ddt:1 does:1 provides:1 restoring:1 bg:1 obey:3 equivalent:1 weil:1 2m:5 imaginary:1 periodically:1 about:1 dˆ:1 freedom:1 angeles:1 obeys:1 consequently:2 mathematical:1 integral:5 phase:5 hermitian:2 because:1 references:2 determine:1 operator:6 σp2:7 ellipse:2 vˆ:1 initial:5 los:1 quadratic:2 handbook:1 way:4 was:4 function:12 form:5 phenomena:1 but:2 bǫ:2 hi:1 subsidiary:1 true:1 smooth:3 us:2 below:1 convince:1 fluctuations:3 problem:5 called:1 mechanics:1 constant:3 abstract:1 describe:1 48a:1 general:4 scientific:1 pˆ:20 formulation:1 partly:1 exist:1 check:2 physical:2 again:1 functions:2 completeness:1 no:5 when:4 other:3 papers:1 company:1 conclusion:1 korn:2 models:2 nonclassical:2 covariance:1 commutator:2 important:1 variable:2 mω0:3 mω2:2 omega:1 coupling:1 interval:2 curve:2 mass:3 presenting:1 time:15 cpq:1 having:1 4a:2
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quant-ph9803019.txt |@word consider:3 pointing:1 switched:1 rev:5 results:1 leads:2 roy:1 scalar:1 computation:4 amplified:1 row:1 whose:1 depend:1 april:1 nonlocal:1 finally:2 those:1 under:1 tr1:1 applied:5 telegraph:1 far:1 induce:1 wave:1 exact:1 condition:1 look:1 entire:3 level:2 solution:1 large:3 vector:1 small:4 referred:2 noted:1 solutions:2 smaller:1 deutsch:1 consistent:1 sin2:1 approximation:1 second:6 dynamics:18 functioning:1 linear:2 trick:1 what:1 nonlinear:33 appear:1 section:1 brief:1 uniform:1 above:3 international:1 acknowledgments:1 satisfy:1 evolving:1 simultaneously:2 chose:1 naudts:1 never:1 equals:2 atoms:1 represented:1 teoretycznej:1 quite:1 equations:6 change:2 obtained:1 great:1 hamiltonian:2 rests:1 leaves:1 vectors:1 allows:1 prior:1 amount:1 products:1 stressed:1 makes:2 involves:1 projection:2 danger:1 logical:1 addressed:1 apply:2 use:7 would:3 prove:1 contains:2 toffoli:1 uniqueness:1 ψt:3 properties:1 doubt:2 therefore:4 indiana:1 type:9 more:5 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quant-ph9803020.txt |@word represent:1 concept:1 consider:1 remarkable:1 similarity:1 crucial:1 four:2 broader:1 morphology:3 scr:1 whose:2 pointing:1 graph:1 finally:1 under:1 visualizing:1 worth:1 belonging:1 2rl:3 very:1 connects:1 wave:9 witten:1 exact:1 hamiltonian:2 developing:1 solution:3 discrete:1 vector:1 math:2 eigenvalues:1 work:1 grateful:1 periodicity:2 direct:1 cosh:1 approximation:2 second:3 manipulating:1 reine:1 chem:1 theory:1 even:1 nano:1 d2:1 celebrated:1 brief:1 expressed:5 reminiscent:1 new:4 increasing:1 consisting:1 satisfy:1 full:2 respectively:2 here:3 contemplate:1 cylindrical:1 sinh:1 path:1 along:1 balian:1 change:3 obtained:2 cyclical:2 algebra:1 amount:1 periodic:1 resulting:2 loop:1 adopting:1 makes:1 relation:2 jackiw:1 emerge:1 yamada:1 useful:1 family:2 anomalies:1 should:1 dna:1 takes:1 would:3 distinct:1 positive:1 negative:3 next:3 depicted:2 ψn:2 therefore:3 bender:2 ψm:2 type:1 until:1 more:2 separated:1 introducing:1 composite:1 becomes:1 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quant-ph9803021.txt |@word ambiguities:4 consider:1 rev:3 results:4 fapesp:1 leads:4 roy:1 computation:5 2r2:5 inverse:1 equivalence:3 tr:2 hirshfeld:1 passage:1 presents:1 th:2 ingredient:1 applied:1 string:1 g1:2 very:2 rise:1 contemporary:1 maskawa:1 wishes:1 every:1 difference:1 school:1 hamiltonian:29 turns:1 applicable:1 bypassed:1 falck:1 enforce:1 sin2:12 rivers:1 second:2 pass:2 further:1 implemented:1 canonical:24 even:1 established:1 abd:1 brackets:9 expressed:3 find:2 constrast:1 above:8 ˆi:2 ˆj:1 method:1 full:1 led:1 lee:3 prescriptions:1 here:4 analysed:1 sinn:1 reported:1 girotti:1 path:20 xα:4 equations:1 appears:1 change:1 obtained:9 instituto:1 study:1 studied:2 allows:1 reason:1 controversy:1 poisson:2 hospitality:1 adopting:1 invalidate:1 via:1 bertolami:1 explained:2 total:1 unit:1 conventional:4 working:1 remains:1 physics:4 calculation:1 therefore:2 centre:2 usp:2 more:2 operators:1 apparent:1 odinger:6 curvature:7 surface:3 former:1 particular:1 known:5 iii:1 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quant-ph9803022.txt |@word katz:1 consider:1 depends:1 varying:1 results:6 integration:1 leads:8 ρjj:3 consists:1 perturbations:2 gi:2 whose:1 certainly:1 anticipation:1 depend:1 γr:15 pˆj:1 tr:12 presents:1 finally:5 does:2 indicate:1 present:2 stable:2 discretization:1 include:1 indicating:1 verkerk:1 supported:1 g2:26 g1:22 far:6 rise:1 account:1 subject:1 wave:20 electron:4 manipulated:1 resonant:4 experimentally:2 exact:2 condition:5 treating:1 immediately:1 level:2 bonifacio:11 nucl:1 differentiating:1 solution:5 integrated:1 large:2 phase:2 annihilates:2 science:1 small:7 optics:34 solutions:3 correct:2 smaller:2 2k0:3 zj:25 insignificant:1 consistent:1 sign:2 approximation:4 likely:1 doppler:1 further:4 dynamics:3 eik2:1 eik1:1 theory:16 bilinear:1 what:2 nonlinear:1 appear:1 rate:9 witnessed:1 cˆg:1 section:5 analogously:1 expressed:1 uniform:1 wiggler:1 below:1 version:1 goes:1 berman:1 upset:1 new:3 method:2 contrast:4 body:1 full:2 led:1 degree:2 respectively:3 examining:1 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quant-ph9803023.txt |@word limited:1 measurements:1 caused:1 magnetic:2 spie:2 splitting:4 four:1 bellingham:1 computation:3 edu:1 consists:1 expressions:1 research:2 subjects:1 causes:1 whose:3 aug:1 young:1 including:1 finally:1 indicate:1 stable:1 stochastic:2 indicating:1 overlaps:1 division:1 g2:2 g1:2 susceptible:1 very:1 frequencies:6 results:5 print:2 ωz2:1 sidebands:4 summarized:1 resonant:2 experimentally:1 difference:7 exact:1 cool:2 leads:1 basics:1 δt:1 modulator:1 level:5 meant:1 positions:1 standards:1 leave:1 small:2 still:2 upper:6 abbreviated:1 smaller:1 oscillation:2 consistent:2 pulse:7 sign:2 rate:6 initialized:2 theory:1 even:1 fine:1 sum:1 near:2 d3:7 experiment:2 above:1 shared:1 d1:7 edited:1 simultaneously:1 respectively:3 spacing:1 here:3 atoms:2 operating:1 separation:2 address:2 ratio:1 along:11 equations:1 naval:1 photomultiplier:1 institute:1 larger:2 allows:2 suggests:1 published:1 extra:1 eiφ:1 singlephoton:1 apply:1 unit:1 eye:1 would:1 army:1 give:2 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quant-ph9803024.txt |@word limited:1 sci:1 consider:10 induces:1 forbidden:2 results:3 leads:6 roy:9 generalize:1 spiridonov:1 consists:1 follow:2 whose:5 certainly:1 inverse:1 depend:1 violate:1 paris:1 graph:2 presents:1 finally:7 those:11 under:4 applied:2 belonging:1 very:2 soni:1 rise:5 choice:2 witten:4 nieto:1 exact:2 condition:31 hamiltonian:18 turns:1 solution:16 leave:1 solved:2 convenience:1 small:1 eigenvalues:8 inspection:1 equation:14 b202:1 dutra:1 sin2:2 literature:1 sign:1 zero:1 further:3 theory:1 spectral:10 aim:1 appear:4 morse:8 section:10 http:11 remain:2 expressed:3 indian:1 above:9 deift:1 new:11 method:23 wavefunctions:1 simultaneously:1 devries:1 respectively:3 qµν:1 here:10 behaviour:6 exceptions:1 asymmetry:3 γx:1 ansatz:2 cos1:1 others:1 concluding:1 consideration:1 obtained:3 remark:2 roychoudhury:1 institute:2 studied:2 allows:2 leaving:1 aforementioned:1 quotient:1 oschl:5 varshni:1 via:10 family:3 hermite:1 expect:3 visible:4 apply:1 tools:2 planck:2 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quant-ph9803025.txt |@word footing:1 partial:1 consider:2 rev:1 rovelli:1 results:2 leads:1 ρjj:1 entropy:1 computation:2 whose:5 terms:5 presents:1 quasi:2 under:2 include:1 montevideo:1 applied:1 belonging:1 very:8 choice:1 matrices:2 condition:3 solution:1 occurs:3 hartle:1 solved:1 vector:1 science:1 small:2 eigenvalues:2 occurrence:1 consistent:14 sign:1 approximation:2 imply:2 further:1 dynamics:1 linear:1 even:10 what:7 apparatus:6 near:1 expressed:1 version:2 new:5 satisfy:1 evolving:1 never:4 here:2 explore:1 objects:1 consideration:2 observing:1 change:3 obtained:5 instituto:1 rigorously:4 institute:1 involved:1 vectors:1 allows:6 p2:1 resulting:5 stressed:1 domains:1 california:1 changes:1 involves:1 via:1 useful:2 griffiths:1 family:2 suddenly:1 logically:1 tools:1 causal:7 unit:2 tn:2 use:3 additive:1 projector:2 would:9 prove:2 distinct:1 positive:5 coupled:2 negative:1 calculation:1 therefore:8 taken:6 theoretical:1 more:3 introducing:1 composite:1 acceptable:1 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quant-ph9803026.txt |@word represent:3 monte:3 transitions:1 gr:5 provost:1 caused:1 magnetic:5 particular:4 dynamic:1 results:12 ds:4 leads:1 rapid:1 generalize:1 stochastically:2 consists:1 preferable:1 contributions:1 2r2:1 consider:2 whose:6 object:1 simon:4 depend:1 calculate:7 producing:1 deterministic:3 dp:1 acting:3 environment:3 finally:1 present:6 th:1 under:3 stochastic:38 presentation:1 broaden:1 γe:6 divergent:1 p2:2 labels:1 returned:1 straightforward:1 evolves:2 very:3 frequencies:6 connects:1 geometrical:9 sons:1 putting:1 resonant:4 join:1 simplify:2 matrices:2 condition:10 treating:1 immediately:2 level:38 ref:3 ρf:2 solution:4 occurs:2 noiseless:3 discrete:2 math:1 sine:1 small:6 relation:1 hospitality:1 correct:2 smaller:1 force:18 zj:2 zf:6 parameterization:2 estimates:2 approximation:8 civita:1 second:10 complicates:1 dissipation:1 concludes:1 rigorous:2 further:4 dynamics:35 implemented:1 carlo:3 required:1 spectral:6 established:1 what:2 appear:8 deeply:1 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quant-ph9803027.txt |@word composed:1 ui:3 measurements:2 consider:1 show:1 being:1 indeed:1 authors:1 notations:1 paper:1 relation:1 statistical:1 argued:1 still:1 based:1 system:4 density:1 relativity:1 completes:1 signals:5 only:2 does:2 systems:3 theorem:10 mail:1 save:1 ρb:2 do:4 misinterpretation:2 possible:1 corollary:1 untenable:2 every:3 words:2 using:1 now:1 helpful:1 evolution:1 equality:1 like:1 did:1 follows:1 trc:1 arxiv:1 michael:1 identified:1 transmission:1 spaces:1 frame:1 essential:1 function:1 acknowledgment:1 set:1 reference:4 national:1 revised:2 operator:1 imply:1 mar:1 cloning:14 impossible:1 quantum:7 extended:1 eq:1 exists:1 nonexistence:2 even:1 what:2 essence:1 kiev:1 since:1 thank:1 computing:1 manipulations:1 version:4 between:1 new:1 ρt:1 benjamin:1 respectively:1 jumps:1 stefan:1 teleportation:10 completely:2 although:1 org:1 hilbert:1 projector:2 ukraine:2 institute:1 theorems:4 contradiction:2 introduction:1 due:1 schumacher:3 discussions:1 argue:1 fallacy:2 comment:2 there:3 conclude:1 4i:2 ac:4 outcomes:1 cba:3 references:1 another:1 frames:3 apc:1 given:3 described:1 classical:1 would:2 remains:1 positive:2 etc:1 three:1 their:2 therefore:1 ph:5 pi:4 was:2 consistent:1 sort:1 corresponding:1 form:1 academy:1 operators:2 ti:2 andrew:1 but:1 ρba:8 particular:1 hold:1 former:1 states:2 ρc:22 made:1 vladimir:2 us:1 replaced:1 westmoreland:3 following:1 paci:3 proof:8 mechanics:1 claim:2 formulated:1 unitary:1 remained:1 vi:4 abstract:1 general:1 involve:3 contradicts:1 exist:2 formulation:1 pψ:2 constructed:1 information:1 no:14 latter:1 holds:4 same:1 any:1 note:1 sciences:1 valid:1 quant:5 tii:2 ordinary:1 tρ:2 simultaneity:1 map:3 elements:1 superluminal:6 may:1 use:1 includes:1 most:1 wrong:1 connected:1 entanglement:2 ab:1 ubi:2 recent:1 attempt:1 sets:1 steane:1 vector:1 mash:1 equivalently:1 so:1 ρvi:2 allow:2 time:4 coordinate:1 physics:1 fact:1
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quant-ph9803028.txt |@word represent:1 fe2:1 consider:3 penrose:1 lagrangian:7 magnetic:18 global:1 results:2 gx:2 roy:2 scalar:10 generalize:2 grateful:1 consists:1 expressions:1 hole:1 looking:1 depend:2 calculate:1 tx:2 electricity:2 contained:1 kγ:1 finally:3 those:2 εijk:1 breach:1 maryland:1 include:1 summarizes:1 string:1 orthogonal:2 very:2 f23:1 wave:1 electron:11 difference:1 condition:16 look:3 immediately:1 did:2 turns:1 solution:16 cabibbo:2 large:1 convenience:1 vector:12 originally:1 fµν:1 force:1 concise:1 direct:1 riesz:2 cosh:1 imply:1 plenum:1 dordrecht:1 theories:1 theory:19 bilinear:1 aim:1 asim:3 plays:1 brackets:1 diag:1 sum:1 d3:2 current:2 version:1 above:3 new:9 acknowledgments:1 respectively:5 modify:1 here:3 met:2 objects:1 tangent:1 free:5 ratio:1 xα:2 equations:29 appears:1 obtained:2 dχ2:2 allows:1 denominator:1 suggests:1 professor:1 stressed:1 suitable:1 spacetime:3 der:2 quotient:1 via:1 extra:1 contrarily:1 compare:1 replace:1 total:1 establish:1 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quant-ph9803029.txt |@word beckers:1 sci:1 varying:1 results:2 leads:5 roy:2 ge:1 spiridonov:1 maxima:1 go:1 hole:1 whose:1 technique:5 finally:1 program:1 unnecessarily:1 γl:6 anharmonic:1 te:1 worth:1 global:1 deforming:1 g2:17 g1:12 orthogonal:2 very:1 witten:1 summarized:1 nieto:2 difference:1 deformations:1 condition:1 illustrated:2 hussin:1 hamiltonian:12 turns:1 solution:2 leave:1 elsewhere:1 eigenvalues:5 subindex:1 enforce:1 possibility:2 wronskian:1 coordinate:1 sukhatme:1 direct:2 centrifugal:1 second:9 further:2 situated:1 index:1 appear:2 above:1 hull:1 new:7 method:3 satisfy:1 wavefunctions:1 simultaneously:2 respectively:2 here:3 behaviour:4 free:2 address:1 concluding:1 equations:2 appears:1 change:3 restrictive:1 changed:1 allows:1 suggests:1 amount:1 permit:1 makes:2 plotted:1 family:23 ipn:2 asymptotic:2 working:1 probabilities:1 beginning:1 helvetica:1 next:1 comparing:1 depicted:1 ψn:10 therefore:1 ψl:20 associated:1 type:1 more:6 introducing:1 comparison:1 oscar:1 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quant-ph9803030.txt |@word unavoidable:1 consider:1 forbidden:1 leads:2 manages:1 confirmation:1 four:3 transmission:1 consistent:1 design:1 even:1 stands:1 consistently:1 experiment:2 shared:1 never:1 teleportation:5 here:1 institute:1 leaves:1 contradiction:2 ignoring:1 schumacher:3 bob:21 examining:1 useful:1 apply:1 causal:2 use:1 would:4 therefore:2 until:1 more:1 separated:1 becomes:1 operators:2 particular:1 known:1 ma:1 westmoreland:2 arrive:1 example:1 point:1 process:1 relativistic:1 bennett:1 states:5 lorentz:5 allowed:2 dennis:8 teleport:1 discussion:1 means:1 how:1 answer:2 brassard:1 simplicity:2 mar:1 description:3 barnum:1 after:3 different:2 hence:1 revealed:1 attempt:2 so:1 pleasure:1 subsequently:2 order:2 enk:1 soon:1 course:1 paper:1 including:1 still:1 before:3 thank:1 relativity:6 actually:1 systems:1 inconsistencies:3 main:1 colleague:1 combination:2 introduce:1 warranted:1 they:2 half:1 now:4 possess:1 always:2 found:1 side:2 hard:2 obtains:1 combining:2 quantum:14 laboratory:1 operation:5 special:4 shown:1 since:2 rev:3 particles:4 performs:5 correct:2 standard:7 reason:1 california:1 put:1 jozsa:2 her:9 could:1 place:1 leading:1 consequence:1 uses:1 assign:1 first:3 there:6 utilizes:1 probability:2 done:1 another:1 aharonov:1 given:4 rewritten:1 similarly:1 unknown:3 their:1 observations:1 wootters:2 frame:3 reversed:1 albert:1 part:1 signaling:7 authors:1 copy:4 completes:1 kind:1 fuchs:2 distinguishes:1 namely:1 future:1 crepeau:1 were:1 outcome:5 result:5 bridge:1 well:1 argument:3 seem:1 any:1 latter:1 note:2 sakurai:1 finding:1 sure:1 norman:1 who:3 device:1 why:1 declares:1 clear:1 principle:1 mechanical:1 velocity:1 entertaining:1 usual:2 physics:1 fact:1 violation:1 inconsistent:2 find:2 knowledge:1 state:24 should:1 only:6 do:1 his:4 invoke:1 get:1 zurek:1 joint:3 cannot:1 him:2 reading:1 communicates:1 arxiv:1 she:2 view:1 observer:1 observes:1 violated:1 relative:1 see:3 cloning:8 discussions:1 close:1 violates:2 mechanically:1 written:1 between:2 caves:1 ends:1 terms:1 nature:1 however:2 both:4 many:1 according:4 whole:1 bell:2 simple:1 ca:1 moreover:1 transformations:1 due:2 treat:2 ph:3 addison:1 corresponding:2 observers:1 maximally:1 those:1 will:3 information:2 suppose:1 applies:3 unitary:7 spacelike:1 von:1 thus:2 technology:1 containing:1 same:2 tells:1 quant:3 emphasize:1 party:1 gets:1 events:1 assigns:1 i0:4 upon:1 hand:1 moment:1 moving:1 recent:1 framework:1 nevertheless:1 epr:6 claims:1 possesses:1 justify:1 protocol:3 obtain:1 rest:1 yes:1 superluminal:12 nonrelativistic:2 seems:1 signals:1 pasadena:1 combine:1 lett:3 theorem:6 transformation:2 march:1 measurement:14 entangled:1 using:1 advanced:1 particle:3 follows:1 signal:1 performing:1 alice:23 loses:1 either:1 arbitrary:1 neumann:1 classical:3 provided:1 confirm:1 measurements:2 comments:1 measuring:1 dieks:1 wesley:1 although:5 carol:9 publishing:1 about:1 usa:1 completing:1 constituting:1 mixed:1 purported:1 statements:1 communication:3 into:1 within:1 obtaining:1 copies:1 pair:3 parties:1 frames:1 van:1 prepare:1 initial:2 way:1 company:1 himself:1 form:1 collapsed:1 but:2 hear:1 collapses:1 he:5 applying:1 whether:1 up:1 devices:1 ui:5 stages:1 mechanics:7 describe:3 linearity:1 resultant:1 peres:1 single:1 incorrect:2 compared:1 paradox:2 no:9 detail:1 reality:1 application:1 other:2 naive:1 conclusion:3 problems:2 a1:11 ui0:3 chris:1 assume:1 interval:1 time:1 imprecise:1 having:1
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quant-ph9803031.txt |@word concept:5 partial:4 consider:2 magnetic:7 varying:2 results:2 scalar:1 lewenstein:1 consists:2 sch:1 compact:1 whose:1 amplification:9 depend:1 calculate:1 technique:1 presents:1 charge:5 compensate:1 preserved:2 under:1 worth:1 case:4 roc:1 g2:7 g1:20 far:2 tends:1 iǫi:1 exact:1 condition:6 riemann:1 dij:3 hamiltonian:2 knight:1 solution:9 large:1 vector:2 indices:1 inspection:1 der:1 upper:8 averaged:1 consistent:5 sign:1 approximation:1 dalton:1 zero:5 further:2 substitute:1 theory:9 bilinear:1 what:1 nonlinear:1 advantageous:1 section:1 expressed:1 find:2 current:9 poles:3 ˆf:12 ˆi:4 ˆj:7 ˆk:2 consisting:1 satisfy:3 edited:1 gµ:3 full:6 respectively:3 component:1 equals:1 here:5 atoms:1 following:3 address:1 concluding:1 causality:4 along:2 equations:9 change:1 obtained:1 convert:1 rests:1 involved:1 studied:2 abrikosov:1 narrow:2 jˆk:4 appropriately:2 jˆi:1 via:1 spatially:3 app:2 addressed:1 summation:1 apply:1 total:1 causal:3 unit:1 use:3 prove:3 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quant-ph9803032.txt |@word partial:2 consider:12 switched:1 assembles:1 roc:1 leads:1 proposition:1 gb:1 expressions:1 centers:2 synthetic:2 technique:3 contained:1 environment:1 finally:2 under:2 stochastic:1 anharmonic:4 case:14 supported:1 springer:1 geometrical:2 prog:1 sons:1 every:9 p2α:2 redefinition:1 experimentally:1 exact:1 condition:3 cool:1 europhys:5 level:5 transmission:1 hr:2 discrete:5 independence:1 science:1 small:1 biological:2 markov:1 noted:2 possibility:1 occurrence:1 hs:4 approximation:5 second:3 enhancement:1 further:2 dynamics:4 chem:1 theory:1 even:1 index:2 nonlinear:1 stands:4 iterating:4 brackets:3 section:16 localization:3 annals:1 above:3 lifshitz:1 new:10 method:3 condensed:1 morgan:1 degree:2 mechanisms:1 component:2 composed:4 atoms:3 explore:2 flores:4 free:1 others:1 equations:7 appears:2 change:4 obtained:3 remark:3 barchielli:1 study:3 studied:2 approaches:1 controversy:1 p2:1 poisson:3 usually:2 valparaiso:1 fourier:1 changes:3 criticism:1 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quant-ph9803033.txt |@word eigendecomposition:1 partial:2 consider:6 maximum:7 suggests:1 results:4 tripartite:1 entropy:6 computation:2 edu:2 go:1 saturating:1 whose:1 calculate:3 fellowship:1 tr:6 send:1 does:3 present:1 under:2 opt:1 eβ:4 division:2 01b:1 supported:1 consequently:1 very:4 conjectured:1 connects:1 focus:1 every:2 surprise:1 matrices:6 electronics:1 magic:4 presented:2 tra:4 trc:1 trb:4 list:2 standards:1 section:4 barbara:3 upper:10 work:3 says:2 deutsch:1 consistent:4 maximization:3 sign:1 rate:4 summer:1 pass:1 further:1 what:1 abc:4 appear:1 d2:1 assistance:36 analogously:1 find:5 public:1 above:2 shared:1 increasing:1 consisting:1 contrast:1 supporting:1 systematic:1 lee:1 ρab:13 awschalom:1 respectively:1 realizations:1 ρai:3 teleportation:2 here:8 explore:2 change:1 suggest:1 obtained:1 convert:1 sender:1 institute:3 root:1 study:1 studied:2 i4π:2 ignoring:1 p2:1 resulting:1 procedure:1 schumacher:1 formation:11 bob:16 makes:1 tasks:1 useful:1 00b:1 namely:2 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quant-ph9803034.txt |@word concept:3 sci:2 chinese:3 crucial:1 magnetic:1 both:5 rod:1 existing:1 leads:1 eds:1 generalize:1 go:2 displaying:1 reasoning:1 particles:2 certainly:1 depend:1 ceases:1 shanghai:2 charge:11 excluded:1 under:8 teaching:1 ingredient:2 p2:2 woman:1 returned:1 very:4 implicitly:1 caught:1 conditions:1 wave:10 bjorken:1 electron:19 every:1 summarized:1 li:1 trouble:1 difference:1 condition:1 perceived:1 accompanying:1 ref:6 occurs:1 try:1 solved:2 dealt:1 combine:1 inertial:2 20th:5 enjoy:2 prevent:1 force:2 dealing:1 prediction:1 sign:2 past:1 second:2 rigorous:1 further:4 dynamics:1 yang:1 even:4 established:3 what:8 clock:4 selected:1 mw:1 expressed:1 current:1 version:1 above:8 new:3 momentum:1 method:2 contrast:2 body:3 deemed:1 full:2 lee:1 ibid:1 modify:1 equals:4 here:1 understanding:2 lack:2 believed:1 china:1 twentieth:1 alone:1 consideration:1 drell:1 70s:1 equations:1 change:3 contraction:2 publisher:1 great:3 indivisible:1 brilliant:1 involved:1 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quant-ph9803038.txt |@word ibid:5 code:1 partial:1 consider:1 remarkable:1 caused:1 varying:3 results:5 ghrist:1 ciudad:2 computation:1 localized:3 compact:2 increase:4 griffin:1 inverse:1 technique:2 baym:1 ıa:7 finally:2 behave:2 spain:3 stable:3 norm:1 applied:1 global:1 advantage:1 orthogonal:1 very:6 induce:1 wave:1 manipulated:1 experimentally:1 moura:1 exact:1 condition:4 clouds:1 hamiltonian:1 dodd:1 applicable:1 integrated:1 large:9 solved:1 shuryak:1 science:2 small:11 possibility:1 application:1 smaller:1 force:7 lewenstein:2 prediction:2 literature:1 approximation:5 zero:1 profiles:1 substituting:1 dynamics:3 theory:1 even:6 established:1 nonlinear:17 trapping:15 stoof:1 trivial:1 section:4 while:3 d3:2 current:6 scientists:1 new:4 increasing:1 method:2 coefficient:1 evolving:1 mec:1 favourably:1 here:6 atoms:3 tiesinga:1 objects:1 galilean:1 directions:1 along:4 strong:1 equations:5 change:2 obtained:2 great:1 naval:1 involved:2 study:4 larger:2 allows:1 completely:1 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quant-ph9803039.txt |@word concept:2 consider:2 dynamic:1 results:2 osi:4 scalar:1 expressions:1 localized:1 rmki:1 depend:1 irrelevant:1 tr:2 stochastic:3 fatal:1 far:1 wave:4 electron:4 condition:2 switches:1 hamiltonian:2 turns:1 large:1 vector:1 small:1 inertial:4 unaware:1 work:1 miller:1 consistent:1 strunz:2 approximation:1 second:3 further:1 even:3 nonlinear:1 stands:1 apparatus:2 deliberate:1 intersect:1 obvious:2 boost:2 satisfy:1 edited:1 respectively:1 reported:2 along:1 standard:6 equations:9 change:2 box:1 institute:1 vectors:1 completely:1 makes:1 pearle:2 invalidate:1 depart:1 plenum:1 outcomes:1 sixty:1 apply:3 unit:1 would:2 prove:1 remains:2 call:1 archives:1 taken:1 themselves:1 relax:1 becomes:1 odinger:2 controlling:1 particular:1 known:3 must:1 equation:4 averaged:2 ρl:1 theories:2 reproduce:1 lorentz:1 values:3 following:1 my:2 example:3 claim:1 lρ:1 relativistic:15 states:3 contradicts:1 mixture:1 sense:2 axis:1 awkward:1 write:1 how:1 pure:1 ordinary:1 ensemble:1 mar:1 our:1 derived:1 plane:4 compatibility:1 counter:3 lost:2 parameterized:1 so:4 representation:1 order:1 typical:1 interpretation:1 indeed:1 pointed:1 vary:1 soon:1 interpreted:1 wiener:1 its:3 chosen:2 forms:1 systems:1 mail:1 main:1 might:2 non:11 processes:1 elementary:1 they:3 now:1 easily:1 dirac:11 each:1 found:1 related:1 frames:1 expect:1 measurement:2 quantum:11 relates:1 eq:9 out:2 shown:1 space:5 restricted:1 since:1 rev:1 research:2 seriously:1 reader:2 print:1 ref:1 she:1 foundation:1 theory:9 free:1 quite:1 assures:1 reason:2 york:1 lajos:1 r1:3 r2:3 turn:2 retain:1 assign:1 first:4 origin:1 already:1 features:1 relate:1 ℓv:3 philosophical:1 directly:1 open:1 guess:1 reference:4 similarly:1 introduction:1 eqs:2 system:4 their:7 too:1 kµ:5 shifted:1 petruccione:2 calculations:1 continuous:2 authors:1 translation:2 abandoning:1 diffusion:5 distance:2 unfortunately:1 breuer:2 zero:1 preparation:1 matter:1 a42:1 historical:1 sees:1 generalization:1 need:2 seen:2 any:1 strength:1 note:1 instance:5 shall:1 measures:1 nothing:1 measured:1 why:1 average:1 velocity:1 physics:3 hyper:9 particularly:1 ikµ:1 show:1 violation:1 supported:1 notations:1 inconsistent:2 hungary:1 trivial:1 aρ:2 parameters:1 should:1 local:1 do:5 his:2 hungarian:1 di:4 between:1 expectation:5 ones:2 rest:2 new:1 years:1 budapest:1 arxiv:1 summary:1 nν:4 observer:13 frame:4 result:1 fail:1 recently:2 nuclear:1 diverge:1 state:14 various:1 kfki:2 preserve:1 terms:3 initially:2 however:1 observable:4 uncertainty:1 according:1 attributed:1 context:1 experimental:2 unitarily:2 unclear:1 point:1 reasons:1 cf:2 coincidence:2 respect:1 three:2 been:1 reduction:3 slowly:1 basic:1 ph:2 choose:2 both:3 observers:5 fund:1 observe:1 understand:1 c2:3 spin:3 present:1 myself:1 value:3 will:5 rests:2 while:2 situation:1 unitary:7 surface:1 claimed:1 different:1 author:1 same:3 quant:2 split:1 widely:1 finite:3 residing:1 used:1 moving:3 invariance:5 well:4 consistency:1 model:1 mistaken:2 relevant:1 transforms:2 predicts:2 generator:1 density:1 lett:1 identical:1 march:1 read:1 replace:1 like:3 particle:1 follows:1 ignore:1 arbitrary:1 become:1 reduced:1 right:1 latters:1 lead:1 measurements:1 does:1 who:2 scientific:1 equivalent:3 broken:1 bp:14 diosi:1 concreteness:1 origins:1 o:5 compatible:1 mixed:1 own:2 markovian:1 into:3 down:1 hermitian:1 references:1 operator:2 her:1 initial:3 way:2 troubling:1 was:1 function:2 but:3 hu:1 failure:1 construction:2 lindblad:1 he:1 minkowski:1 up:3 us:1 limit:4 planes:4 demonstrate:1 percival:1 define:1 nµ:2 gisin:2 constant:1 abstract:1 measure:3 general:1 exist:1 formulation:2 physical:1 functions:2 otka:1 no:2 when:1 application:1 other:1 normal:1 nv:4 conclusion:1 superposition:1 models:1 a1:2 a0:7 a3:3 a2:2 implies:1 dψ:1 assume:2 together:1 time:6 n0:7 n1:2 n2:2 n3:2
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quant-ph9803040.txt |@word limited:1 truncated:1 results:7 four:2 follow:2 expressions:1 preserves:1 terms:1 calculate:1 finally:2 does:3 preserved:1 case:5 advantage:1 zhang:1 very:6 implicitly:1 choice:6 electron:1 worst:1 tridiagonal:4 difference:2 matrices:14 condition:3 hamiltonian:27 wegner:10 turns:1 applicable:2 large:23 solved:3 small:17 eigenvalues:7 application:1 smaller:2 disordered:1 consistent:1 sign:7 approximation:1 second:7 gn:11 dynamics:1 odd:1 linear:1 even:7 will:4 what:1 appear:1 section:6 expressed:1 version:1 above:8 new:30 method:4 condensed:2 fock:1 equals:2 here:3 behaviour:6 pseudospin:1 hkn:3 ansatz:6 hkm:2 const:1 quite:1 equations:65 obtained:6 lipkin:10 ruprecht:1 larger:4 allows:1 reason:2 amount:1 simply:1 published:1 g2n:10 suitable:2 plotted:1 useful:12 scales:3 apply:5 conventional:1 andreas:1 takes:1 remains:1 contains:2 hilbert:3 few:4 nucl:3 therefore:13 iteratively:1 reorder:1 more:6 knows:1 successful:1 becomes:2 operators:2 factor:1 validity:2 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quant-ph9803042.txt |@word ibid:5 caused:1 graham:1 brownian:1 results:10 leads:2 eds:3 giulini:1 controversial:1 go:1 contributions:1 b288:1 heller:1 ulis:1 alamos:5 bx4:1 anglin:3 environment:4 preserved:1 th:5 stable:1 stochastic:3 include:2 presentation:1 dramatically:1 division:2 zhang:1 far:1 dynamic:1 springer:3 focus:1 lyapunov:7 figs:2 irreversibility:1 affect:1 zibin:1 little:1 bringing:1 condition:3 paz:5 milburn:1 washes:1 evolved:1 level:4 cause:1 solution:3 b285:1 large:3 solved:2 small:6 optics:1 smaller:1 force:3 ten:1 folds:1 consistent:3 direct:1 dimensional:1 second:3 today:1 timescales:2 value:1 substituting:1 dynamics:8 implemented:2 linear:1 even:6 established:1 nonlinear:4 localization:1 near:1 experiment:1 berman:1 new:6 appeal:1 contrast:1 body:1 supporting:1 chose:1 degree:1 respectively:2 here:4 reported:2 explore:1 focused:1 others:1 along:1 equations:10 logarithmic:3 obtained:1 appreciated:1 study:3 studied:2 allows:1 p2:2 resulting:1 changes:1 numerical:3 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quant-ph9803048.txt |@word secondly:1 quarks:2 consider:4 remarkable:2 magnetic:2 results:2 leads:7 roy:1 follow:1 gm:6 voids:1 issues:3 gh:1 dimensionality:1 show:1 spirit:1 charge:5 ıb:1 under:1 stochastic:2 g2:2 very:5 frequencies:1 conditions:1 idealised:1 electron:14 encounter:3 entire:3 quantized:1 eds:1 issue:1 applicable:1 t1:1 large:7 discrete:1 small:2 cms:1 force:3 dealing:1 consistent:4 d3:1 zero:2 value:4 further:5 estimated:1 theory:6 universities:1 what:2 appear:3 giving:1 section:1 near:2 3t:1 reminiscent:4 experiment:1 above:10 international:1 ptp:1 temperatures:1 justification:2 respectively:1 equals:2 here:4 behaviour:4 holistic:1 decay:2 alone:1 based:1 along:1 coupling:2 equations:1 appears:1 deduced:1 obtained:1 stellar:1 balance:1 dehmelt:1 technical:1 root:1 resulting:1 balances:1 emerge:1 via:1 scales:1 spooky:1 merely:1 explained:1 viz:1 neutrino:15 total:1 planck:4 unit:1 use:3 proceed:1 would:2 remains:1 handedness:4 negative:1 next:4 comparing:1 memory:1 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quant-ph9803049.txt |@word represent:2 partial:1 pointing:1 scl:2 forbidden:1 global:1 results:1 illustrated:1 xxxv:1 houches:1 go:2 zinn:1 whose:3 depend:1 catastrophe:10 paris:1 tail:1 critical:2 present:1 excluded:1 stable:2 anharmonic:3 hibbs:1 very:1 implicitly:1 choice:1 every:1 trough:1 ma:3 difference:1 exact:1 condition:2 leads:1 presented:1 ref:1 solution:6 large:1 catastrophes:5 small:1 optics:2 degeneracy:2 cosh:1 approximation:9 fold:1 second:6 castro:1 further:2 linear:1 appear:4 euclidean:1 sum:1 selected:1 expressed:1 tunnelings:2 aperiodic:1 above:1 new:15 3a:1 increasing:1 codimension:2 full:3 mω:6 never:1 here:3 identifications:1 olica:1 sinh:1 others:1 directions:1 path:21 along:8 extrema:7 equations:3 appears:1 change:3 referring:1 obtained:1 instituto:1 arrive:1 study:2 larger:1 allows:1 periodic:5 resulting:1 action:15 changes:3 useful:1 saunders:1 counts:1 linearly:1 readily:1 plot:2 use:4 takes:3 positive:1 morphogenesis:1 negative:7 classically:1 depicted:2 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