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quant-ph9902012.txt |@word represent:1 code:2 scl:1 ost:1 existing:2 four:2 entropy:14 computation:2 analogous:1 resources:1 orthogonal:2 difference:1 matrices:3 transmission:1 speculations:1 sign:2 zero:2 traveling:1 b131:1 dynamics:1 linear:1 even:1 what:2 abd:1 reconstruction:1 shared:1 outgoing:1 measurements:1 concepts:1 component:1 teleportation:3 here:4 objects:6 cerf:2 incoming:1 shift:2 amount:2 action:1 changes:1 composed:1 via:9 spatially:1 logical:3 boolean:3 rψ:1 unit:1 clifford:1 diagramm:1 use:2 feb:1 takes:1 working:1 codewords:1 positive:1 ψq:6 ψv:4 negative:3 few:1 nucl:1 a52:1 memory:2 encode:1 diagrams:5 more:3 separated:1 formally:1 conclusions:1 emission:1 disruption:1 interaction:2 known:1 work:3 labeled:1 minimum:1 values:1 sent:1 mr:2 spontaneous:1 example:1 give:1 process:1 bennett:4 states:11 anihilation:2 numbers:1 arise:1 information:47 superstrings:1 pure:2 ensemble:1 description:1 algebra:1 after:1 diagram:5 law:3 sq:47 register:2 cosmology:1 ψe:5 ones:1 so:5 correlation:3 representation:1 over:2 interpreted:1 stability:1 mathematicians:1 paper:1 through:1 mentioned:2 fidelity:1 still:1 perfect:1 group:1 ln:2 interesting:1 cryptology:1 degrees:1 choose:1 main:1 teleportations:1 symmetrization:1 combination:1 they:1 now:1 represents:1 dirac:5 2c:13 mean:1 spinor:1 ee:1 energy:2 idea:2 operator:3 measurement:1 quantum:45 operation:1 eq:4 shannon:2 ru:2 shown:1 matrix:6 space:7 since:2 rev:6 denotes:2 particles:1 contained:2 rm:1 rn:1 correct:1 log2:7 theory:3 pub:1 complicated:1 members:1 definition:2 pairs:1 backwards:2 recovering:1 created:1 geometry:2 could:1 computers:1 adjoint:2 first:1 initial:1 probability:1 coding:6 done:1 precisely:2 given:2 antiparticles:2 introduction:1 interact:1 system:2 relations:1 their:1 realization:1 bits:8 gives:2 appearence:1 representing:1 wiesner:1 double:1 second:1 project:1 amplitude:1 membranes:1 well:1 correction:3 weinfurter:1 any:1 ideas:1 analog:2 analogy:4 play:2 trace:1 shall:1 connected:2 pair:3 consequences:1 ebits:4 vertices:1 exp:1 physics:4 shor:2 think:1 show:2 supported:1 based:3 state:16 only:1 going:1 means:1 cannot:1 reversal:1 new:1 processes:4 podolsky:1 arxiv:1 bag:3 qe:4 contain:1 correlations:1 flip:2 see:3 packed:1 qubits:11 written:2 between:9 progress:1 preserve:1 barenco:1 initially:2 flow:3 ji:8 sleator:1 uncertainty:1 agree:1 connection:1 qubit:19 kets:1 asymptotically:1 dimensional:2 anti:7 moreover:1 described:4 transformations:1 basis:2 union:1 strategy:1 combined:2 ph:1 fig:7 corresponding:2 sufficient:1 noncommutative:1 ebit:4 maximally:2 case:1 p0:2 p1:2 single:1 value:2 error:13 characterizing:1 unitary:3 von:7 positrons:1 dual:3 interacts:1 grant:1 same:1 propensity:1 cbits:4 complex:1 quant:1 pauli:2 several:2 independent:2 used:1 moment:1 epr:4 without:1 sets:1 know:1 gates:1 proposed:1 being:3 rosen:1 vacuum:6 obtain:4 isolated:1 stored:1 transforms:1 previous:1 kluwer:1 density:7 lett:3 republic:1 iσ:1 transformation:1 quarks:4 possible:1 entangled:5 ρkl:4 using:2 bit:5 correcting:1 particle:4 follows:3 reduces:1 works:1 adami:2 because:1 old:1 neumann:7 classical:6 czech:2 conditional:6 some:3 mirror:2 transport:1 scale:1 opposite:2 equivalent:5 each:2 hilbert:5 about:3 actual:1 freedom:1 capable:2 o:1 plus:1 mixed:1 projectors:2 h2:4 readable:1 into:2 phase:2 references:1 einstein:1 elementary:6 methods:1 there:4 question:1 transform:1 start:1 conservation:4 physicists:1 way:1 was:2 creation:1 elsewhere:1 form:3 smolin:1 but:2 applying:2 characteristic:1 maximum:1 ur:1 problem:1 define:4 similar:1 called:3 ac:1 associated:1 computing:3 defined:2 qid:4 abstract:1 general:1 peres:1 conserved:2 praha:1 physical:4 codes:1 no:4 when:1 virtual:4 application:1 other:2 role:4 superdense:6 superposition:4 divincenzo:1 models:1 vertex:9 transported:2 meaning:1 important:1 variable:1 regime:1 required:1 holes:2 rule:1 mass:1 time:7 cleve:1 decoherence:3
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quant-ph9902013.txt |@word slope:1 partial:2 consider:5 rev:20 amplifier:25 results:4 exceeding:1 leads:4 eds:4 quadrature:1 francesco:1 schumaker:1 remarkably:1 issues:1 factorizing:1 devoted:1 whose:4 preserves:2 amplification:2 breached:1 paris:12 tr:2 ts:1 finally:2 squeezing:22 those:3 th:1 under:12 analogous:1 applied:1 tanh:1 amplitudes:2 consequently:1 orthogonal:2 very:3 frequencies:2 rise:1 wave:4 figs:1 a132:1 mixing:1 experimentally:2 difference:1 exact:15 condition:4 treating:1 splitter:13 squares:2 mollow:1 exits:1 hamiltonian:15 turns:2 trb:2 solution:1 large:1 min:2 small:1 eigenvalues:1 shows:1 optics:14 noted:1 zm:4 smaller:1 periodicity:1 sin4:2 direct:3 hillery:3 cosh:1 approximation:64 second:3 value:5 notwithstanding:1 dynamics:3 approached:1 bilinear:2 what:1 nonlinear:6 appear:1 brackets:1 giving:2 sum:4 consistently:1 3i:1 subspaces:4 3c:2 new:1 3a:1 increasing:1 method:3 ˆn:2 full:2 crouch:1 degree:4 respectively:3 even:3 here:3 diagonal:1 reported:2 them:1 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quant-ph9902014.txt |@word limited:1 code:4 partial:1 consider:5 results:3 entropy:3 denotes:1 issues:1 content:1 certainly:1 technique:4 send:4 under:1 insights:1 sent:2 case:2 very:3 rise:1 conditions:1 wave:1 manipulated:1 every:1 experimentally:1 condition:1 internally:3 presented:2 turns:1 michael:1 solution:1 large:1 admissible:6 vector:1 generalize:1 noted:1 upper:2 sign:4 approximation:1 second:6 cost:1 perspective:1 further:3 copenhagen:1 linear:1 what:4 appear:1 apparatus:2 deeply:1 specification:1 uniform:2 steiner:1 experiment:13 above:2 new:5 method:6 convergences:1 teleportation:9 here:2 desired:1 fairly:1 others:3 ratio:1 equations:1 appears:5 change:1 obtained:3 sending:1 naval:1 larger:2 allows:1 completely:1 prior:1 amount:26 opinion:1 adopting:1 studies:1 pearle:1 composed:1 emerge:2 via:2 useful:3 hardy:1 addressed:2 stern:2 causal:1 fbm:1 use:3 feb:1 would:7 positive:1 continuous:5 predictions:2 classically:3 opposed:1 type:4 percival:1 more:4 yes:1 formally:1 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quant-ph9902015.txt |@word limited:1 dynamic:40 consiste:1 consists:1 whose:1 paris:10 processus:5 under:2 characterised:2 rise:1 réelle:2 every:2 experimentally:1 voir:1 internally:5 selfconsistently:2 solution:38 vector:2 unifying:1 force:1 decoherent:1 loi:1 consistent:7 direct:3 10e:1 feasibility:1 second:2 qualitatively:5 estimated:1 even:5 incompatible:9 neg:4 exactly:1 selected:2 above:17 new:8 increasing:1 ever:5 consisting:3 notions:2 fiz:1 never:4 here:5 atoms:1 refinement:1 represented:5 auxiliary:5 contraction:1 obtained:22 balance:1 rigorously:4 completely:7 permit:1 prints:1 instr:1 explained:1 arborescence:2 highly:7 élémentaire:3 total:4 unit:1 tels:1 quasi:3 would:4 delocalised:2 occupying:1 interlace:1 call:3 therefore:11 type:5 separated:2 nauka:1 supporters:1 solitons:1 correspondingly:3 transiently:3 hole:1 εn0:1 complexité:1 permits:2 theories:1 deficiencies:1 exceptions:1 give:1 degenerate:1 keep:1 absolute:1 dürr:1 jusqu:1 provide:3 feature:1 nontrivial:1 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quant-ph9902020.txt |@word limited:1 consider:2 lack:2 focus:1 commute:1 computation:2 consists:1 whose:1 depend:1 orthonormalized:1 quasi:2 manifolds:3 stochastic:1 presently:1 p0j:8 rise:3 springer:4 results:2 cellular:1 halting:1 hamiltonian:1 turns:1 notes:1 large:5 discrete:4 vector:5 small:1 eigenvalues:1 mahler:3 zm:11 findings:1 deutsch:2 sign:1 irreducibility:1 dynamics:9 functioning:1 odd:5 machines:2 even:9 nonlinear:1 plays:1 appear:1 iterating:1 sum:2 mechanics:1 find:1 current:1 version:1 new:6 ˆn:1 y2:2 full:3 respectively:2 here:2 disastrous:1 operating:1 address:1 z4:2 along:3 respect:1 appears:2 z2:2 z3:2 vectors:1 allows:1 amount:1 periodic:10 resulting:2 usually:1 fourier:1 changes:1 composed:2 emerge:1 scales:1 requiring:1 marked:1 highly:1 apply:1 total:3 circumvent:1 feb:1 superpositions:2 would:2 remains:1 contains:1 pˆij:1 few:1 automata:1 therefore:1 ψm:5 taken:1 generators:1 type:1 introducing:1 becomes:2 operators:2 apparent:1 berlin:1 correspondingly:1 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quant-ph9902021.txt |@word externally:1 consider:3 rev:20 results:4 menon:2 leads:2 jawaharlal:1 entropy:1 follow:1 calculate:1 iii:2 technique:1 tr:4 rf:1 γt:1 finally:2 behave:1 th:1 under:2 include:1 applied:1 amplitudes:1 orthogonal:1 very:3 frequencies:3 rise:6 differently:1 resonant:1 experimentally:1 difference:2 matrices:1 condition:3 discovered:1 europhys:1 incoherent:2 level:5 knight:2 integrating:2 t2:12 t1:10 solid:3 vector:1 optics:1 configurations:1 aβα:1 smaller:1 oscillation:4 consistent:1 hillery:1 approximation:2 second:3 may:1 manipulating:1 quite:1 scientific:1 even:3 what:1 appear:1 sum:2 near:4 agrees:1 experiment:1 above:3 method:2 coefficient:1 lee:2 ibid:1 respectively:4 never:1 modify:1 here:7 plenio:2 inversion:2 address:1 concluding:1 19d:2 along:2 sine:3 equations:3 appears:2 19c:1 19b:2 obtained:1 suitably:1 aks:5 study:5 studied:2 periodic:1 published:1 resonance:1 studies:1 cancellation:2 plotted:1 uniquely:1 vic:33 via:1 useful:1 scaled:1 modulated:7 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quant-ph9902022.txt |@word consider:7 results:1 grateful:1 bvd:1 consists:1 research:1 compact:4 whose:2 iii:1 tr:3 those:1 th:1 under:7 characterised:1 ra:2 applied:1 conjecture:1 kent:1 straightforward:1 orthogonal:1 far:2 manipulated:1 mixing:2 difference:1 matrices:8 condition:1 tra:1 trb:1 solution:1 sǫ:3 vector:1 annihilates:1 small:2 eigenvalues:5 noted:1 upper:1 computation:1 sign:1 zero:24 street:1 enhancement:1 further:1 scientific:1 even:1 established:1 what:1 filtration:1 invertible:5 expressed:1 new:2 increasing:1 consisting:1 respectively:1 never:1 teleportation:1 here:5 favourable:1 them:2 ratio:1 equations:2 obtained:6 sending:1 institute:1 leaves:1 schumacher:2 action:1 bob:18 suitable:2 uniquely:2 appropriately:1 tasks:1 outcomes:1 brought:3 decrease:2 use:2 takes:2 would:2 massar:1 positive:7 ψi:5 call:1 therefore:1 taken:1 exhaustive:1 theoretical:1 more:1 separated:2 bennett:3 distillation:1 operators:3 factor:3 carrying:3 everywhere:1 particular:1 known:2 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quant-ph9902023.txt |@word concept:3 customary:1 consider:3 global:1 desirable:1 splitting:17 leads:3 scalar:1 generalize:3 shimony:1 consists:1 calculate:1 aug:1 equivalence:1 tr:1 finally:1 does:6 swap:1 under:3 concurrences:2 sent:1 straightforward:1 far:1 2re:2 swallows:1 results:3 wavy:1 every:2 matrices:1 condition:2 splits:1 illustrated:1 swapping:1 presented:1 turns:2 brother:2 fewer:1 vector:2 splitted:2 small:2 eigenvalues:4 ups:1 upper:3 abbreviated:1 employing:1 deutsch:1 direct:1 hillery:4 zero:3 design:1 qualitatively:1 machines:1 subscripts:1 established:1 what:2 giving:1 section:1 3n:1 above:5 shared:1 learned:1 increasing:2 preserved:1 contrast:1 degree:2 exchange:2 fmax:1 applies:1 teleportation:16 here:3 asymmetry:1 plenio:2 others:1 along:1 appears:1 violate:1 cerf:1 study:2 studied:2 allows:1 completely:1 ab1:1 amount:3 resulting:6 procedure:1 schumacher:1 action:2 bob:31 fulfill:2 buˇzek:4 vii:3 outcomes:1 addressed:1 apply:2 total:3 bra:1 use:3 would:4 massar:1 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quant-ph9902024.txt |@word partial:1 chain:3 rev:6 results:5 commute:1 entropy:1 computation:1 consists:1 row:3 relationships:1 whose:1 const:2 calculate:2 irrelevant:1 environment:11 finally:1 those:1 under:1 include:1 dramatically:1 case:9 performs:1 orthogonal:1 geometrical:1 common:1 randomness:3 incoherent:1 presented:1 turns:1 notes:1 large:2 discrete:2 vector:4 subscript:1 indices:4 mahler:5 upper:1 y0:1 version:1 deutsch:2 trend:1 zc:3 zero:1 dynamics:5 odd:4 even:6 appear:1 iterating:1 incompatible:1 specification:1 selected:1 networks:1 sequential:1 obvious:2 acknowledgments:1 quenched:1 full:3 respectively:1 component:1 equals:1 here:7 selective:1 along:2 strong:1 observing:1 z1:5 change:1 4p:1 vectors:2 spheres:1 periodic:6 resulting:4 usually:1 changes:1 composed:1 via:1 followed:1 visible:1 total:1 conventional:1 feb:1 superpositions:3 would:2 remains:2 quasi:1 hilbert:1 few:1 noting:1 call:1 opposed:1 m2:5 type:8 composite:3 becomes:1 operators:4 apparent:3 berlin:1 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quant-ph9902025.txt |@word transitions:1 consider:1 chain:1 magnetic:2 results:9 projected:1 illustrated:1 comments:1 computation:2 consists:1 partial:1 primes:1 certainly:1 referring:1 auckland:3 subjected:3 technique:1 including:1 environment:4 finally:1 those:2 under:1 stochastic:1 include:1 dramatically:2 fishman:1 case:1 far:1 keeping:1 wave:4 every:1 figs:1 resonant:3 affect:1 difference:1 entire:1 caesium:3 modulator:1 hamiltonian:10 fewer:1 large:3 mm:2 small:4 optics:4 upper:2 smaller:2 consistent:1 prediction:3 pulse:13 zero:1 displays:4 further:1 dynamics:2 chem:1 even:1 wyatt:1 ccd:1 trapping:2 rate:5 brackets:1 giving:1 section:5 slight:1 contributed:1 while:4 find:1 cell:1 experiment:10 above:2 pristine:2 new:2 increasing:1 movement:4 agreement:1 kicked:16 escaping:3 respectively:3 atoms:25 asymmetry:1 focused:1 others:1 2kl:3 along:3 strong:1 observing:2 appears:2 search:1 noticeable:4 dotdashed:1 study:5 studied:2 meiss:1 completely:1 marsden:1 leaving:1 amount:1 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quant-ph9902026.txt |@word stressed:2 consider:1 springer:2 meson:1 rev:9 magnetic:2 global:2 results:7 unchanged:1 existing:1 four:1 facilities:1 mild:1 entropy:4 computation:1 transversally:1 go:1 expressions:2 contributions:1 gr:1 whose:2 certainly:2 tr:1 m2n:1 γt:4 environment:5 finally:3 device:1 those:8 determinations:1 under:4 presentation:1 eikonal:1 applied:2 outside:1 very:8 rise:2 keeping:2 splitting:3 putting:1 summarized:1 experimentally:2 difference:1 matrices:2 condition:5 sc2:1 treating:1 entire:1 hamiltonian:4 turns:2 notes:1 having:2 solution:2 large:2 vector:1 min:3 splitted:2 small:4 eigenvalues:2 alicki:2 optics:9 equation:9 inserting:1 smaller:3 consistent:1 estimates:11 direct:3 literature:1 approximation:1 neglect:1 pass:1 further:7 dynamics:10 estimated:2 theory:3 even:1 index:1 errors:2 apparatus:2 giving:1 interactions:1 experiment:6 vacchini:1 values:7 ghirardi:1 contrast:7 mp:2 evolving:1 meth:1 ibid:1 men:1 modify:3 residual:1 behaviour:2 represented:1 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quant-ph9902027.txt |@word consider:3 rev:2 forbidden:2 global:2 results:1 monti:2 computation:8 go:1 simon:6 producing:1 deterministic:3 program:7 th:3 under:1 insights:1 case:2 random:4 induce:1 wave:8 solves:1 solver:2 altering:1 solution:4 solved:1 small:1 originally:1 deutsch:9 dealing:1 sign:1 likely:1 port:1 substitute:1 even:8 foregoing:1 current:2 version:1 goes:1 new:1 contrast:2 satisfy:1 here:2 behaviour:2 desired:1 represented:8 change:2 box:2 substance:1 involved:1 leaves:3 allows:1 action:1 adopting:1 sticking:1 useful:1 inducing:1 brought:1 boolean:1 readily:3 feb:1 takes:1 working:1 remains:3 tightly:1 qcc:1 call:3 therefore:1 selects:2 more:2 zeroes:1 introducing:2 knows:2 started:1 becomes:2 corrected:1 berlin:1 department:1 known:4 iii:1 must:2 states:1 springer:1 room:1 science:1 challenge:1 work:3 modified:1 grover:6 following:1 example:1 something:1 f0:1 process:1 choice:4 sense:1 purposes:1 cation:1 performed:4 sharp:3 spa:1 information:1 divided:1 feature:3 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quant-ph9902028.txt |@word gw:3 secondly:1 concept:1 consider:8 remarkable:1 rev:3 magnetic:3 particular:1 brownian:3 results:2 four:5 known:16 scalar:1 gc:1 coincidence:2 go:1 follow:5 gm:4 ptp:1 supposedly:1 dimensionality:1 gaeta:1 contained:1 spirit:1 charge:8 equate:1 weyl:1 th:2 under:1 stochastic:9 include:1 indicating:1 prigogine:4 sorkin:1 applied:1 expressing:1 very:3 rise:1 induce:1 wave:1 bjorken:1 electron:11 got:1 difference:1 matrices:1 encounter:3 leads:6 quantized:6 bring:2 did:1 issue:1 list:1 applicable:1 large:7 discrete:7 coincidences:5 dealt:1 small:2 typified:2 noted:7 inconsistent:1 smaller:1 books:1 consistent:6 literature:2 sign:1 approximation:2 bergmann:1 zero:3 narlikar:2 perspective:2 gn:1 further:7 linear:2 even:2 reconciliation:1 what:3 plays:1 sub:1 rd3:1 section:4 mw:2 adhoc:2 wolfe:1 consistently:1 coles:1 above:15 fractional:3 new:7 net:1 ever:2 consisting:1 contrast:1 annalen:1 full:2 lee:4 component:2 here:1 behaviour:3 inverse:1 decay:1 others:2 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quant-ph9902029.txt |@word 2nπ:3 consider:1 rev:13 magnetic:2 varying:1 results:4 leads:1 generalize:2 controversial:1 obtaining:1 expressions:1 centers:1 localized:1 whose:2 certainly:1 depend:1 calculate:2 tr:3 acting:1 γt:2 environment:7 finally:1 tm:1 preserved:1 under:7 stochastic:1 td:1 discontinuously:1 applied:3 supported:1 straightforward:1 kτ:1 very:9 frequencies:2 connects:1 wigner:1 choice:3 electron:1 summarized:1 redefinition:1 experimentally:1 difference:15 condition:7 randomness:1 exponential:1 level:4 bonifacio:3 unusual:1 solution:4 damped:5 large:3 discrete:1 zeh:1 nmr:1 small:10 shows:2 round:1 degeneracy:1 upper:3 work:5 grateful:1 oscillation:2 regained:1 request:1 jump:1 rate:13 larmor:1 traveling:1 further:1 ρn:4 even:2 index:1 what:1 nonlinear:1 developed:1 appear:4 apparatus:5 completely:1 giving:1 diffusing:1 waiting:4 version:1 goes:6 scientists:1 new:4 jumps:1 contrast:1 paradoxical:1 pioneering:1 degree:1 respectively:1 fock:2 modify:1 here:7 fisica:1 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quant-ph9902030.txt |@word represent:2 since:8 partial:1 consider:6 springer:2 similarity:4 crucial:2 lack:1 amplifier:2 results:13 deteriorating:1 illustrated:1 eds:1 quadrature:28 delays:1 per:1 houches:1 rahmen:1 go:1 schumaker:1 amplified:1 research:1 ˆb2:5 gr:1 looking:3 certainly:1 γx:4 overlapping:2 violate:1 arthurs:3 respectively:1 pˆk:1 γp:4 disability:1 participants:1 shall:2 expressing:1 finally:2 efficiencies:1 squeezing:49 present:3 under:1 analogous:4 large:5 swap:2 sent:7 ingredient:1 p2:2 labels:1 amplitudes:16 performs:2 orthogonal:1 far:2 frequencies:13 2re:4 administered:1 fav:14 relatively:1 wave:4 manipulated:1 every:9 sidebands:1 mixing:2 experimentally:1 grant:1 electronics:1 condition:3 common:1 milburn:1 splitter:10 school:1 swapping:39 presented:5 did:4 ref:18 atr:1 proposals:1 pˆ1:11 discrete:4 pˆ3:2 bangor:1 phase:8 pˆ4:3 subscript:2 small:2 darpa:1 singlemode:1 optics:4 round:1 upper:1 smaller:4 tel:19 coefficient:1 measurable:2 pulse:3 cosh:8 threshold:2 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quant-ph9902032.txt |@word represent:6 monte:1 partial:1 consider:5 particular:3 results:11 osi:2 overlap:1 grateful:1 go:1 faster:1 gk:4 depend:2 calculate:2 auckland:3 tr:1 tm:34 tj:8 those:1 stochastic:1 γa:1 labels:3 orthogonal:2 very:2 ρc:2 wave:3 electron:1 sons:1 every:1 jack:2 fall:1 treating:3 four:2 incoherent:1 presented:2 notes:1 t0:17 viable:1 large:1 discrete:5 small:1 markov:3 optics:2 upper:1 averaged:1 lewenstein:1 oscillation:1 consistent:1 strunz:1 approximation:3 surrounding:1 rate:3 perspective:4 dynamics:2 carlo:1 click:2 imamo:1 brackets:1 section:1 waiting:2 version:1 above:5 new:7 increasing:1 σf2:1 method:12 contrast:1 σf1:3 edited:2 full:1 concepts:1 here:3 atoms:4 asymmetry:1 possibility:1 represented:1 equations:2 change:2 referring:1 parameters:2 burstein:1 yablonovitch:1 larger:1 experience:1 tσi:1 usually:1 fourier:2 makes:1 glu:1 plotted:4 useful:1 castin:2 compare:1 private:1 outcomes:1 summation:2 total:1 research:1 plot:1 feb:1 proceed:1 commun:1 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quant-ph9902033.txt |@word partial:3 consider:5 springer:1 2b:2 reversibility:1 results:3 leads:1 entropy:3 grateful:1 consists:1 incommensurable:1 contributions:1 whose:1 depend:1 remarkable:1 concerned:1 equivalence:1 nonlocal:1 answered:1 finally:2 present:5 th:1 under:2 circumstances:1 resources:9 ingredient:1 applied:2 departament:1 straightforward:1 far:4 none:1 fan:1 swapping:1 presented:3 tra:1 knight:2 large:3 anna:1 eigenvalues:1 shows:2 upper:3 smaller:1 lewenstein:2 βl0:1 second:1 mk:1 implemented:1 even:1 aim:1 what:3 stands:1 sum:1 gether:1 version:1 above:1 shared:7 ˆj:1 increasing:2 here:7 strategies:2 teaches:1 ensembles:1 obtained:3 convert:3 involved:2 study:4 allows:1 contradiction:2 accomplished:2 bennett:2 schumacher:1 hospitality:1 bob:4 uniquely:1 tasks:1 addresses:1 family:1 outcomes:1 achievable:1 support:1 use:2 additive:2 asymptotic:5 would:7 remains:1 positive:3 estructura:1 ψj:4 classically:2 call:2 therefore:4 m2:1 taken:1 achieving:1 more:6 introducing:1 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quant-ph9902034.txt |@word represent:1 stressed:1 consider:3 penrose:2 similarity:1 magnetic:4 varying:1 destroyed:1 results:4 ds:2 leads:1 weinberg:1 scalar:3 supplement:4 rebbi:1 parameterization:1 consists:1 follow:1 expressions:4 spacetime:1 gi:1 factorizing:1 relationships:1 certainly:2 referring:2 concerned:1 vs:9 ts:2 passage:1 charge:8 unpleasant:1 tj:1 arisen:1 face:1 ti:4 analogous:2 eβ:4 worth:1 necessary:1 ta:3 potentially:1 belonging:1 g4:11 amplitudes:1 g2:11 straightforward:2 iǫt:13 pages:2 reader:1 misunderstanding:1 wave:34 iφ:17 corollary:1 valued:2 putting:1 trough:1 allowed:3 mixing:1 affect:3 varshalovich:1 matrices:3 condition:11 wrs:1 squares:1 tekin:1 immediately:1 hamiltonian:3 turns:1 gibbs:3 t2:5 solution:2 t0:31 t1:5 try:1 discrete:11 convenience:2 vector:9 yong:1 demonstrated:1 uller:1 ǫj:3 relation:8 referred:2 noted:3 harish:1 possibility:3 limitations:2 employing:1 tem:1 10b:1 10c:1 consistent:2 10a:1 sin2:5 direct:1 13a:1 sign:2 translating:1 itself:8 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quant-ph9902035.txt |@word aguilera:1 represent:1 externally:1 consider:5 varying:1 leads:7 constants:1 follow:1 soc:1 relationships:1 whose:4 inverse:2 equivalence:1 acting:1 environment:73 finally:4 under:3 stochastic:1 analogous:1 must:3 norm:1 case:10 jensen:2 very:2 frequencies:1 rise:1 wave:1 em:8 continued:1 condition:7 treating:1 illustrated:2 34a:2 34b:2 hamiltonian:10 pacs:1 solution:3 occurs:1 large:8 convenience:1 vector:2 small:4 gauge:1 originally:1 configurations:1 inserting:1 consistent:1 approximation:10 second:2 evaluated:1 notwithstanding:1 further:3 ter:1 canonical:1 even:2 established:1 what:4 contained:1 clock:4 section:5 expressed:1 version:1 values:3 appeal:1 method:7 satisfy:3 full:2 led:1 degree:1 exchange:1 respectively:1 component:1 here:7 canonically:1 asymmetry:6 ansatz:2 separate:2 making:1 alone:5 consideration:1 along:2 equations:5 appears:4 separation:1 generalizing:1 institute:1 study:1 vectors:1 approaches:1 experience:1 dri:3 action:1 fourier:3 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quant-ph9902036.txt |@word epeau:1 partial:5 rev:1 keep:1 lack:1 four:3 tripartite:1 pkq:1 generalize:1 edu:1 follow:1 bank:2 whose:1 certainly:1 paris:1 equivalence:7 nonlocal:1 thapliyal:2 critical:1 those:1 whatsoever:1 under:16 analogous:2 norm:2 applied:1 global:1 string:1 orthogonal:15 very:3 none:1 me:1 corollary:2 every:2 should:4 telling:1 trouble:1 difference:2 matrices:31 common:1 tri:3 induced:1 michael:1 fewer:1 encoding:3 succession:1 manifestly:1 eigenvalues:15 caltech:1 prevent:2 des:1 sin2:2 second:5 bitstring:1 further:1 canonical:1 even:4 what:3 sub:5 section:6 shares:2 decoding:1 3k:2 above:4 ilm:1 shared:5 method:1 coefficient:1 full:3 degree:3 ρab:1 respectively:2 here:4 diagonal:3 5dimensional:1 ei:1 cos2:2 berkeley:2 alone:6 mayers:1 change:2 obtained:7 generalizing:1 institute:2 involved:1 leaves:1 changed:4 allows:1 leaving:1 suggests:1 amount:1 resulting:1 pick:1 action:7 hospitality:1 bob:18 makes:1 via:11 divide:2 va:8 julia:1 outcomes:4 send:1 langlois:1 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quant-ph9902037.txt |@word consider:4 crucial:1 lack:1 rˆ:1 fig1:5 go:1 contributions:1 row:8 whose:1 depend:3 finally:1 th:1 under:3 interchange:2 conjecture:1 global:1 very:3 wave:9 electron:10 stays:1 difference:1 condition:2 xiaodong:1 positions:3 t2:4 solution:7 t0:1 t1:5 try:1 vector:2 small:1 gauge:2 force:2 zi:3 edu:1 direct:1 sign:2 past:1 pass:1 chen:1 further:2 rough:1 even:4 what:5 apparatus:7 clock:4 experiment:1 goes:1 new:3 method:4 satisfy:2 interrupting:1 component:1 equals:1 here:6 free:9 sinh:17 address:1 path:6 along:1 strong:1 equations:1 z1:6 interpret:2 extreme:1 obtained:1 cern:1 spacial:3 vectors:1 cambrige:1 weird:1 changes:3 projection:2 1st:2 total:3 univ:1 causal:1 unit:1 aitchison:1 use:2 feb:1 found:1 positive:4 bundles:1 negative:7 call:1 more:9 becomes:4 everywhere:1 particular:4 known:2 cases:2 iii:2 valued:1 word:3 equation:12 work:1 mv:1 concepts:2 meet:1 spontaneous:1 example:1 history:1 control:1 compare:2 omit:1 give:1 calculation:1 sphere:6 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quant-ph9902049.txt |@word monte:1 concept:1 trigonometric:1 four:1 consists:6 query:2 certainly:2 graph:3 tween:1 helps:1 bqp:1 include:1 resources:1 p2:2 evolves:1 very:1 choice:1 me:1 corollary:1 every:4 telling:1 exact:6 t6:1 turns:3 solution:1 t0:12 occurs:2 try:1 solved:1 vector:2 harry:1 small:2 upper:1 smaller:4 says:1 sin2:3 approximation:1 elegant:1 second:9 cost:1 carlo:1 even:1 what:2 richard:1 sum:1 uniform:4 version:3 above:5 method:1 told:1 never:1 modify:1 here:4 change:4 box:8 search:4 larger:2 allows:2 accomplished:1 extremes:1 usually:1 makes:1 involves:1 merely:1 marked:38 summation:1 apply:2 total:2 plot:3 use:7 feb:1 superpositions:1 would:1 remains:2 positive:1 give:4 next:2 few:2 ψn:1 taken:1 type:1 more:7 becomes:3 basically:1 particular:3 known:8 cases:1 logarithm:1 states:7 equation:1 work:1 modified:2 grover:32 values:2 following:5 elegantly:1 my:2 attain:1 unmarked:2 stated:2 calculation:1 purposes:1 involve:1 minimum:7 numbers:2 want:3 allowed:2 unphysical:1 tolerant:2 absolute:2 end:1 rather:1 means:1 algorithms:1 write:2 how:1 fourth:1 answer:2 optimal:7 sin:8 inputs:5 transforming:1 after:3 variant:2 different:1 ronald:1 applications:1 third:4 neglect:1 fortunately:2 so:8 allow:3 worst:7 order:6 over:5 course:2 paper:2 wolf:1 still:3 its:1 before:1 thank:1 ln:5 actually:7 better:2 choose:4 maximal:3 good:1 matches:1 propose:1 evolution:1 symposium:1 rotation:2 now:4 easily:2 february:1 several:1 each:7 2l:1 repeating:1 mean:1 ei:1 series:1 reduce:1 quantum:10 our:2 happen:1 out:5 shown:1 rp:1 increase:3 may:1 adjust:1 performs:1 gov:1 correct:3 shows:3 theory:1 guess:1 standard:1 imagine:1 remainder:1 finite:1 care:1 could:1 computers:1 times:3 exponentially:1 facilitate:1 think:1 first:10 there:4 probability:22 2kθ:2 number:42 reaches:1 clear:1 done:1 thick:1 zalka:3 given:6 introduction:1 unknown:2 least:1 calculations:1 especially:1 gives:7 hoyer:1 derandomization:1 exactly:1 part:11 than:6 coefficients:1 serv:1 detection:1 subroutine:6 unfortunately:1 iteration:2 zero:1 amplitude:8 anyways:1 argument:2 say:2 2t0:3 need:2 element:8 clearly:2 angle:2 rotations:1 able:1 note:6 high:1 take:1 finding:3 performance:2 most:3 significant:1 phase:6 probabilistic:1 why:1 don:5 takes:1 average:1 proceedings:1 mechanical:1 typically:1 random:8 speedup:1 find:7 based:1 proposed:1 implementation:1 explain:1 enough:1 only:8 black:8 factor:3 local:5 achieve:2 continuity:1 do:1 goes:1 get:7 de:1 probably:1 stoc:1 acm:1 runs:4 querying:1 arxiv:1 consisting:1 nθ:5 qc:1 queries:18 fixed:1 fault:3 set:2 reference:1 bounds:1 relative:2 see:7 computer:1 result:1 close:1 optimum:1 techniques:1 ways:1 subsequent:1 review:1 state:7 various:1 between:1 theta:1 geometric:1 tolerance:1 checks:1 terms:1 qubits:1 improve:1 cos:4 improved:2 many:5 annual:1 equal:1 ch:1 point:1 simple:4 asymptotically:2 corresponds:2 cx:2 simply:1 iterations:11 ct:1 described:1 basis:1 been:1 interest:1 ph:4 pi:1 universal:1 obtained:1 buhrman:1 essentially:1 last:4 careful:1 case:7 p1:2 look:1 exponential:1 solid:1 value:2 will:6 while:4 error:13 ve:1 thus:10 worry:1 containing:1 perform:1 make:1 amount:2 same:1 any:6 parts:3 quant:4 modification:1 gets:1 difficult:1 used:2 hand:3 running:2 uses:2 recent:1 prescribed:1 lower:2 task:1 database:1 well:1 analysis:1 obviously:1 academic:1 without:1 exponentials:1 gates:3 just:4 rotated:1 candidate:1 guaranteed:1 except:1 improvement:2 add:1 easy:6 input:4 real:2 checking:2 possible:3 possibly:1 increases:1 know:2 using:3 bit:2 rotate:1 necessary:1 like:1 success:4 admittedly:1 yields:1 either:1 multiplicative:2 output:1 works:2 reduced:3 because:2 classical:3 some:8 searching:2 choosing:1 specified:1 peter:1 wrongly:1 provided:1 avoid:1 steps:8 run:6 slight:1 step:4 hadamard:1 approximating:1 simpler:1 about:13 actual:2 certainty:1 o:1 page:1 practical:1 range:9 plus:1 greatly:2 2k:1 previously:1 into:1 integral:1 bound:3 remarks:1 appropriate:1 right:1 references:1 determine:2 additional:1 classically:2 initial:4 approximate:1 fast:1 pages:1 quadratic:1 way:1 call:2 function:3 form:1 but:7 back:1 failure:1 hl:2 line:1 true:1 observation:1 applying:1 assessment:1 maximum:2 us:7 below:5 limit:1 problem:6 called:1 constant:3 28th:1 computing:1 abstract:1 doesn:1 general:1 reliability:2 check:2 constructed:2 again:1 functions:1 dotted:1 no:4 dashed:1 whereas:1 when:6 other:5 outputs:1 really:2 christof:1 elements:28 superposition:4 sided:1 uniformly:3 precision:1 cleve:1 algorithm:45 invest:1 lanl:1 time:1 oracle:1 once:1
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quant-ph9902050.txt |@word four:1 entropy:12 consists:4 localized:2 const:1 calculate:2 presents:2 matlab:1 under:2 worth:1 conjecture:8 pinch:1 solution:1 convenience:1 vector:19 indices:1 vincenzo:2 approximation:1 likely:2 estimated:1 even:3 errors:1 liberty:1 above:9 new:2 equals:4 here:4 reported:2 plenio:5 represented:4 interpret:1 violate:1 obtained:31 study:5 changed:1 characterizing:3 changes:4 projection:1 highly:1 brought:1 total:5 plot:3 would:2 jozsa:1 negative:6 noting:1 therefore:9 until:2 composite:3 naive:1 decomposed:1 berlin:1 dirichlet:5 equilateral:1 word:1 work:8 example:3 impose:1 give:1 bennett:2 organized:1 effort:1 caution:1 degenerate:1 provide:2 verify:3 how:8 answer:4 field:1 efficient:4 description:2 after:1 lay:2 effects:1 attempt:1 appreciate:1 differ:1 algorithms:1 decreasing:2 order:6 operations:1 interpretation:4 diagonalizes:1 over:9 diagonalized:1 fix:1 exhibits:1 better:1 fig:25 schmidt:1 versus:4 eventually:1 them:5 often:1 they:6 represents:3 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quant-ph9902051.txt |@word represent:1 partial:4 consider:6 results:5 gx:5 leads:1 follow:2 expressions:3 contributions:2 reasoning:1 whose:5 hold:1 calculate:7 technique:1 tp:4 demonstrate:1 tn:42 finally:5 tm:6 tj:1 present:1 ti:1 connecting:1 analogous:2 tb:261 indicating:1 ta:241 case:3 supported:1 amplitudes:3 g2:5 advantage:1 rise:2 summarized:1 matrices:2 four:3 obvious:2 solves:2 hamiltonian:7 positions:1 michael:1 solution:7 t1:200 solved:1 small:1 eigenvalues:1 lines:1 dcn:1 des:1 deutschen:1 det:13 arnimallee:1 jump:1 zero:1 value:11 gn:1 further:1 odd:5 substitute:1 theory:7 spectral:1 index:1 nonlinear:3 appear:1 advantageous:1 g21:1 giving:3 section:9 expressed:5 current:13 version:1 axel:1 above:1 new:3 consisting:1 satisfy:2 κm:5 full:3 respectively:8 even:8 here:2 desired:2 explore:1 inverse:1 smearing:9 others:1 represented:1 path:24 along:1 quite:1 equations:1 appears:1 contraction:3 obtained:3 remark:2 generalizing:2 parameters:1 involved:2 study:1 vectors:1 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quant-ph9902052.txt |@word consider:1 show:1 relation:1 consists:1 landau:1 eigenstates:2 before:1 density:1 state:7 mail:1 consideration:1 into:2 correspondence:1 eigenfunction:2 watching:1 far:1 period:1 ϕi:2 ϕk:2 ϕj:2 during:1 now:1 eigenvalue:1 february:1 particle:11 podolsky:3 always:2 university:1 arxiv:1 joined:1 large:2 discrete:1 steps:2 arbitrary:1 found:1 successively:1 classical:1 observes:2 some:3 born:1 see:2 result:4 measurement:10 quantum:6 our:1 special:1 shown:1 describing:1 matrix:1 nondegenerate:1 review:1 since:2 definite:1 current:1 enough:1 experiment:2 above:2 lifshitz:2 replaced:1 gov:1 consisting:1 measuring:9 after:3 behavior:1 initially:1 gedanken:3 here:2 step:3 references:1 address:1 described:1 appears:3 observer:3 ukraine:1 observable:2 interaction:1 changed:1 equal:1 minds:1 assure:1 place:1 devices:3 whole:2 waited:1 probability:1 wave:7 number:1 simply:1 einstein:3 elementary:2 defined:1 feb:1 takes:1 usa:1 ψk:2 make:1 there:1 subdivide:2 system:6 been:1 ai:2 ψi:4 therefore:1 ph:1 ψa:2 theoretical:1 function:6 chapter:1 corresponding:1 definition:1 becomes:1 moscow:1 but:1 correspondingly:1 particular:1 russian:1 bypassing:1 springer:1 kharkov:2 cij:1 setup:1 second:2 us:1 assume:1 below:1 values:1 ms:1 sum:1 stages:1 distance:1 mechanics:3 nauka:1 process:3 well:1 abstract:1 topic:1 arrangements:1 need:1 any:2 verlag:1 functions:1 paradox:9 no:1 divided:1 means:2 rosen:3 how:1 parts:1 quant:1 take:1 department:1 pacs:1 may:1 measures:4 meaning:1 value:1 away:1 device:17 fi:2 konstantin:1 b258:1 considered:2 lanl:2 epr:7 observe:1 time:1 observables:1 physics:1 order:1
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quant-ph9902053.txt |@word represent:1 consider:7 results:3 computation:4 edu:1 consists:2 query:9 depend:1 tv:3 graph:1 tu:1 ts:1 tm:1 norm:2 division:1 very:2 splitting:2 vertex:1 corollary:1 every:2 should:1 rm:2 difference:2 beginning:3 progression:1 notes:2 list:8 try:1 vector:2 small:1 upper:1 smaller:3 lecture:2 second:6 insertion:2 hybrids:1 10q:1 substitute:1 index:1 giving:1 section:1 access:1 sequential:1 new:2 method:1 respectively:1 modify:1 berkeley:3 represented:1 observing:1 change:1 search:20 technical:1 inspired:1 allows:1 derandomization:1 resulting:1 published:1 studies:1 examining:2 technique:1 useful:2 projection:2 replace:1 decrease:1 littlestone:1 total:2 use:4 feb:1 superpositions:10 would:1 prove:2 probabilities:3 ψs:8 next:8 ψj:6 classically:3 ψi:53 therefore:6 until:1 optimizing:1 becomes:1 known:2 must:5 valued:1 science:5 focs:1 grover:7 splittings:1 following:2 example:1 proof:15 claim:5 give:1 process:1 beals:1 bennett:1 purposes:1 pieces:3 states:3 collision:2 acm:1 counting:1 unordered:3 guarantee:1 information:1 needs:4 end:4 recursive:1 buhrman:4 s1:4 get:2 how:2 speeding:1 answer:4 instead:1 brassard:3 inputs:9 may:1 after:2 ronald:2 xlm:17 lemmas:1 correspond:1 st:3 rather:1 complexity:2 so:2 decreasing:1 putting:1 ith:2 interpreted:1 paper:4 still:1 its:2 before:2 xl:2 subinterval:1 maps:1 lm:8 decreases:2 better:1 mail:1 main:2 them:4 return:1 greater:1 introduce:1 hamilton:2 optimal:1 now:1 easily:1 term:3 several:1 solves:1 university:1 inequality:2 l2:1 each:5 2m:1 goldstone:5 weighted:5 farhi:5 doing:2 idea:1 related:1 measurement:2 quantum:38 our:8 happen:1 out:1 shown:4 space:2 fellowship:1 suggesting:1 formula:1 induction:2 correct:1 shows:3 log4:1 weaknesses:1 log2:19 theory:3 ambainis:2 given:5 vazirani:2 california:1 intermediate:1 inductive:3 definition:2 fixed:1 times:4 length:1 hence:5 baltic:1 first:16 xj:2 xk:12 xi:9 xn:22 probability:14 subdivide:6 number:2 done:2 least:10 another:1 impossible:2 open:1 size:1 1q:4 differ:2 similarly:2 introduction:1 construct:3 returns:1 assumption:1 siam:2 variational:4 bits:2 final:10 gives:3 warmuth:1 hoyer:2 way:2 proving:1 lists:3 part:7 simulate:2 x2:2 x1:22 than:8 finitely:1 distance:7 subroutine:1 sr:9 accessed:1 distinguished:1 projections:1 argument:5 already:1 any:7 majority:2 generalized:1 subintervals:1 algorithms:9 strengths:1 formulas:1 who:1 most:11 takes:1 surprising:1 considered:2 clear:1 partition:1 proceedings:3 mechanical:1 normally:1 sum:5 precise:1 show:4 supported:1 speedup:4 discovered:3 minimizing:1 find:4 tapp:2 schwartz:1 parameters:1 hope:1 enough:2 completes:2 lemma:11 only:9 going:1 factor:1 bernstein:2 preliminaries:1 achieve:1 do:6 triangle:1 quantph:3 means:4 de:6 ϕs:3 cannot:2 ϕi:11 compute:1 queried:8 querying:5 arxiv:1 consisting:1 nayak:1 queries:15 qi:1 cycles:1 set:3 bounds:7 computes:1 computer:5 result:7 close:2 best:2 icalp:1 case:6 state:5 smallest:4 between:7 invariant:2 geometric:1 qubits:2 attention:1 however:3 distinguish:3 improve:2 both:2 last:1 many:2 equal:2 improves:1 qubit:1 adapted:1 appeared:1 ca:1 cf:1 community:1 ashwin:1 learning:1 cs:1 ordered:11 considering:1 combines:1 transformations:4 basis:2 been:2 much:1 ph:9 define:4 corresponding:5 received:1 sufficient:2 subspace:2 optimality:1 improved:2 applied:1 value:1 transformation:5 will:6 while:2 procedure:4 pessimistic:1 unitary:4 ir:4 thus:1 itself:1 claimed:1 limit:1 binary:13 different:7 author:2 same:3 parts:1 quant:9 split:4 incorrectly:1 φi:25 proved:1 gets:2 higher:1 used:6 functions:1 counterparts:1 running:1 uses:2 cycle:1 lower:20 database:1 well:6 solve:1 model:1 distances:1 just:9 less:3 being:4 when:2 obtain:3 intervals:1 world:2 inference:1 speed:2 previous:1 5q:2 theorem:3 input:17 andris:1 take:1 checking:1 showing:1 sums:1 possible:5 using:2 bit:3 execution:1 necessary:4 follows:2 steps:4 arbitrary:1 works:2 gutmann:5 sketch:1 because:1 methods:1 classical:6 sequence:1 some:1 searching:6 repeat:2 28th:1 specified:1 avoid:1 measurements:1 thank:1 comments:1 does:1 measuring:2 problems:2 journal:2 pp:1 step:13 hilbert:1 stage:1 ol:11 ok:5 working:1 o:17 practical:1 wolf:6 slightly:1 into:8 within:1 bound:21 references:1 sipser:5 log:57 area:1 there:4 u1:3 u0:7 fast:2 start:2 cauchy:1 lot:1 analyze:1 was:6 function:1 but:2 olm:26 repeated:2 construction:1 bug:1 applying:3 evident:1 whether:1 ut:12 uv:1 up:4 ui:13 uj:1 problem:10 similar:3 called:1 later:1 constant:12 computing:4 abstract:1 describe:2 denote:1 examine:2 initial:1 relates:1 distributions:2 again:1 mosca:1 compared:1 no:3 hybrid:2 graduate:1 acknowledgments:1 other:5 conclusion:1 symposium:1 elements:7 superposition:5 june:1 polynomials:1 important:1 independently:2 implies:6 auxiliary:1 algorithm:27 assume:3 interval:11 together:2 searched:1 cleve:1
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quant-ph9902054.txt |@word consider:1 rev:17 splitting:1 quadrature:1 whose:2 recurrence:2 squeezing:8 include:1 indicating:1 p2:1 deforming:1 zhang:1 far:1 frequencies:1 rise:2 wave:4 generalised:1 vibrational:6 hamiltonian:6 knight:2 guo:1 solution:1 large:2 solid:1 vector:1 small:1 optics:2 α2n:2 cosh:1 approximation:2 second:3 further:1 tronic:1 odd:30 even:30 nonlinear:39 sub:5 section:1 while:1 ˆa:4 above:3 vibronic:2 occupation:7 funtion:2 satisfy:1 edited:2 ibid:5 respectively:5 behaviour:5 ansatz:1 sinh:1 relaxation:1 obtained:2 antisymmetric:1 study:2 studied:2 reason:2 changes:1 involves:1 holmes:2 appropriately:1 via:1 useful:1 highly:1 seligman:1 feb:1 contains:1 negative:2 comparing:1 taken:1 more:1 becomes:5 operators:2 odinger:1 potential:4 balakrishnan:1 states:56 valued:2 equation:3 oscillator:7 cat:1 fock:2 values:5 freedom:1 following:1 spontaneous:3 repectively:1 india:1 involve:2 indicates:2 numbers:2 lamb:1 buzek:1 song:1 xˆ:3 very:1 monroe:1 symposium:1 parameter:4 l873:1 oscillatory:5 product:1 de:5 may:1 applications:1 man:3 realized:1 light:1 explicit:1 element:1 acknowledges:1 order:1 operations:1 wigner:1 interpreted:2 produced:1 experiments:2 london:1 statistical:1 jaynes:2 its:2 interesting:3 lm:2 boson:1 degrees:1 choose:1 rabi:1 combination:3 fig:7 walls:2 effects:2 they:1 represents:3 term:1 kerr:1 l2:1 trap:1 references:1 2n:23 2k:2 square:1 generation:3 energy:3 frequency:6 quantum:7 laboratory:1 eq:11 aˆ2:1 shown:3 tombesi:2 matrix:1 driving:1 squared:1 chaos:1 research:1 replacing:1 pˆ2:1 shows:1 linear:2 free:2 davidovich:1 approaches:2 ecs:5 e1:1 e0:1 milburn:2 skagerstam:1 interaction:8 sahoo:1 starts:1 transition:4 times:2 motion:8 nondemolition:2 hence:1 antibunching:3 first:4 there:1 features:3 malkin:1 laguerre:1 number:18 parkins:1 done:1 electronic:4 angular:1 xia:1 given:6 interact:1 system:7 relations:1 master:2 loudon:1 gives:3 trapped:7 ih0:1 optical:1 hillery:1 yurke:2 l2n:1 than:2 coefficients:6 holland:1 rate:1 normalizing:1 annihilation:3 fˆ:4 were:1 powers:1 exhibit:4 argument:1 generalization:2 zero:5 depending:1 self:1 note:2 k1:3 k0:3 scripta:1 centre:2 cummings:2 services:1 class:4 appear:1 considered:1 clear:2 later:2 steady:1 physica:2 kl:2 proceedings:1 exp:5 mechanical:1 physics:3 notion:1 signatures:1 show:2 rotating:3 relation:3 ground:1 feng:1 state:49 l0n:2 only:3 ocs:4 get:1 dyw:1 db:1 dv:1 dt:2 carmichael:1 evolution:1 fields:5 arxiv:1 tuned:2 dodonov:1 fixed:1 set:1 physically:1 klauder:1 flip:1 depends:1 biedenharn:1 discussions:1 macfarlane:1 said:1 commutation:1 blatt:1 marmo:2 symmetric:1 written:1 various:3 between:3 progress:1 caves:1 αn:4 terms:2 nature:2 concentrated:1 both:2 0t:1 many:3 uncertainty:5 equal:2 propagation:1 connection:1 figures:1 logic:1 contribution:1 poissonian:5 harmonic:10 exhibits:3 polynomial:1 respect:1 pp:1 aˆ:5 trajectory:1 due:1 been:2 defined:10 describes:2 basic:1 ph:1 systems:1 peaking:1 photon:1 coherent:54 external:1 general:1 present:1 case:3 laser:9 contexts:1 single:1 value:3 transformation:1 will:2 near:1 squeezed:5 pˆ:1 drs:1 opt:3 unitary:1 vogel:6 vol:1 vk:1 iv:1 ih:2 zaccaria:2 author:1 make:2 radiation:2 wherein:1 unity:1 complex:2 quant:1 wavepacket:1 wilkens:1 gets:1 higher:1 singapore:2 filho:5 sudarshan:2 effect:4 driven:2 ion:17 sivakumar:2 lower:1 elec:1 schr:1 center:6 zagury:1 position:1 usual:1 less:2 being:1 atomic:1 using:2 eigenstates:7 zoller:1 density:1 dicke:1 internal:1 lett:10 constant:1 excited:4 real:3 bichromatic:1 iη:5 increases:3 vacuum:5 integer:1 mod:2 like:3 follows:1 harmonically:2 yields:2 gandhi:1 become:3 stationary:3 mathematical:1 interference:1 classical:3 sideband:3 gilmore:1 atakishiyev:1 ˆij:1 brune:1 neglecting:1 eiη:1 cavity:1 electromagnetic:1 measurements:2 welsch:1 scientific:2 expansion:6 orszag:1 revtex:1 properties:5 world:2 ρˆe:1 basis:3 dependence:1 important:2 wolf:2 obeys:1 introduced:1 ρˆs:3 soc:1 h0:1 schemes:1 accounts:1 operator:14 amsterdam:1 statistics:3 strictly:1 initial:3 mandel:2 matos:5 was:1 function:10 medium:1 north:1 form:1 becoming:2 but:2 λei:1 micromaser:1 ωt:1 ωi:1 limit:5 distribution:9 define:2 called:2 cirac:1 associated:1 int:7 ko:3 abstract:1 am:1 zeng:1 resultant:2 engineering:1 exist:1 typeset:1 again:1 no:2 dashed:1 when:1 field:4 setting:1 conclusion:1 picture:2 denote:2 superposition:6 excitation:1 nonclassical:12 emission:3 generated:4 a2:2 vectors:1 building:1 coupling:1 governed:1 mancini:1 mass:6 time:1 meystre:2 having:1
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quant-ph9902055.txt |@word logarithms:1 partial:1 consider:2 remarkable:1 rev:7 roy:2 scalar:1 hyper:1 computation:10 constants:2 follow:1 dα:1 factorizing:1 whose:1 inverse:1 violate:1 integral:1 ohya:1 graph:2 rf:1 factoring:1 groundstate:1 environment:14 program:2 th:1 stochastic:12 must:2 worth:1 accardi:3 belonging:1 performs:1 evolves:1 very:4 frequencies:3 conditions:3 limiting:2 print:3 every:3 2γt:1 emphasized:1 matrices:8 condition:7 exponential:1 hamiltonian:16 guo:1 solution:2 large:2 solved:1 vector:6 small:5 eigenvalues:1 configurations:3 says:1 grateful:1 deutsch:1 zd:4 consistent:1 d3:1 approximation:7 zero:4 delivered:1 dynamics:4 implemented:1 volovich:7 machines:5 spectral:6 plays:1 power:1 section:1 expressed:1 uniform:2 cell:7 above:3 bαα:2 deal:1 new:5 principal:1 acknowledgments:1 satisfy:2 degree:1 ρab:2 respectively:2 l1:1 discrete:2 here:12 behaviour:1 following:7 explore:1 same:6 directions:1 equations:1 obtained:2 vazirani:1 property:1 tapes:1 institute:1 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quant-ph9902061.txt |@word represent:1 ali:2 rev:4 magnetic:4 both:1 roy:1 commute:1 entropy:1 edu:1 dα:9 whose:1 careful:2 patches:1 similar:1 concerned:1 byrd:5 must:1 helps:2 under:4 analogous:3 circumstances:1 case:7 straightforward:1 parameterize:1 truhlar:1 wave:1 matrices:9 condition:2 higgins:1 hamiltonian:17 evaluation:1 vector:5 indices:1 eigenvalues:6 equation:5 degeneracy:8 upper:1 h13:1 parameterization:13 sin2:27 approximation:4 fold:7 second:1 further:1 chem:1 aim:1 what:4 appear:1 richard:1 sum:1 expressed:3 find:1 indian:1 3n:1 above:2 method:5 full:1 never:1 khanna:2 here:11 identifications:1 simon:4 cos2:13 groups:1 represented:2 path:1 appropriate:1 equations:2 change:2 calculate:1 obtained:2 great:1 ref:6 parameters:7 studied:2 allows:1 reports:1 spheres:1 periodic:1 published:1 action:6 changes:1 composed:1 useful:1 although:3 brought:1 total:1 unit:1 use:4 feb:1 takes:1 would:10 prove:1 bundles:1 next:1 anticommutation:1 greub:1 therefore:1 taken:2 more:1 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quant-ph9902062.txt |@word replacing:3 represent:11 code:5 partial:1 consider:12 explicit:1 people:2 results:4 four:12 p01:1 p00:1 generalize:2 comments:1 computation:8 foundations:1 go:1 sci:1 expressions:1 children:3 causes:1 row:5 whose:13 inverse:1 pb1:1 calculate:2 alamos:5 technique:4 trivial:2 languages:1 rightmost:3 program:4 those:4 th:3 γl:1 eprint:5 nodes:9 knotted:1 case:19 belonging:3 string:8 advantage:2 orthogonal:4 very:7 could:4 netlib:1 every:1 commute:6 allowed:2 entries:22 matrices:110 condition:1 partitions:1 siam:1 symplectic:1 exponential:1 dij:3 level:22 positions:12 notes:1 make:7 fewer:2 deals:2 discrete:3 demmel:1 unrelated:1 phase:15 simulates:1 science:1 small:1 3b:21 ci2:2 proof:2 degeneracy:1 says:1 ga:4 bo:1 dealing:2 direct:10 literature:1 sign:1 zero:13 pass:1 further:2 implemented:3 odd:3 gm:1 required:1 even:5 aba:1 what:7 adds:1 sheng:1 indicated:1 diag:23 sum:10 associate:3 analogously:1 expressed:20 paige:1 henceforth:5 90o:6 optimization:11 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