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quant-ph9703022.txt |@word limited:12 concept:1 partial:1 consider:13 noncomputable:3 maximum:3 incurred:1 skip:1 saves:2 reversibility:4 results:6 existing:1 leads:1 executing:1 entropy:1 comments:1 computation:135 merkle:4 nwo:1 centimeter:1 issues:1 extra:8 cwi:3 inverse:1 depend:1 remarkable:1 prefixes:1 producing:3 segments:11 technique:1 corrections:1 factoring:1 removal:2 intensive:1 superficially:1 finally:3 program:32 device:6 acs:4 th:1 under:2 tg:28 nodes:12 presentation:1 resources:5 inform:1 conjecture:2 random:4 string:15 advantage:1 linked:1 could:1 reader:2 springer:1 dokl:2 nanotechnology:1 corollary:7 every:4 should:1 winning:9 exact:1 appropriately:1 common:2 entire:4 beginning:2 provide:2 presented:1 did:2 turns:2 list:2 t0:1 t1:5 large:15 discrete:2 minimizing:1 erasures:21 minimal:4 tk:26 section:1 small:3 optics:1 enforce:1 upper:3 too:2 smaller:2 compensated:1 restated:1 deutsch:5 direct:1 literature:1 elegant:1 second:2 cost:38 design:1 dev:1 go:1 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quant-ph9703027.txt |@word precise:1 iǫ1:1 dynamik:1 consider:6 pointing:4 illustrates:3 localizes:1 elektron:1 results:1 fluids:1 leads:1 eds:3 entropy:2 computation:12 edu:1 consists:2 research:1 cases:1 localized:2 particles:30 preserves:1 boghosian:4 number:8 remarkable:1 graph:1 concerned:1 equivalence:1 xx:1 factoring:1 tween:1 charge:1 indicate:3 preserved:2 under:2 analogous:1 fermionic:3 indicating:1 summarizes:1 applied:2 amplitudes:14 hibbs:1 advantage:1 r11:1 very:1 frequencies:1 implicitly:1 continues:1 wave:45 reinterpret:1 electron:1 cellular:6 summarized:1 emphasized:1 exact:3 condition:3 partitions:1 groups:1 illustrated:1 solves:3 presented:1 transmission:1 die:1 shock:1 solution:9 large:2 discrete:9 vector:7 small:1 eigenvalues:5 noted:1 solutions:3 upper:1 approximately:2 disordered:1 dealing:1 cond:1 parameterization:1 direct:1 past:1 likely:1 design:1 displays:1 defines:1 implemented:3 distance:1 monster:1 even:5 spacetime:2 appear:2 fact:3 section:20 brief:1 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quant-ph9703034.txt |@word represent:1 externally:1 caused:3 magnetic:2 separates:1 results:8 four:2 yamamoto:1 faster:2 contributions:3 reasoning:1 causes:3 compact:1 increase:1 γx:6 depend:1 γs:2 iii:2 intensive:1 finally:2 mediated:1 present:2 under:3 stochastic:1 slowest:1 include:2 γd:2 p2:19 amplitudes:2 straightforward:2 orthogonal:8 very:11 frequencies:1 discrepancy:1 rise:2 unaltered:1 seemingly:1 geometrical:1 electron:12 experimentally:5 difference:19 exact:1 condition:2 milburn:1 illustrated:1 level:1 anisotropy:31 solution:6 large:3 vector:9 phase:2 small:4 eigenvalues:4 shows:6 optics:2 originally:1 application:1 smaller:4 oscillation:5 estimates:1 direct:3 literature:1 approximation:2 le1:1 likely:1 timescales:13 enhancement:2 further:5 dynamics:11 theory:4 even:2 nonlinear:1 adds:1 appear:3 section:5 axes:4 near:1 expressed:1 current:11 experiment:3 poles:2 above:5 pulls:1 new:2 contributes:1 unintentionally:1 full:1 degree:1 respectively:1 component:3 indicator:2 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quant-ph9703040.txt |@word code:3 consider:2 maximum:1 caused:2 commute:1 computation:4 edu:1 vl2:6 knill:2 tr:1 environment:13 finally:1 critical:1 preserved:2 marks:1 decohered:9 include:2 g2:3 advantage:1 very:1 wave:1 condition:4 paz:1 hamiltonian:11 supports:1 guo:3 ri:3 large:2 ml:8 eigenvalues:2 optics:1 prevent:4 slower:1 cooperative:3 foundation:1 fragility:1 approximation:1 second:2 qeccs:4 further:1 chem:1 theory:2 what:2 nonlinear:2 sub:3 sum:1 dephasing:2 expressed:1 decoding:3 current:1 above:2 new:3 increasing:1 method:1 multitude:1 satisfy:1 respectively:3 error:9 here:3 atoms:1 following:7 plenio:1 china:3 address:1 active:1 based:1 coupling:2 change:1 extreme:2 involved:1 inspired:1 commonly:1 usually:1 useful:1 transformations:1 substitution:1 sloane:2 duce:1 unit:2 use:2 superpositions:1 ul1:6 vol:1 call:1 cnot:2 ψl:2 memory:3 encode:3 goldenberg:1 type:2 more:6 introducing:1 bennett:1 knows:1 becomes:4 operators:6 under:2 berlin:1 particular:1 known:1 foundations:1 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quant-ph9703041.txt |@word concept:1 partial:2 consider:5 alternatives:1 focus:2 leads:1 entropy:2 follow:1 remarkably:1 whose:1 eligible:1 tr:13 williamstown:1 monotonically:2 under:2 worth:1 resources:1 applied:1 orthogonal:2 every:1 exact:2 convexity:1 four:3 magic:8 level:1 turns:1 correct:1 large:2 vector:1 math:2 eigenvalues:12 optics:1 smaller:1 deutsch:1 direct:1 matrices:7 elegant:1 zero:17 further:1 quite:2 αi2:1 even:2 what:1 adds:1 appear:1 expressed:8 agrees:1 axial:1 above:3 shared:2 increasing:1 consisting:1 justification:1 degree:1 here:1 atoms:1 ranges:1 desired:1 plenio:1 directions:2 along:6 strong:1 appears:1 ensembles:3 trans:1 popescu:3 larger:1 approaches:2 suggests:1 schumacher:2 conveniently:1 makes:2 uniquely:1 spatially:1 extra:1 unit:2 use:1 takes:1 would:3 prove:2 probabilities:2 positive:2 negative:2 next:1 definiteness:1 ψi:4 therefore:1 criteria:1 taken:1 theoretical:1 more:3 separated:1 reversibly:1 particular:3 known:1 foundations:1 cases:1 hold:3 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quant-ph9703044.txt |@word concept:1 partial:1 consider:2 similarity:1 results:1 φ1s:1 2r2:1 polinomials:1 row:1 compact:3 inverse:1 depend:1 zone:2 passage:1 th:11 worth:1 norm:7 carried:1 applied:2 miele:1 amplitudes:2 advantage:2 connects:1 geometrical:2 electron:2 every:1 chamseddine:3 prof:3 affect:1 difference:1 exact:1 condition:6 entire:1 school:1 immediately:1 hamiltonian:5 cause:1 applicable:1 large:1 discrete:2 vector:4 eigenvalues:2 mangano:1 hospitality:1 tel:1 foundation:1 mi:1 consistent:2 sin2:4 approximation:2 zero:3 evaluated:2 infimum:1 further:1 dynamics:1 situated:3 spectral:4 index:5 stands:1 giving:1 section:2 contracted:1 erf:4 reasoning:1 experiment:2 above:1 sup:5 new:3 full:1 modify:2 dimensionality:1 represented:3 path:2 along:1 standard:1 appears:1 change:7 differential:1 zones:2 involved:1 study:1 larger:3 usually:2 πa:1 changes:1 involves:1 via:1 useful:1 9l:2 tau:1 hermite:2 explained:1 replace:2 visible:1 naimark:2 pythagorean:1 apply:1 total:1 sch:1 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quant-ph9703047.txt |@word operations:1 interpretation:1 consider:2 meson:1 being:1 hyperplanes:1 over:1 nσ:5 interpreted:4 russian:1 scalar:1 yudin:1 world:1 alternative:1 mesons:2 speed:6 its:1 fifth:1 note:1 hold:1 decay:2 spin:1 equivalence:1 seems:1 conjugation:14 forms:2 source:1 charge:18 potential:3 transformed:3 antiparticle:2 theorem:1 mail:1 distinguish:1 hoffman:1 transformation:4 momentum:1 details:1 correspondence:3 p2:1 them:1 explained:1 far:1 there:1 iγ:13 impossible:1 p0:5 introduce:1 number:1 2p:2 electron:1 negative:3 reversal:4 vacuum:4 diag:1 now:1 matrices:6 yu:1 qp:1 inversion:9 dirac:12 particle:12 twice:1 follows:1 transposition:1 arxiv:1 t2:2 solution:1 composition:1 try:1 discrete:2 2g:1 common:1 fields:1 inversions:1 inherent:1 repeating:1 conclusion:1 characterized:1 replacement:1 characteristics:5 application:1 right:1 methods:1 classical:1 polar:1 2e:2 hγ:2 energy:4 some:1 conditions:1 exists:1 sign:1 relative:4 carry:1 namely:1 connect:1 table:1 quantum:8 our:1 eq:7 inverted:1 puts:2 out:2 established:1 shown:2 cψ:5 matrix:2 space:11 events:1 electromagnetic:3 interactions:1 research:1 vector:2 izv:1 between:4 formula:1 electric:1 ref:1 lifshits:1 movement:1 satisfy:2 theory:7 nature:2 placing:1 proc:1 possibility:1 pitaevski:1 realization:1 replacements:1 here:6 directions:1 rus:1 electrical:1 equations:2 properties:5 observer:2 takes:1 obtained:1 both:1 schweber:1 carried:1 0t:2 a0:10 institute:1 rule:2 taking:2 similarly:2 discussed:1 july:1 russia:1 σz:1 σy:8 σx:3 place:1 consequence:2 view:1 expression:2 ψp:4 gamma:1 first:1 γp:1 necessary:1 symmetry:8 point:1 maxwell:1 into:6 xa:2 corresponds:1 due:1 dimensional:3 improbable:1 because:1 references:1 relations:2 another:1 summation:1 respect:3 cp:5 unit:1 ct:3 relativistic:1 use:2 placed:1 transformations:4 second:1 basis:2 introduction:1 px:1 initial:3 transform:1 kurchatov:1 compositions:1 their:2 pa:12 m2:1 ph:1 scheme:2 was:2 define:2 function:7 nauka:2 interrelation:1 corresponding:1 relationship:1 received:1 nikov:2 moscow:4 factor:1 photon:1 coincides:2 gap:2 hut:2 assumption:1 reflecting:2 hup:2 huq:2 redefined:2 iπ:1 x2:2 c2:4 x0:72 role:1 true:1 gab:1 present:3 he:1 case:2 account:4 mc:21 accordance:2 ut:16 equation:15 work:3 uq:24 up:16 us:4 column:3 following:6 property:1 example:1 uc:4 result:3 aa:10 separated:1 ab:1 symmetries:4 rewrite:1 electrodynamics:1 abstract:1 thus:1 additional:1 evidence:1 states:1 exist:1 cone:1 hyperplane:5 seen:1 parity:2 ψq:10 invisible:2 fizika:1 permutational:1 physical:2 lif:1 form:2 perform:1 describes:1 make:1 when:1 admit:1 mechanism:1 event:1 write:1 field:3 nuclear:1 complex:1 quant:1 take:3 significance:1 finding:1 so:1 coincide:1 subject:1 parameter:1 operators:2 vuzov:1 accuracy:1 formulas:1 play:1 mar:1 exp:1 see:1 index:1 may:8 γup:3 functions:1 possible:1 action:1 beta:1 important:1 connected:2 formulae:1 phase:1 qψ:7 invariance:3 shirokov:1 workshop:1 kept:1 center:1 consequences:1 2mc:2 considered:1 light:7 explicit:2 correspond:1 su:1 more:1 ψt:9 attaining:1 fundamental:3 time:7 addition:2 alembert:1 charged:2 physics:2 left:1
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quant-ph9703051.txt |@word now:2 remarkable:1 depends:1 formula:3 commun:1 results:3 feature:2 notations:2 ρa:2 thermal:16 paper:2 relation:1 atomic:2 statistical:7 edu:1 consists:1 appears:1 either:1 d2:1 gh:1 q1:1 q0:2 q2:4 gen:2 dp2:2 aug:1 density:2 ln:1 interesting:1 tr:4 ds:5 absence:1 parts:1 squeezing:1 systems:2 under:4 mail:2 constant:1 main:2 momentum:1 gives:1 opt:2 case:1 non:2 tanh:3 than:1 distance:12 champaign:1 genera:1 significance:2 db:1 p0:2 number:2 vallee:1 ds2f:1 they:1 invariant:1 change:1 using:1 dt:4 tick:1 matrices:1 paraoanu:2 coth:5 dq:3 qp:1 displaced:6 indeed:2 qt:1 only:3 purely:1 turns:1 university:1 arxiv:1 scalar:4 2z:1 sin:2 leave:1 berlin:1 clocks:1 yields:1 ifa:1 qg:1 follows:3 found:3 optics:1 bucharest:2 2kt:2 because:2 computed:2 sinh2:1 ed:1 springer:1 cosh:1 ωa:1 see:2 used:1 result:5 measure:1 quantum:6 our:1 dynamics:2 damped:1 out:1 what:1 matrix:2 rate:1 space:2 urbana:2 rev:1 consequence:1 diverge:1 symmetric:1 state:12 conclusions:1 geom:1 between:8 term:1 new:2 geometric:1 ro:1 suffices:1 correct:1 math:4 shows:3 horia:1 aρ:1 noise:1 recently:1 computation:1 collet:1 initially:1 parameters:3 gardiner:1 each:1 here:1 reported:1 vanishing:1 inverse:1 complicated:1 expansion:1 sinh:11 making:1 analyzed:1 slater:2 euclidean:1 properties:1 milburn:4 transformations:3 box:2 both:1 uiuc:1 property:1 pt:1 p2t:1 institute:2 similar:2 study:1 transition:4 allows:1 called:1 practical:1 prior:1 impure:2 jeffreys:1 mixed:1 scutaru:3 βh:2 ubner:2 first:2 origin:1 riemannian:1 romania:2 equivalently:1 ipf:1 features:1 probability:4 distinguishability:1 previously:2 josza:1 tanh2:1 while:1 three:1 dimensional:4 taylor:1 ann:1 kossakowski:1 respect:2 improvement:1 readily:1 considering:1 given:3 pq:1 described:1 temperature:4 usa:1 their:1 remains:1 initial:1 system:4 been:5 hilbert:2 characterize:1 few:1 difference:1 master:1 bz:1 certain:1 dt2:1 bures:8 was:4 theoretical:2 speaking:1 pg:1 obtained:5 θi:1 corresponding:1 obtains:1 form:1 square:1 quantities:1 dxµ:1 cos:2 curvature:6 volume:2 coherent:4 extended:1 studied:1 known:3 wilcox:1 squeeze:1 dissipative:1 ph:1 p2:3 states:19 mg:2 p1:1 compute:1 pacs:1 mod:2 type:1 equation:2 βt:4 oscillator:1 ωt:4 value:1 po:2 geometry:1 ds2b:2 behavior:1 sech:1 squeezed:4 contribution:2 iqf:1 treated:1 example:2 characterizing:1 numbers:1 magurele:2 noticed:1 unitary:4 associated:2 fubini:1 dp:1 ip:1 metric:5 recover:1 dxν:1 proven:1 general:1 ii:1 ap:1 provost:1 fearn:1 il:1 close:1 distinguishable:1 st:1 dβ:2 nonunitary:1 verlag:1 spaces:1 compared:1 concrete:1 suggest:1 responsible:1 when:3 vanishes:1 same:1 illinois:1 locally:1 other:3 quant:1 pure:4 becomes:2 department:3 so:2 more:2 finite:1 displacements:2 accuracy:1 independent:1 literature:1 altered:1 any:4 rhs:1 via:1 dv:1 parametrized:1 hence:1 moment:1 but:2 formulae:1 infinite:2 spin:3 class:1 changes:1 qt2:1 following:4 twamley:2 well:3 roughly:1 element:2 braunstein:4 equally:1 part:1 green:1 does:1 exp:15 kt:2 coordinate:1 model:1 physics:6 lett:3 gµν:1 quantity:2
quant-ph9703052.txt |@word ibid:2 represent:1 concept:2 evidence:1 consider:2 gp:2 interference:2 magnetic:14 varying:1 focus:1 four:2 eds:2 selection:1 houches:1 edu:1 monroe:1 localized:3 devoted:1 whose:3 inverse:1 referring:1 disposal:1 vinogradov:1 deterministic:1 tr:1 environment:2 charge:1 does:3 device:1 those:1 under:5 stochastic:3 analogous:1 include:1 worth:1 applied:2 random:1 takes:1 far:2 frequencies:3 τnm:1 rise:3 relatively:1 yurke:1 results:2 sons:1 figs:1 jacob:1 affect:1 emphasized:1 exact:1 electronics:1 squids:1 nonselective:7 differentiated:1 regarding:1 quantized:1 level:5 knight:2 notes:2 fragile:1 solution:2 viable:2 leave:1 solved:1 vector:1 small:2 eigenvalues:1 optics:1 equation:5 configurations:1 simson:1 strongly:2 averaged:1 slower:1 evaluating:1 oscillation:2 cessa:1 direct:2 feasibility:1 rate:1 timescales:1 picked:2 qualitatively:2 dynamics:16 attributable:1 odd:1 even:1 established:1 what:1 plays:1 appear:1 apparatus:2 giving:2 trivial:1 section:2 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quant-ph9703053.txt |@word february:1 mar:1 causality:1 violate:1 arxiv:1 photon:1 been:1 states:1 single:1 paper:1 quant:1 ph:1 withdrawn:1
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