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quant-ph9806055.txt |@word surrounded:1 partial:2 peshkin:4 caused:1 magnetic:9 lack:1 results:2 leads:2 eds:2 scalar:2 follow:1 issues:1 consider:1 whose:3 depend:1 zone:11 subjected:1 arif:2 nonlocal:2 presents:1 present:2 under:3 analogous:1 division:2 far:1 wave:15 electron:1 fall:1 difference:2 condition:3 exits:1 hamiltonian:3 did:1 notes:2 try:1 convenience:1 vector:1 gauge:4 torques:3 force:24 direct:1 unpolarized:1 aip:1 second:5 index:4 what:4 cimmino:3 section:4 brief:2 uniform:3 current:1 version:3 above:1 allman:2 new:3 lee:1 here:3 atoms:1 reported:2 cylindrical:1 represented:1 path:1 along:1 observing:2 appears:1 change:1 lipkin:1 identifiable:1 shift:15 allows:1 commonly:1 p2:1 amount:1 narrow:1 emerge:2 spatially:1 plenum:1 objectively:3 neutrons:8 improbable:1 thought:2 should:2 kobayashi:1 use:1 usa:1 distinct:2 positive:1 contains:3 negative:1 therefore:2 taken:1 zorn:1 type:2 more:1 sharing:1 apparent:1 conducting:2 carrying:1 charged:1 known:1 foundations:1 iii:2 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quant-ph9806056.txt |@word sci:1 consider:7 illustrates:1 berry:4 results:4 illustrated:2 eds:2 commute:1 computation:1 edu:1 expressions:1 whose:3 heller:1 inverse:2 umd:1 alamos:2 deterministic:1 tr:7 presents:1 finally:4 th:3 under:4 maryland:4 circumstances:1 presentation:2 p2:4 conjecture:2 very:1 quantization:1 standards:1 wave:3 surprise:2 exact:2 mw2:1 exponential:1 hamiltonian:4 tanh:2 b285:1 large:1 vector:2 small:1 inspection:3 oscillation:1 oscillator:1 direct:2 hillery:1 second:3 value:7 insertion:1 equal:1 dynamics:1 chem:1 canonical:2 even:5 what:7 nonlinear:8 plays:1 appear:2 section:4 selected:1 3w:1 near:1 3h:1 en:3 mq:3 ever:1 consisting:2 full:1 den:1 relates:1 respectively:4 here:5 possibility:1 kwang:1 based:2 along:1 quark:1 change:1 ensembles:1 obtained:1 remark:1 institute:1 vectors:1 resulting:1 poisson:3 action:2 mz:1 emerge:1 highly:3 ipq:1 apply:1 ipy:8 tools:2 planck:1 unit:4 derivatives:4 use:2 takes:5 would:1 remains:1 positive:3 give:1 negative:1 next:2 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quant-ph9806057.txt |@word limited:1 logarithms:1 transitions:1 consider:3 washed:1 eternally:1 desirable:1 splitting:1 switches:1 commute:1 go:1 follow:1 issues:1 looking:1 certainly:1 inverse:1 depend:1 catastrophe:1 technique:1 charge:2 investigation:1 elliptic:1 under:6 analogous:1 friendly:1 norm:1 case:1 supported:1 distorting:1 far:2 frequencies:1 φb:1 none:1 wave:8 electron:3 resonant:4 little:1 exact:3 condition:1 leads:3 level:16 issue:1 solution:5 solved:3 vector:2 small:3 eigenvalues:1 hospitality:1 optics:1 unexpected:1 force:1 oscillation:1 direct:1 approximation:11 zero:6 lepage:1 link:1 qualitatively:1 dynamics:1 linear:1 what:2 plays:1 appear:1 rate:1 analogously:1 expressed:1 current:2 experiment:2 above:4 scientists:1 values:2 method:5 satisfy:1 meg:1 full:1 backreaction:2 whose:1 never:1 spacing:3 here:6 atoms:4 behaviour:4 cos2:2 situation:2 directions:1 path:2 equations:4 implicit:1 change:1 obtained:1 chaotic:1 study:1 larger:1 ravndal:1 suggests:1 accomplished:1 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quant-ph9806060.txt |@word unavoidable:1 partial:3 consider:1 rev:4 commute:1 entropy:2 consists:1 follow:1 inverse:1 depend:2 deterministic:2 under:2 stochastic:1 amplitudes:1 boucher:1 rise:2 decide:1 difference:2 nonselective:4 hamiltonian:3 positions:1 solution:10 trf:1 small:1 eigenvalues:2 hcm:2 direct:3 second:4 further:1 dynamics:3 linear:3 established:1 what:2 nonlinear:1 appear:3 apparatus:7 symbolically:1 expressed:1 kisil:1 above:1 consisting:1 contrast:1 satisfy:1 qm1:3 qm2:3 modify:1 here:1 diagonal:1 determinism:2 ansatz:1 equations:3 appears:2 change:3 box:1 antisymmetric:1 institute:1 contradiction:2 poisson:4 action:1 opinion:1 changes:1 equivalence:1 followed:1 discontinuous:1 namely:1 derivatives:2 use:1 proceed:1 would:16 probabilities:3 negative:2 ψj:8 ψi:16 therefore:1 characteristics:1 taken:1 type:1 qcm:10 formally:1 composite:1 becomes:2 operators:5 odinger:3 normalized:1 particular:1 evolves:1 valued:1 equation:13 theories:1 values:4 concepts:2 example:1 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quant-ph9806061.txt |@word consider:1 splitting:1 leads:3 roy:1 quadrature:2 whose:3 inverse:2 squeezing:9 those:2 indicating:1 case:2 deforming:2 zhang:1 far:1 results:1 difference:1 annihilated:2 level:2 knight:1 large:2 annihilates:4 small:1 zero:6 further:1 scientific:2 nonlinear:13 sub:5 section:5 brief:1 ˆa:2 above:1 ˆm:1 funtion:1 satisfy:1 edited:1 respectively:3 behaviour:1 obtained:3 study:1 suggests:1 products:1 action:4 suitable:1 involves:1 matos:1 useful:1 vii:1 seligman:1 use:1 takes:2 positive:1 negative:8 properties:5 comparing:1 becomes:5 operators:4 normalized:1 cases:1 iii:2 balakrishnan:1 valued:4 deformed:2 equation:4 oscillator:3 fock:3 values:15 mehta:2 making:1 f2:2 expanding:1 india:1 states:58 indicates:1 sense:1 holds:2 feature:1 srinivasan:1 symposium:1 parameter:4 l873:1 replacing:1 applications:1 fd:1 choice:1 meaningful:1 man:1 realized:2 sectors:1 explicit:2 correspond:1 sj:1 si:1 sm:3 acknowledges:1 order:2 s0:2 wigner:1 eqs:1 interpreted:2 produced:1 london:2 its:1 lm:3 exhibits:2 fig:4 deformation:1 them:1 greater:1 walls:1 effects:1 they:5 discuss:1 always:3 2n:7 mean:4 series:1 energy:1 hypergeometric:1 frequency:1 measure:1 quantum:1 laboratory:1 summary:1 eq:7 shown:5 space:1 since:1 rev:7 research:1 gˆj:4 may:1 denoted:2 shows:2 linear:1 approaches:2 turnout:1 definition:1 skagerstam:1 interaction:2 sahoo:1 nonnegative:3 motion:1 hence:1 saxena:1 antibunching:1 features:2 number:16 done:2 given:11 introduction:1 adjoint:2 construct:6 their:2 intermediate:1 normalization:2 eqn:1 loudon:1 gives:1 trapped:1 x2:1 than:2 coefficients:1 limiting:1 annihilation:3 determined:1 were:1 exhibit:2 generalization:2 say:1 built:1 self:1 ryzhik:1 generalized:1 added:11 centre:1 jun:1 gradshteyn:1 phase:1 class:2 considered:1 calculated:1 ko:1 typeset:1 proceedings:1 exp:1 mechanical:1 physics:3 sector:6 show:2 relation:3 substituting:1 feng:1 state:44 de:1 dv:1 fields:1 arxiv:1 method:3 set:4 achieved:1 physically:2 klauder:1 depends:1 result:1 biedenharn:1 discussions:1 close:5 commutation:2 review:1 marmo:1 written:6 various:1 between:3 αn:4 terms:2 nature:2 initially:2 however:2 premultiplying:1 both:3 many:1 taking:1 uncertainty:3 connection:1 figures:1 filho:1 variance:6 contribution:1 expression:4 comes:1 relevant:1 cn:3 poissonian:7 harmonic:2 dimensional:2 polynomial:1 atakishiyev:1 aˆ:20 basic:1 expected:1 ph:1 define:2 corresponding:3 photon:18 coherent:39 c0:2 present:2 p2:3 macfarlane:1 value:3 while:2 squeezed:1 irrespective:1 drs:1 opt:2 unitary:1 vogel:1 vi:1 thus:4 anil:1 iv:2 ii:1 zaccaria:1 agarwal:2 different:2 author:1 recursion:1 radiation:3 complex:2 quant:1 finite:2 higher:1 singapore:2 sudarshan:1 ion:1 infinite:3 sivakumar:1 identity:1 center:1 well:1 academic:1 firstly:1 dimension:2 usual:1 actions:1 reviewed:1 atomic:1 using:5 eigenstates:13 tables:1 conjugates:1 field:6 quadratures:1 nonegative:1 lett:3 real:4 iα:1 showing:1 vacuum:7 press:1 integer:7 mod:2 like:5 follows:1 yields:2 either:1 integrals:1 become:4 stationary:1 mathematical:1 classical:3 mˆ:1 gilmore:1 cavity:2 electromagnetic:1 measurements:1 gandhi:1 obey:1 expansion:3 revtex:1 imaginary:1 super:1 hilbert:1 world:2 discussed:1 wolf:1 introduced:2 services:1 references:1 determine:1 operator:22 statistics:3 strictly:1 there:1 mandel:3 was:1 function:9 form:5 denoting:1 but:2 repeated:1 construction:1 repeatedly:2 atom:2 applying:2 up:1 limit:5 distribution:5 similar:1 called:2 aa:2 constant:2 defined:6 abstract:1 am:1 general:1 ap:1 exist:1 constructed:4 ni:2 nj:1 compared:2 tara:1 when:7 application:1 valid:1 nonclassical:9 prepared:2 commutator:1 important:2 sides:1 building:1 mass:1 n2:1 starting:1 chaturvedi:1
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quant-ph9806062.txt |@word represent:1 consider:2 rev:3 global:2 splitting:1 intracavity:1 leads:1 scalar:1 computation:1 expressions:2 reynaud:3 paris:3 αeff:11 finally:1 compensate:1 those:1 th:1 under:1 10ghz:3 case:4 breathing:1 straightforward:1 very:2 frequencies:5 rise:1 brossel:1 focus:1 difference:1 rapidities:2 four:1 level:3 transmission:2 positions:1 t2:1 solution:1 ri:2 large:4 solved:1 small:4 enhance:1 setup:1 smaller:2 oscillation:11 demonstrations:1 superimposed:2 zero:2 enhancement:2 incidentally:1 odd:1 even:1 aim:2 sud:1 adds:1 appear:1 sum:1 dephasing:2 lhomond:1 above:1 sup:3 continously:3 increasing:1 erieure:3 contrast:3 coefficient:1 respectively:1 gathered:1 here:3 behaviour:1 tangent:1 making:1 sine:2 appears:1 obtained:8 study:2 stretching:1 allows:1 reason:1 resulting:2 resonance:4 plotted:1 composed:1 emerge:2 explained:1 conditions:1 coinciding:1 total:4 use:2 takes:1 would:3 sake:1 mirrors:12 predictions:2 jaekel:3 france:2 therefore:3 associated:2 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quant-ph9806063.txt |@word managed:2 consider:3 splitting:8 four:14 generalize:1 anticorrelated:1 go:2 whose:2 ır:1 breached:1 irrelevant:1 send:14 finally:1 protocols:4 sent:10 summarizes:1 applied:1 wished:1 string:10 orthogonal:1 very:2 bratislava:1 decide:1 difference:1 prevents:1 securely:1 entire:2 school:1 presented:2 transmission:1 knight:1 having:1 eve:4 try:1 vector:1 phase:3 round:1 invariably:2 discover:1 hillery:1 sign:1 second:4 greenberger:1 implemented:2 odd:2 substitute:1 even:3 established:3 what:21 errors:11 xor:1 appear:1 richard:2 chicago:1 assistance:3 axes:1 expressed:4 access:3 transmit:1 above:3 new:4 method:4 edited:1 simultaneously:1 exchange:1 applies:1 teleportation:5 here:3 explore:1 protection:1 meet:1 active:1 along:2 directions:2 appears:1 sending:1 institute:1 leaves:1 larger:1 allows:2 accomplished:1 resulting:1 action:2 implement:5 makes:2 cti:1 buˇzek:1 useful:2 secure:2 requiring:1 manage:1 private:1 hardy:1 duce:1 establish:3 use:9 cheating:7 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quant-ph9806064.txt |@word science:1 agency:1 consider:1 produces:1 caused:1 over:1 random:1 scattered:1 results:2 years:1 atomic:1 statistical:1 existence:1 d2:1 localized:1 caurier:1 ensembles:1 density:2 chosen:1 fractal:5 conclude:1 complex:2 exhibits:1 should:1 presents:1 only:1 cantor:3 systems:3 th:1 role:1 must:1 rob:1 do:1 supported:1 comm:1 increased:1 mandelbrot:1 de:3 springer:1 manfredi:1 scaling:1 increases:1 sons:1 effects:2 kokubun:1 compound:1 confined:3 bunde:1 highly:1 matrices:1 gen:1 mod:1 eigenvalue:6 like:3 semi:3 follows:1 havlin:1 arxiv:1 large:1 realistic:1 polymers:1 small:2 eigenvalues:1 optics:2 mean:1 en:1 financial:1 classical:5 ed:2 energy:3 some:1 maximum:1 result:1 measure:1 quantum:2 chem:1 berger:1 best:1 subject:1 spectral:1 what:1 excitation:1 solved:1 nuclear:2 chaos:4 publish:1 colloids:1 state:1 between:1 values:2 boundary:1 conditions:1 acknowledgments:1 math:1 nature:2 equivalent:1 attention:2 ısica:1 residual:1 effect:1 following:1 devil:2 complicated:1 properties:1 exclusion:1 obtained:1 received:1 enormous:1 interaction:1 last:1 irregular:1 asakura:1 geometry:1 many:1 study:4 la:1 example:1 length:1 surfaces:1 berry:2 ltd:1 domains:1 inspired:1 finds:1 control:1 computational:1 almeida:1 probability:1 point:1 potentials:1 numerically:1 bound:1 system:1 dimensional:1 up:1 addressed:1 analyzing:1 lu:1 addisonwesley:1 reached:1 establish:1 clustering:2 toy:1 takes:1 indicate:1 ordering:1 interact:1 question:1 due:1 been:1 defined:1 approach:1 too:1 calculations:1 brazilian:1 ph:1 john:1 structures:3 theoretical:1 fig:4 function:1 shell:2 form:1 trapped:2 phenomena:1 company:1 uozumi:1 jun:1 odinger:2 but:1 berlin:1 v0:3 koonin:1 schr:2 tive:1 funda:1 producing:1 present:2 especially:1 kind:1 kimura:1 freeman:1 sta:1 showed:1 sity:1 dep:1 was:1 equation:2 work:2 particle:5 value:3 um:1 meredith:1 limit:4 behavior:1 those:1 accessed:1 problem:4 more:1 similar:1 region:2 exhibit:1 detailed:1 ab:1 sees:1 san:1 rescaled:1 chaotic:1 pro:1 spectrum:4 ao:1 general:1 states:1 rio:2 minimum:1 duan:1 arise:1 seen:3 solutions:1 universidade:1 mercier:1 regime:1 exploratory:1 shown:1 deserve:1 latter:1 cumulative:1 when:3 lett:2 field:1 potential:8 quant:1 ig:1 chichester:1 dimensionless:3 physical:1 principle:1 brazil:1 francisco:1 multiple:1 staircase:2 models:1 wiley:1 dx2:1 helping:1 heterogeneous:1 regular:1 nucleus:2 ergy:1 waves:1 infinite:2 te:1 nuclei:1 structure:1 sp:1 lower:1 chemistry:1 constructed:1 reflection:1 starting:1 spectra:1 well:1 walls:1 order:2 omez:1 so:1 grande:2 time:1 coordinate:1 model:2 salasnich:1 physics:2 fractals:2 fact:1
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quant-ph9806065.txt |@word code:5 consider:1 chain:1 results:1 entropy:3 edu:1 go:1 equivalences:1 inverse:2 λic:1 graph:1 environment:1 helps:1 th:3 ti:5 resources:1 conjecture:1 straightforward:1 continues:1 application:1 convexity:3 entire:1 achievability:2 level:1 transmission:6 notes:1 michael:1 large:1 small:2 upper:1 smaller:2 says:1 consists:1 rate:41 linear:1 established:1 what:1 λri:2 giving:1 sum:1 decoding:1 version:1 above:1 led:1 exchange:1 respectively:1 applies:1 here:3 excess:1 strong:4 great:1 larger:2 makes:1 followed:2 marginal:7 amherst:1 achievable:3 total:1 establish:1 use:2 asymptotic:1 would:3 few:1 doubt:1 therefore:1 criteria:1 taken:1 theoretical:1 more:2 formally:1 composite:2 becomes:2 acceptable:1 λd1:1 eλ:3 particular:1 must:1 me:1 ma:1 ρi:3 averaged:1 three:1 example:2 proof:6 give:2 process:2 discussed:1 minimum:2 information:20 end:1 goal:1 rather:1 holds:1 hampshire:2 criterion:3 pure:6 significance:1 ensemble:1 map:1 description:1 barnum:1 may:7 space:7 applications:1 fe:1 data:3 lemmas:1 element:1 se:1 operations:2 help:1 over:4 distortion:38 course:1 through:1 fidelity:7 still:1 perfect:1 derive:1 willing:1 systems:1 constitutes:1 might:3 easier:1 greater:2 transmissions:2 effects:1 they:1 discuss:1 easily:1 february:1 sufficiently:1 iff:1 inequality:3 each:3 side:1 domain:1 schemes:1 ei:6 simplicity:1 expect:1 measure:3 substantially:1 our:1 operation:11 noiseless:4 ρr2:4 frontier:1 since:3 increase:1 induced:1 ri:16 theory:10 e1:4 e2:5 definition:5 pairs:2 interaction:1 r1:3 r2:11 could:2 feasible:1 length:1 hence:1 think:1 first:1 informations:1 already:1 saving:1 features:1 probability:2 omitted:1 coding:7 number:2 channels:2 another:1 given:3 checked:1 rewritten:1 similarly:1 introduction:1 system:3 least:2 rates:1 perfectly:1 gives:1 copy:1 grace:1 require:1 likely:1 minus:3 lowest:1 epr:1 need:2 seem:1 tells:3 subsystems:2 zero:1 min:1 lim:1 note:1 channel:11 play:1 trace:1 rhs:1 effecting:1 subadditivity:4 most:1 pair:1 observation:1 failure:2 average:7 points:1 mechanical:1 fact:1 quantity:2 decidedly:1 show:1 reductions:1 spaces:1 analogue:1 d2:7 d1:6 q1:13 q2:19 tracepreserving:1 than:6 lemma:6 only:3 achieve:2 do:1 goes:1 get:1 de:2 overall:1 joint:2 cannot:1 closure:1 arxiv:1 bad:1 qi:2 qn:1 set:2 decided:1 college:1 result:1 fail:1 techniques:1 said:1 inequalities:1 positivity:1 qubits:3 state:7 approach:1 notice:1 terms:1 initially:2 confusion:1 analogues:1 both:1 ρq1:12 ρq2:7 taking:1 equal:2 relevant:1 asymptotically:1 whatever:1 adjoining:1 2nr:4 described:1 second:1 howard:1 due:2 much:1 ph:1 define:1 nri:2 theorem:1 coherent:8 last:2 protocols:1 case:6 myself:1 tolerate:2 evaluated:1 will:5 near:1 error:6 property:2 purifying:1 unitary:1 von:1 thus:4 excessively:1 ic:11 worry:1 perhaps:1 same:2 any:1 parts:1 quant:1 finite:1 difficult:1 used:5 infinity:1 hand:1 compared:1 uses:1 entanglement:8 lower:1 well:1 roughly:1 obviously:1 savings:1 log:2 position:1 model:1 dimension:2 usual:1 stringent:1 just:2 less:3 sources:1 thanks:1 λd:1 useful:1 yet:1 adding:1 disturbance:6 density:4 except:1 source:14 superadditivity:2 requiring:1 relevance:1 input:1 real:2 nielsen:1 showing:1 possible:2 increases:1 world:2 modifications:1 appearing:1 like:2 follows:6 ignore:1 communications:1 either:1 pipelining:2 reduced:2 terminology:1 right:1 neumann:1 classical:7 sequence:1 some:1 examples:1 convex:2 nonzero:1 dimensions:1 avoid:1 per:3 does:1 noise:1 minimization:1 peculiarly:2 processing:1 although:2 become:1 hilbert:2 noisy:7 usa:1 theorems:1 accepts:1 introduced:1 block:6 into:3 bound:4 λe1:1 copies:2 fidelities:1 because:1 operator:4 rely:1 deal:1 justifying:1 there:2 long:1 start:1 low:1 way:1 was:3 function:14 form:4 jun:1 but:2 encode:2 truncation:1 isis:1 versions:1 whether:1 bounds:1 us:4 achieving:1 limit:1 problem:1 entropies:2 constant:3 defined:6 encodings:1 linearity:1 general:2 quantum:11 single:1 initial:1 dλ:3 inf:1 defines:2 again:1 mutual:1 codes:1 no:3 when:1 rewriting:1 tight:2 role:1 test:1 nonincreasing:1 nr:2 confine:1 deviation:1 ρr1:10 symbol:1 problems:1 emission:2 deriving:1 bounded:1 allowing:1 sides:1 using:2 assume:1 required:2 curve:1 requires:1
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quant-ph9806067.txt |@word magnetic:9 four:15 consists:1 whose:2 calculate:2 paris:1 presents:1 under:4 ontological:1 worth:1 matolcsi:4 replaces:1 every:2 summarized:1 solution:12 vector:25 indices:3 force:16 consistent:1 estimates:1 direct:7 elegant:1 second:4 tangential:1 even:4 established:4 supplied:1 birkhoff:1 establishes:1 new:10 increasing:1 never:2 here:21 path:1 κr:3 obtained:8 study:3 orthogonalization:1 spacetime:66 projection:2 replace:1 brought:2 unitary:1 total:2 schilling:1 unit:4 derivatives:5 would:1 motivate:1 negative:3 call:2 therefore:5 m2:13 cαβ:5 type:1 successful:1 odinger:27 correspondingly:4 hold:3 must:2 me:1 mg:1 rα:7 work:4 theories:2 example:19 indicated:1 give:13 relativistic:32 organized:1 weinberg:1 want:1 absolute:143 end:1 provide:4 feature:3 how:18 answer:2 gordon:7 description:5 replacing:1 after:17 parallel:11 constants:4 third:1 greek:1 decreasing:2 operations:6 restriction:2 interpretation:5 over:5 expects:1 london:1 japan:3 satisfies:3 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quant-ph9806068.txt |@word consider:3 rev:12 leads:3 avalanche:1 shimony:1 consists:1 issues:1 devoted:1 pˆb:2 violate:1 johansen:1 nonpositive:3 nonlocal:8 analogous:1 case:4 impinges:1 orthogonal:1 wave:1 should:1 difference:1 splitter:6 incoherent:2 presented:1 transmission:2 knight:1 trb:1 indices:1 warszawa:1 optics:1 upper:2 employing:1 sin2:2 za:1 hillery:1 second:1 odd:1 port:1 even:1 established:1 expressed:1 ˆa:1 homodyning:1 experiment:7 above:2 obvious:1 ever:1 contrast:1 pioneering:1 pˆa:2 outgoing:1 simultaneously:1 respectively:2 here:1 understanding:1 canonically:1 operating:1 represented:1 strong:1 obtained:1 simultaneous:1 resulting:1 studies:1 followed:1 projection:5 marginal:1 highly:1 first:1 hardy:1 addressed:1 reflected:1 total:1 readily:1 plot:2 use:1 takes:2 usa:1 probabilities:3 positive:5 resolves:1 contains:2 definition:1 depicted:1 type:3 theoretical:2 more:2 separated:2 nauki:1 operators:3 holt:1 tested:1 berlin:1 everywhere:2 particular:1 known:1 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quant-ph9806069.txt |@word consider:2 lack:1 results:1 four:1 shimony:1 violate:1 johansen:1 nonpositive:1 nonlocal:2 squeezing:2 analogous:2 subtleties:1 applied:3 expressing:1 straightforward:2 very:1 void:1 quadruplet:1 wave:12 experimentally:1 knight:1 large:1 solved:1 small:1 warszawa:1 optics:1 upper:1 smaller:1 version:1 consistent:1 za:1 cosh:3 design:1 even:1 expressed:1 experiment:2 goes:1 obvious:1 led:1 respectively:2 never:1 equals:1 sinh:1 based:1 strong:3 obtained:4 remark:1 shift:1 characterizing:1 makes:1 composed:1 deterministic:1 spatially:1 sign:2 outcomes:1 first:1 addressed:1 vaccaro:1 plot:1 use:1 asymptotic:1 would:1 positive:8 negative:1 definition:1 calculation:1 depicted:1 therefore:1 defining:1 separated:1 difficulty:1 nauki:1 operators:1 apparent:1 everywhere:2 normalized:1 particular:2 known:1 foundations:1 negativity:3 speakable:1 originally:1 theories:4 labeled:1 values:2 following:2 example:3 proof:2 leonhardt:2 indicated:1 process:2 states:3 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quant-ph9806070.txt |@word crucial:1 results:1 leads:1 philosopher:1 go:1 adhere:1 reasoning:6 relationships:1 whose:1 certainly:3 hold:6 depend:2 ac03:1 concerned:1 deterministic:1 acting:1 nonlocal:1 answered:1 does:5 under:14 analogous:1 include:1 division:1 very:2 translations:1 choice:20 liability:1 every:1 conception:1 difference:1 condition:22 entire:2 disturb:2 progression:1 level:1 did:2 cause:1 proposals:1 occurs:2 leave:2 small:3 provided:2 commented:1 disclaimer:1 concluded:2 owned:1 says:7 occurrence:1 dealing:1 consistent:1 prediction:5 imply:1 rigorous:1 even:2 established:1 what:14 adds:1 appear:3 apparatus:1 brackets:1 fine:1 expressed:2 experiment:11 above:3 scientists:1 expresses:1 connected:1 schilpp:1 led:1 concepts:1 commercial:1 here:7 following:2 free:20 berkeley:3 alone:1 consideration:3 along:1 equations:1 appears:13 change:10 knowledge:1 obtained:3 great:1 shift:2 employees:1 changed:1 allows:3 step:3 experience:1 suggests:1 simultaneous:1 products:1 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quant-ph9806072.txt |@word dewitt:1 consider:3 remarkable:1 similarity:1 amplifier:2 results:5 leads:1 overlap:1 computation:1 amplified:5 nwo:1 whose:1 amplification:7 depend:1 supported:1 γn:1 cumulants:4 include:1 mehta:1 ra:1 letokhov:3 applied:3 photocount:5 far:1 brownian:1 wave:2 experimentally:1 difference:2 matrices:3 electronics:1 partitions:1 entire:1 transmission:1 bessel:1 solution:2 deals:1 small:2 eigenvalues:2 optics:8 zh:1 disordered:6 approximation:1 second:2 exter:1 concludes:1 expressions:1 substitute:1 linear:4 what:1 near:1 above:2 new:2 waveguide:4 method:2 coefficient:2 edited:2 outgoing:2 fiz:1 eksp:1 component:1 equals:1 here:1 excess:2 represented:1 strong:2 equations:1 obtained:2 woerdman:1 incoming:2 thirty:1 spontaneous:8 studied:1 approaches:1 example:4 resulting:1 poisson:2 published:2 shaded:1 studies:1 plotted:2 blackbody:1 via:3 substitution:1 replace:2 brought:1 addressed:1 counts:2 unit:2 plot:1 use:2 would:3 remains:1 positive:1 century:1 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quant-ph9806073.txt |@word partial:6 rev:3 results:5 leads:4 grateful:1 gm:14 devoted:1 depend:3 calculate:1 concerned:1 finally:1 present:2 γm:3 under:2 g0:2 far:1 wave:15 normalizability:1 rm:14 emphasized:1 difference:4 condition:11 vidensk:1 solves:2 presented:1 turns:1 gui:1 solution:16 large:9 discrete:2 convenience:1 ml:1 thereupon:1 upper:2 employing:1 sin2:4 zero:19 subtle:1 further:1 theory:2 even:1 established:3 section:11 brief:1 version:1 above:11 new:1 method:4 coefficient:2 outgoing:1 respectively:2 guangzhou:1 equals:2 here:6 behaviour:3 china:4 possibility:2 address:1 consideration:1 equations:2 eikr:2 logarithmic:1 box:1 shift:5 studied:1 resonance:3 involves:1 appropriately:1 useful:1 eimθ:4 while:7 decrease:1 total:7 establish:2 use:2 eψ:1 would:1 remains:3 ψs:1 h0:2 negative:2 next:6 comparing:1 linear:1 ψi:1 therefore:6 m2:3 taken:3 associated:1 more:6 becomes:4 odinger:3 eν:2 everywhere:1 normalized:2 proceed:1 particular:4 known:1 must:1 account:3 ma:1 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quant-ph9806079.txt |@word measurements:25 allowed:1 consider:3 maximum:1 rev:10 magnetic:11 results:2 leads:2 commute:3 sci:1 denotes:1 scr:1 whose:2 simon:2 depend:3 concerned:2 deterministic:1 environment:1 compensate:1 th:1 under:18 tf:1 division:1 orthogonal:1 very:3 continues:1 inhibit:2 induce:1 choice:1 noncyclic:1 cook:2 matrices:1 generalised:2 illustrated:2 hamiltonian:5 proposals:1 large:4 discrete:3 vector:3 succession:1 small:3 relation:1 says:1 prediction:4 second:2 equal:1 incidentally:1 further:2 dynamics:14 theory:4 what:2 plays:1 giving:3 sum:1 expressed:1 experiment:4 above:4 new:3 method:1 ihτ:1 pioneering:1 full:1 ibid:1 respectively:1 component:1 here:8 understanding:1 behaviour:2 desired:1 objects:1 pati:5 path:5 along:5 standard:1 equations:1 change:1 obtained:4 shift:5 study:1 vectors:1 through:5 resulting:1 bhandari:5 action:1 succesive:1 implement:1 history:1 studies:1 azimuthal:1 projection:5 neutrons:1 limn:1 total:2 qze:6 unit:1 additive:4 proceed:2 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quant-ph9806082.txt |@word epeau:1 partial:3 consider:2 rev:15 global:1 results:3 four:1 entropy:1 computation:1 consists:1 research:2 devoted:1 increase:1 certainly:1 hold:1 calculate:2 send:1 created:1 supported:1 company:1 finally:4 indicate:2 protocols:2 under:7 connecting:1 include:2 resources:2 applied:1 collaborate:1 straightforward:2 orthogonal:4 far:2 choice:3 wishes:3 affect:1 ln:2 illustrated:1 swapping:1 presented:2 transmission:1 knight:5 large:1 convenience:2 further:1 eigenvalues:2 optics:1 noted:1 upper:1 murao:1 hillery:4 second:2 greenberger:2 permutations:1 port:13 machines:2 even:4 optimize:1 appear:2 deliberate:1 section:12 reminiscent:1 above:5 shared:1 consisting:2 contrast:2 simultaneously:1 degree:1 exchange:2 respectively:2 teleportation:15 here:2 understanding:1 iσy:1 inverse:1 operating:1 aid:1 represented:1 along:1 obtained:4 sending:1 remark:1 sender:1 ahead:1 study:2 allows:5 leaving:1 amount:6 simultaneous:1 resulting:1 procedure:8 permutation:2 action:1 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quant-ph9806083.txt |@word lagrangian:1 decays:2 four:11 consists:6 whose:6 γx:10 violate:1 paris:1 γp:6 γt:13 γn:1 under:2 conjecture:17 rise:5 every:15 solution:2 convenience:1 vector:2 consistent:5 direct:1 approximation:8 surrounding:1 second:7 rigorous:2 q1x:1 even:8 incompatible:1 ˆz:1 liberty:1 establishes:1 new:5 contributes:1 ever:2 consisting:7 evolving:2 notions:1 never:2 r6n:8 here:6 atoms:3 asymmetry:1 represented:6 path:40 calculate:1 digits:1 rigorously:2 study:6 changed:1 suitable:5 appropriately:1 classification:1 explained:4 highly:3 brought:1 total:1 unit:5 derivatives:1 indeterministic:3 negative:2 m1:14 therefore:43 m3:10 m2:17 type:29 zeroes:2 odinger:4 hold:5 circumstances:1 mn:3 mi:4 theories:10 macroscopically:10 mv:8 mq:6 concepts:1 my:1 mx:1 indicated:5 give:6 relativistic:2 stressing:1 involve:1 indicates:1 attribution:1 guarantee:1 provide:4 verify:1 travel:1 feature:1 machine:4 how:8 answer:6 description:4 undergoing:1 after:7 minimized:1 summarize:6 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quant-ph9806093.txt |@word secondly:1 jason:1 consider:4 magnetic:2 results:1 four:1 expressions:1 reˆ:2 row:1 ır:1 depend:1 dα1:2 γt:10 environment:13 γi:2 tk:46 ρse:2 under:4 case:2 supported:1 amplitudes:1 frequencies:1 modes:5 bratislava:1 reconstructions:1 matrices:1 hamiltonian:4 tre:1 solution:2 t0:34 t1:1 solved:1 vector:1 trr:1 optics:1 lˆ:1 upper:2 force:1 excited:2 sin2:2 zero:1 value:1 further:1 dynamics:7 odd:1 theory:1 employ:1 what:1 invertible:4 expressed:3 above:1 new:2 ˆk:2 ated:1 respectively:2 here:3 understanding:1 following:1 inverse:2 cos2:8 address:1 represented:1 consideration:1 equations:1 change:3 obtained:3 institute:1 studied:1 reason:1 twamley:1 action:1 resonance:1 changes:1 uniquely:1 golden:1 buˇzek:1 private:1 poyatos:4 apply:2 total:1 derivatives:1 takes:4 negative:1 properties:2 therefore:1 reflects:2 formally:1 th:2 composite:3 operators:13 particular:2 cases:1 ρa:1 evolves:1 account:2 defines:1 gabriel:1 equation:12 work:1 det:1 ρs:1 fock:1 values:2 thin:1 freedom:1 already:1 fulfill:1 example:4 def:3 archetypal:1 leonhardt:1 transition:2 mirrors:2 process:4 states:7 performed:2 tan:1 acts:1 utilize:1 how:5 pure:1 sin:8 map:2 description:1 singular:2 may:2 wiley:2 applications:1 ω2k:1 waves:1 wave:3 data:6 response:1 λ2k:2 short:1 inversion:1 effective:1 explicit:1 cosmology:1 so:9 order:3 se:4 help:2 reservoir:3 over:1 soon:1 paper:4 london:1 statistical:1 reconstruct:6 its:3 rapidly:1 τk:5 decay:6 chosen:1 interesting:1 erators:1 2λt:10 degrees:1 systems:2 superoperators:2 main:1 non:1 propose:1 finitedimensional:1 they:2 now:3 nor:1 february:1 finite:1 level:8 mode:1 each:1 found:2 arxiv:1 ek:1 evolve:1 t2:1 energy:1 society:1 frequency:2 erty:1 measure:1 tˆ:10 our:5 eq:16 out:2 shown:1 matrix:18 space:5 rev:3 δi1:4 δi2:2 denotes:1 acting:1 numerical:1 linear:3 recurrence:1 interactions:1 1s:1 governing:1 completely:2 york:2 definition:1 interaction:1 starts:2 omit:2 times:1 turn:1 length:1 exponentially:2 onto:1 interact:1 initial:12 probability:1 ona:2 reflected:2 radiate:1 thick:1 open:6 given:12 termined:1 tor:1 eqs:1 system:28 construct:1 grow:1 indicate:2 assumption:2 master:11 pavel:1 1e:1 scheme:1 gives:1 academy:1 environmental:1 part:1 superoperator:8 eliminated:1 specify:1 dynamical:1 determines:1 approximations:2 depends:1 tomographic:1 annihilation:1 determined:4 tion:2 providing:1 lines:1 cohen:1 spectrum:1 spect:1 lim:2 isolated:1 note:5 sciences:1 ideal:1 davies:1 radiates:1 ρˆe:4 twolevel:1 pair:1 measured:7 why:1 constructed:1 principle:1 exp:2 kt:1 left:1 physics:2 fact:3 show:1 filed:1 rotating:2 spaces:1 find:4 ground:1 finally:1 knowledge:3 parameters:1 written:3 analytic:1 only:2 explicitly:3 coefficients:1 population:1 do:2 reconstruction:6 dependent:4 express:1 instance:1 during:2 dt:8 subscript:1 dp:1 areas:1 evolution:10 differential:1 atomic:4 set:5 reference:1 physically:1 2c:1 j1:34 j2:32 see:5 result:2 discussions:1 terms:2 project:1 interacting:2 dipole:2 label:1 state:21 various:1 closed:1 αi:1 neither:1 conditions:5 recently:1 iδi:1 initially:6 thank:1 both:1 cos:6 many:2 taking:2 density:9 equal:1 opˆ:1 futher:1 qubit:1 expression:4 experimental:1 unitarily:1 ci:2 point:1 simple:1 corresponds:1 environments:1 dimensional:4 described:1 basis:3 arbitrary:1 due:2 been:2 basic:1 ph:1 fig:2 determinant:1 corresponding:5 photon:2 essentially:1 royer:1 c1:2 c0:2 spin:1 present:2 applied:1 k2:38 processes:2 discrete:2 choices:1 will:2 while:1 k1:39 unitary:1 coupled:2 von:1 reads:3 ie:2 ignacio:1 different:1 anymore:1 perform:1 make:1 radiation:1 same:1 reconstructed:4 complex:1 quant:1 big:1 electro:2 independent:1 i1:29 absorb:1 i2:24 ωk:2 recent:1 numbered:2 task:1 center:1 zerotemperature:1 nevertheless:1 whole:1 obviously:1 academic:1 firstly:3 model:1 usual:1 proposed:2 λt:11 moments:1 obtain:1 transforms:1 λk:1 zoller:3 hint:1 irradiated:1 royal:1 except:2 exclusively:1 lett:3 cesta:1 diagonalization:1 input:2 transformation:2 kick:1 aspects:1 evaluate:1 possible:2 spanned:1 know:2 vacuum:3 press:1 formal:1 helpful:1 alternatively:2 specific:1 follows:6 output:4 works:1 essential:1 right:1 neumann:1 sequence:2 creation:1 back:1 examples:2 specified:6 proper:1 peter:1 describing:2 cavity:7 measurements:2 comments:1 does:3 louisell:1 propagating:1 δi:4 references:1 hilbert:6 after:1 stage:1 tracing:1 discussed:1 ρˆa:1 reduced:4 consequently:1 ρˆs:5 communication:1 into:4 three:1 slovak:1 determine:5 operator:6 rows:1 assumed:3 there:2 question:1 ci2:2 ci1:4 slovakia:1 was:1 convolutionless:1 function:1 form:5 governs:3 hs:5 jun:1 but:2 atom:20 line:3 utilizing:1 he:4 applying:1 rate:4 us:5 below:1 fermi:1 ωa:2 problem:1 cirac:3 constant:2 defined:4 ak:1 describe:1 influence:1 general:5 quantum:7 single:3 exist:1 rule:1 tomography:1 check:1 physical:2 functions:2 liouvillian:14 when:3 detail:1 field:11 elements:5 prepared:4 vectors:4 sider:1 coupling:1 algorithm:6 assume:6 packets:3 governed:3 equivalently:1 time:25 starting:1
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quant-ph9806094.txt |@word concept:1 partial:11 consider:20 subindices:1 keep:1 global:4 results:11 leads:4 entropy:6 computation:4 intricate:1 follow:1 expressions:4 gk:4 issues:1 forget:1 compact:1 whose:1 certainly:1 repetition:1 terms:10 integral:1 b3:1 iii:8 concerned:3 involve:1 acting:2 shall:1 intensive:2 thapliyal:1 estructura:1 asking:1 indicate:1 spain:1 supplies:1 under:2 mutandis:1 include:2 tb:15 resources:5 started:1 applied:1 belonging:2 lack:1 departament:1 expressing:1 orthogonal:4 far:4 reader:1 ψk:28 geometrical:2 replaces:1 ρts:10 allowed:1 wich:1 mixing:17 ln:3 difference:2 exact:2 condition:11 adjective:1 6x6:1 presented:6 ref:1 list:2 item:1 vector:8 min:14 manifestly:5 eigenvalues:4 refer:1 upper:8 smaller:5 says:1 zi:2 haar:1 ρm:1 consistent:2 sin2:1 consists:4 zero:4 cost:2 equal:4 further:5 implemented:2 interested:1 bernstein:1 even:4 will:61 what:9 projectors:5 plays:1 appear:1 iterating:1 giving:1 ρti:2 assistance:3 associate:1 ρs:136 supplied:6 version:3 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