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quant-ph9811022.txt |@word ibid:1 represent:1 ui:1 steiger:1 consider:6 magnetic:1 retain:2 bandgap:1 results:6 p20:1 four:1 known:1 ge:1 follow:2 issues:2 whose:1 u3:6 const:1 calculate:1 corrections:1 opportunities:1 essentialy:1 environment:1 finally:2 does:5 those:1 include:2 dramatically:1 ωt0:1 summarizes:1 p2:2 vlj:1 amplitudes:1 performs:1 advantage:1 sitting:1 far:2 hughes:1 wave:31 suggesting:1 probability:13 figs:1 decide:1 resonant:2 experimentally:2 difference:2 splits:1 splitter:25 mξ:4 jhe:2 hamiltonian:2 transmission:3 forth:3 t2:1 integrated:1 large:1 eur:1 vector:1 affect:3 small:6 enhance:1 refer:5 optics:1 limitations:1 strongly:1 smaller:2 force:2 destroys:1 probabilities:3 sign:3 approximation:8 rate:4 design:2 displays:1 realistic:1 dynamics:1 splitting:2 theory:1 even:2 established:1 what:1 trapping:3 nano:1 giving:1 nakata:1 exactly:1 localization:1 contributed:1 expressed:2 find:5 experiment:2 ito:1 localized:2 above:1 new:3 abele:1 waveguide:1 method:1 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quant-ph9811026.txt |@word limited:1 measurements:1 sci:1 consider:3 pointing:1 squared:1 brownian:6 results:2 leads:1 discreteness:4 ciudad:1 entropy:3 follow:1 remarkably:1 localized:5 gh:2 whose:4 depend:2 doe:1 eigenbasis:5 alamos:2 nonlocal:3 anglin:1 environment:36 th:1 stable:2 tegmark:1 include:1 worth:2 alternating:1 protective:1 straightforward:1 outside:2 very:1 frequencies:3 springer:2 electron:1 every:1 additional:1 experimentally:1 difference:1 exact:3 vast:1 illustrated:1 induced:2 hamiltonian:22 t6:1 lengthscale:1 t2:1 scalar:5 t1:14 large:1 discrete:2 optics:1 enforce:1 work:1 sign:1 approximation:5 second:4 further:1 dynamics:3 linear:3 even:5 dial:1 preferences:1 apparatus:2 sum:2 selected:6 above:4 new:1 net:1 coefficient:1 edited:1 hern:1 ibid:1 mω:3 never:1 here:3 understanding:1 objects:1 free:4 eikx:1 alone:2 sieve:4 equations:2 appears:1 change:2 obtained:5 study:2 larger:2 completely:1 resulting:1 suggestion:1 action:1 fourier:4 studies:1 involves:1 york:1 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quant-ph9811027.txt |@word hº:3 ix:1 ab:10 t2:14 mc:1 4a2:3 h2:4 tr:21 ann:2 h1:4 uau:1 xr:2 xi:2 dº:5 pχ:7 b2:13 convex:1 φij:8 λj:5 λi:7 a1n:2 id:1 cn:1 abp:2 ehs:12 min:6 lim:3 u1:2 2λi:8 u2:3 ψj:2 φa:2 6t3:1 ψi:15 quant:1 3ab:1 αi:3 ph:1 pi:2 a11:2 log2:14 σu1:1 sº:1 hs:3 hi:3 a4:1 4ab:1 c2:11 nov:1 ds:5 uσ:1 2t:1 dim:1 σi:1 λ2i:1 evn:7 conv:1 2s:2 ρi:3 arxiv:1 pξ:8 9t2:1 a2:20 ui:1 2a2:1 s2:4 pφ:4 pψ1:3 2ab:5 an1:2
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quant-ph9811028.txt |@word limited:2 katz:1 consider:1 rev:13 forbidden:1 particular:2 results:4 four:6 quadrature:2 woods:1 garching:1 expressions:1 depend:1 corrections:1 groundstate:1 finally:1 program:1 squeezing:7 th:1 under:4 stochastic:4 γa:12 include:1 worth:1 p2:1 amplitudes:1 very:4 frequencies:10 springer:1 splitting:1 refractive:1 resonant:7 exact:1 condition:2 level:3 evaluation:1 itamp:1 standards:1 large:3 solved:1 small:9 optics:6 noted:2 inconsistent:1 upper:1 compensated:1 oscillation:10 deutsch:1 hindered:1 direct:1 pulse:1 past:1 ators:1 enhancement:1 air:1 even:4 will:1 nonlinear:9 plays:1 sθ:2 rate:6 cell:2 above:2 new:2 consisting:2 contrast:1 κl:3 respectively:1 realizations:1 residual:1 here:7 atoms:5 reported:1 zibrov:2 relaxation:3 strong:1 equations:8 obtained:1 naval:1 losses:3 allows:1 completely:1 resonance:4 fourier:9 studies:1 zubairy:1 via:3 useful:2 yuen:1 vapors:1 welch:1 quenching:1 planck:1 use:3 proceed:2 χ2j:1 few:8 noting:1 taken:1 type:2 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quant-ph9811029.txt |@word customary:2 consider:7 crucial:2 forbidden:1 results:13 leads:1 eds:2 ginzburg:1 commute:1 gn:10 expressions:2 denotes:7 contributions:1 cases:2 localized:2 optical:1 compact:1 whose:10 griffin:1 inverse:2 depend:2 calculate:1 eα:5 equivalence:2 tr:7 tp:3 shall:3 environment:23 list:1 quasi:9 behave:1 squeezing:1 those:4 stable:6 lin:1 connecting:1 include:1 crest:1 divergent:2 applied:1 conjecture:1 amplitudes:1 outside:1 very:16 bilinear:2 account:2 choice:2 rotational:1 every:2 experimentally:1 difference:4 exact:2 condition:4 treating:3 notations:1 pre:1 exponential:1 immediately:1 hamiltonian:15 did:3 turns:1 integrating:1 tre:3 solution:1 large:12 vector:1 recall:2 small:23 gauge:1 ueda:1 optics:1 equation:5 degeneracy:2 application:2 ruostekoski:1 smaller:2 renormalized:2 zg:15 sin2:2 literature:1 cosh:1 approximation:6 zero:6 evaluated:6 eiϕ:7 ien:1 leakage:10 quite:2 theory:2 even:5 established:1 what:2 nonlinear:7 appear:1 apparatus:3 giving:1 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quant-ph9811035.txt |@word concept:1 transitions:2 consider:3 remarkable:2 illustrates:1 rev:13 magnetic:1 both:11 results:7 illustrated:3 p02:2 p01:2 stops:1 consists:1 follow:1 involved:1 contributions:1 c1:33 causes:1 restrictions:1 whose:1 certainly:1 hold:1 ceases:1 concerned:1 pˆj:1 environment:1 quasi:5 mediated:1 those:2 under:16 must:4 passed:1 eliminate:1 eigenstate:1 amplitudes:9 takes:1 outside:1 very:7 frequencies:1 end:1 wave:15 probability:11 maali:1 figs:8 scholarship:1 resonant:2 exact:9 fragments:1 condition:2 arrange:1 notations:1 kazantsev:1 level:4 experiencing:1 solution:1 damped:4 large:4 discrete:1 convenience:1 settle:1 phase:2 progress:1 small:10 eigenvalues:2 markov:1 referred:1 optics:4 noted:1 upper:1 population:5 smaller:2 obsolete:1 sign:2 approximation:10 second:9 orthogonal:5 equal:2 further:6 dynamics:3 estimated:1 odd:4 quite:2 goes:1 even:8 index:1 what:1 zinn:1 darkness:1 ψn:2 section:3 localization:1 http:4 brief:2 find:2 below:1 experiment:1 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quant-ph9811043.txt |@word represent:1 sci:1 consider:2 switched:1 induces:1 results:2 illustrated:3 scalar:7 computation:3 reson:4 manipulations:1 causes:1 whose:3 certainly:1 integral:1 spin:55 concerned:1 illustrates:1 removal:1 neighbours:1 compensate:2 excluded:1 under:7 analogous:2 applied:8 returned:2 straightforward:4 returning:2 far:1 continues:1 induce:1 choice:1 wishes:1 every:1 fall:1 affect:1 difference:1 exact:3 leads:1 hamiltonian:6 diverging:1 proc:2 t2:1 applicable:1 fewer:1 demonstrated:1 enclosing:2 small:5 compensated:2 receiver:2 incremented:2 bubbling:1 pulse:20 sign:1 generalisations:1 zero:3 street:1 design:1 acid:3 what:1 errors:2 giving:2 axes:1 uniform:1 current:1 experiment:1 new:1 net:1 increasing:1 method:1 contrast:1 satisfy:1 collateral:1 margolus:1 simultaneously:1 ms:2 placing:1 never:1 siegert:3 residual:2 here:1 desired:1 selective:6 groups:1 address:1 represented:1 along:1 strong:4 herv:1 change:1 convert:1 hansen:1 increments:1 leung:2 splitting:2 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quant-ph9811048.txt |@word concept:1 consider:4 magnetic:1 alternatives:1 results:1 scalar:4 whose:1 certainly:1 inverse:1 referring:1 subjected:1 ℜz:3 neighbours:5 those:1 analogous:1 worth:1 divergent:1 amplitudes:4 very:1 wave:3 every:1 affect:2 condition:3 hamiltonian:1 turns:1 vector:7 succession:1 sign:2 second:1 further:3 appear:1 sum:1 contributed:1 expressed:1 undecided:1 acknowledgments:1 contrast:1 full:2 lee:1 2ma2:2 component:1 here:2 understanding:1 desired:1 boghosian:2 quite:1 equations:2 cubical:1 studies:1 gluons:1 iz:2 translational:2 derivatives:1 additive:1 superpositions:1 would:2 covariant:2 positive:2 negative:1 next:3 therefore:2 taken:1 reflects:1 more:1 becomes:1 odinger:10 iii:1 must:1 valued:1 quantized:1 equation:18 work:1 infinitesimal:2 following:1 ninj:1 example:1 dn:9 ma2:1 renormalization:3 links:1 process:3 expanding:1 suggestions:1 assumptions:1 numbers:3 information:2 rather:1 located:1 instead:1 parameter:4 may:1 after:3 hence:2 mendel:1 law:1 natural:1 so:2 fundamental:2 operate:1 order:3 interpretation:1 over:1 move:1 interpreted:1 produced:1 paper:1 through:1 statistical:1 kinetic:2 derive:1 probability:2 coordinates:1 absence:1 complex:3 differently:1 derivative:3 non:1 creutz:1 they:3 nov:1 now:1 nor:1 february:1 always:2 university:1 identified:2 2d:1 magnitude:1 realise:1 found:1 characterized:1 homogeneous:1 square:1 energy:5 inhomogeneous:1 used:1 obtains:1 quantum:5 assumption:4 eq:3 out:3 emerges:1 shown:1 space:4 restricted:1 cubic:3 rev:4 acting:1 theory:4 free:3 standard:2 definition:1 could:1 motion:2 δij:2 consequence:1 first:2 already:1 symmetry:4 omitted:1 variables:1 superpose:1 number:1 another:2 illustrate:1 given:1 cartesian:2 rewritten:1 leading:1 system:1 relations:1 indicate:1 summability:3 statement:1 iaz:2 scheme:2 option:1 continuous:1 part:1 x2:1 than:4 wide:1 kind:1 determines:1 scenario:1 accordance:1 require:1 matter:1 amplitude:1 ia2:4 symmetries:1 intriguingly:1 argument:1 manner:1 emphasizing:1 need:1 seem:1 any:6 wilson:1 efficient:1 convenient:1 latter:1 responsible:1 potential:9 generalized:1 algorithms:1 play:1 most:3 importantly:1 preliminary:1 phase:1 why:1 christ:1 deviations:1 later:1 physica:1 principle:1 exp:2 mechanical:1 quadratic:1 physics:2 fact:1 hyper:1 show:1 timedependent:1 converge:1 purely:1 gauge:6 find:1 parameters:4 explain:1 written:1 only:5 local:1 axiom:2 continuity:1 do:1 preferred:1 lattices:1 dt:4 procedures:1 geometric:1 processes:1 continuum:8 conditions:1 differential:3 twice:1 implication:1 pade:1 exists:2 computer:1 incorporating:1 oldenburg:2 satisfying:1 motional:1 yet:1 state:2 plaquettes:1 progress:1 neither:1 approach:1 terms:10 initially:1 spacing:4 configuration:1 thank:1 cubes:1 last:1 kogut:1 contribution:1 argue:1 expression:1 finds:1 point:2 simple:3 dimensional:1 maintained:1 ab:1 moreover:1 ima2:1 basis:1 int:1 arxiv:1 basic:1 ph:1 universal:1 systems:1 direction:1 ℑz:4 completing:1 gas:1 coherent:4 present:2 case:2 pacs:1 expanded:1 value:1 will:4 cast:1 while:1 identical:1 unitary:1 thus:3 site:4 iv:1 ii:1 suggest:1 parts:1 quant:1 finite:2 higher:2 arrives:1 singlecomponent:1 again:1 nest:1 lutz:1 nj:2 inhomogeneities:1 potentials:1 changing:2 invariance:1 reference:1 schr:10 hopping:19 nevertheless:1 no:2 without:2 coordinate:1 position:5 dimension:1 justify:1 less:1 using:3 eigenstates:2 conclusions:1 nonrelativistic:5 parametrization:1 lattice:20 spread:2 easy:1 input:1 mod:1 eigenstate:1 real:1 iκ:1 term:3 integer:1 essential:1 like:1 particle:7 steps:1 either:1 characterizes:1 evolutions:1 reduced:1 because:3 respect:3 extended:1 quarks:1 instantaneous:1 models:2 assuming:1 arbitrary:1 step:4 2m:3 imaginary:3 bz:1 about:4 idt:2 discussed:1 o:6 simulation:1 dependency:1 range:1 a2:4 extensions:1 greatly:1 discretization:2 cambridge:1 maxwell:1 appropriate:1 references:1 assumed:2 there:1 conservation:2 was:2 function:3 form:4 forming:1 adjusting:1 but:4 link:1 delta:1 convergence:1 intuitive:3 wish:2 differentiable:1 discretized:1 limit:7 similar:1 taylor:2 defined:2 abstract:1 contribute:3 general:6 defines:1 ni:2 functions:3 susskind:1 locality:1 amounts:1 wavefunction:1 when:1 field:3 role:2 spatial:3 department:1 conclusion:1 superposition:2 respects:1 initio:1 uniformly:1 convention:1 important:2 implies:3 requires:1 factors:1 neighbouring:1 mass:4 time:8 starting:1
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quant-ph9811049.txt |@word replacing:1 represent:1 concept:1 consider:3 limited:1 caused:2 magnetic:1 roc:1 results:6 leads:8 generalize:2 lewenstein:1 57b:1 go:1 follow:1 amplified:1 contributions:1 57a:1 causes:4 increase:4 calculate:1 zone:2 collisions:3 description:1 technique:1 contained:2 γt:1 supported:1 charge:1 preserved:1 excluded:1 under:3 kλ:31 details:1 microscopically:1 include:3 ckλ:1 eliminate:1 applied:2 random:2 straightforward:1 g0:1 very:3 rise:1 conditions:4 wave:21 crenshaw:2 distribution:1 refractive:5 resonant:4 em:1 fakult:1 treating:3 splitter:1 gkλ:30 ωin:1 obvious:1 level:6 transmission:1 issue:1 t2:2 solution:8 fewer:1 ri:1 try:1 integro:1 vector:1 small:4 radio:1 drop:1 optics:15 setup:1 possibility:1 upper:1 andrews:2 dilute:1 10b:3 dealing:2 consistent:3 10a:3 estimates:2 direct:2 sign:2 approximation:14 konstanz:6 enhancement:2 pass:2 rigorous:1 dynamics:4 estimated:1 situated:1 substitute:2 theory:4 spectral:1 index:6 what:1 nonlinear:20 plays:2 ip:2 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quant-ph9811050.txt |@word replacing:1 concept:2 consider:4 caused:2 blanchard:1 focus:2 cancels:1 go:1 instantaneous:1 misconception:2 causes:2 particles:3 aug:1 jadczyk:1 producing:1 concerned:1 finally:1 those:3 under:1 breach:1 ontological:5 include:1 zeh:1 versus:1 very:4 frequencies:1 misunderstanding:1 results:6 englert:1 electron:11 sons:1 every:1 decide:1 experimentally:1 emphasized:1 difference:2 exact:1 condition:1 philosopher:2 school:5 regarding:3 beam:1 hamiltonian:1 did:2 turns:1 cavendish:1 applicable:1 culminating:1 occurs:1 detected:2 dealt:1 rev:5 optics:2 noted:3 smaller:5 says:1 exposed:1 consistent:5 sin2:1 pulse:1 past:1 second:1 perspective:2 further:1 copenhagen:11 even:5 established:1 what:6 plays:4 apparatus:4 incompatible:1 giving:1 dr0:6 specification:1 dr2:1 near:1 find:1 current:2 version:4 localized:1 above:3 lifshitz:1 new:4 learned:1 john:1 consisting:1 filled:1 satisfy:1 edited:3 schilpp:2 justification:1 behavior:1 degree:1 exchange:7 respectively:1 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quant-ph9811053.txt |@word measurements:1 partial:3 consider:2 results:4 roy:1 entropy:1 edu:1 expressions:1 research:1 devoted:1 whose:2 inverse:2 aug:1 fellowship:1 concerned:1 tr:2 send:1 presents:1 finally:1 behave:1 those:2 arranged:1 analogous:1 include:1 applied:1 conjecture:2 supported:1 straightforward:1 very:2 tends:2 primed:1 sons:1 telling:1 exact:1 entire:1 trb:1 cascading:1 large:8 vector:4 olkin:1 eigenvalues:7 unexpected:1 force:1 sin2:2 matrices:1 noise:1 picked:1 corner:1 further:1 implemented:1 theory:8 what:2 deeply:1 sum:3 values:1 preserved:1 satisfy:1 jointly:1 understanding:1 following:3 dimensionality:2 others:1 active:1 change:2 obtained:1 almost:1 generalizing:1 increments:5 barnum:1 institute:2 study:1 vectors:2 allows:1 leaving:1 accomplished:1 schumacher:2 proportionality:1 bob:17 ψm:1 schur:1 tasks:1 useful:1 classification:1 julia:1 decrease:2 apply:1 total:1 univ:1 alberti:1 use:3 asymptotic:7 would:3 prove:2 sake:1 positive:1 negative:3 next:3 ψj:1 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quant-ph9811058.txt |@word represent:1 consider:3 commute:1 computation:3 edu:2 gn:1 expressions:1 gl:2 depend:1 knill:1 environment:4 th:1 γl:1 stochastic:2 include:1 supported:1 g2:3 g1:4 orthogonal:2 very:1 wave:1 condition:2 paz:1 hamiltonian:12 knight:1 guo:4 applicable:4 t0:5 occurs:1 science:6 small:1 eigenvalues:1 aβα:7 fragility:1 approximation:2 zero:1 qeccs:12 correspond:1 what:1 nonlinear:1 plays:1 sum:1 expressed:3 above:3 3l:8 order:6 method:1 contrast:1 satisfy:3 respectively:2 here:1 plenio:1 china:3 address:2 represented:5 consideration:1 shift:2 larger:1 products:2 spatially:13 sloane:1 apply:2 alamitos:1 use:2 positive:3 muller:1 few:1 goldenberg:1 type:1 more:4 introducing:1 becomes:1 operators:20 occurred:1 berlin:1 normalized:1 foundations:1 cases:1 hold:1 circumstances:1 high:1 springer:1 avoiding:1 equation:6 work:1 remain:2 grover:1 following:6 example:2 numbers:2 process:4 bennett:1 states:1 effectively:1 σlx:1 attain:2 verlag:1 lamb:2 information:1 goal:1 fortunately:1 env:3 answer:1 symposium:1 ensemble:2 product:1 description:1 may:2 after:7 derived:1 hence:4 gottesman:1 σl1:1 syndrome:2 short:3 natural:1 effective:8 explicit:2 interrupted:2 sk:1 so:1 correlation:4 g12:1 dum:1 developed:1 over:1 paper:2 london:2 fidelity:3 still:1 ieee:1 its:1 diagonalized:1 complicate:3 symmetry:1 decay:1 solving:2 lu:1 systems:1 overcome:1 them:2 good:2 pure:1 practice:2 steane:1 they:1 nov:1 nor:1 represents:4 term:7 always:1 university:1 drop:1 identified:1 reasonable:1 each:1 side:3 schemes:3 independent:5 t2:5 hard:1 reduce:2 quantum:31 assumption:1 approximated:1 eq:12 special:4 divincenzo:1 shown:3 matrix:4 space:1 electronic:2 since:2 rev:20 denotes:2 re:1 seriously:1 rm:4 rn:6 induced:1 correct:6 foundation:1 trajectories:2 circumstance:1 gardiner:3 diagonal:1 reason:1 advantages:1 inevitable:1 interaction:5 r0:1 language:2 r3:1 computers:2 times:2 corrections:1 frequent:1 first:11 pγk:3 initial:2 probability:4 omitted:2 variables:1 clear:1 parkins:2 simplified:2 directly:2 open:1 necessarily:1 rewritten:1 unitarity:1 eqs:1 system:3 least:1 unruh:1 their:1 ukl:3 master:5 wootters:1 bits:1 final:1 recovered:1 diminish:1 republic:1 than:1 coefficients:4 jump:6 kind:3 wiesner:1 second:3 involved:1 project:1 zanardi:1 correction:12 ming:1 need:6 any:1 efficient:1 convenient:1 negligible:1 subject:1 smolin:1 channel:1 combat:3 most:6 errors:16 propagate:1 decohered:1 phase:2 beth:1 class:2 average:3 adopt:1 kl:1 exp:1 normally:1 fact:1 shor:4 show:1 random:3 ending:1 discovered:2 fa:4 chuang:1 lloyd:1 substituting:1 find:2 calderbank:2 q0:3 q3:1 enough:1 should:3 only:3 interested:1 do:1 notation:1 get:2 dependent:1 dd:1 express:1 cannot:1 during:1 dt:3 evolution:6 conditions:2 arxiv:1 qk:2 qn:7 set:1 national:1 maximum:1 detection:1 computer:1 recently:1 techniques:4 detect:2 tensor:3 definite:1 state:13 between:1 before:1 approach:4 αl:10 αn:1 terms:9 ability:1 qubits:9 however:4 hefei:1 derive:1 extent:1 suggested:1 grassl:1 σl:6 many:3 annual:1 according:2 qubit:18 safely:1 comes:1 0m:1 arbitrarily:1 among:1 cn:2 ca:1 pp:1 described:8 transformations:1 trajectory:3 due:2 been:3 describes:1 damping:1 ph:1 pn:3 define:1 corresponding:1 zurek:1 repetition:1 those:1 case:2 p3:1 p0:4 pacs:1 examine:1 will:3 dephasing:1 suppose:1 error:34 35th:1 procedure:5 unitary:1 laflamme:2 refs:1 thus:2 non:2 duan:4 technology:1 perform:1 make:1 belong:1 quant:1 emphasize:1 pauli:1 finite:1 hermiticity:1 evolve:1 calculation:1 used:1 numerical:1 counterparts:1 hand:3 unpublished:1 frequently:1 identity:2 off:1 center:1 pellizzari:2 whole:2 well:1 vaidman:1 concrete:1 model:2 guang:1 proposed:1 less:1 identify:2 zoller:3 density:3 alternate:1 except:2 valid:1 lett:7 iρ:1 input:2 suominen:1 real:1 devised:2 sums:2 possible:1 possibly:1 press:1 using:2 correcting:6 rasetti:1 δnn:1 necessary:1 follows:1 collective:6 yields:1 either:2 become:1 reduced:3 terminology:1 right:3 classical:3 people:1 some:2 recovery:2 demonstrates:1 does:1 proc:3 demonstrated:1 nose:1 noise:20 jumps:2 conventional:5 hilbert:1 noisy:1 pγ:1 o:4 simulation:1 ξk:1 other:3 soc:2 into:3 hermitian:7 promise:1 operator:7 proportional:1 reducing:7 matrixes:2 whaley:1 r2493:1 assumed:1 there:3 vedral:1 lidar:1 los:1 hef:2 much:1 was:1 δll:2 complete:1 form:2 collapsed:1 denoting:1 but:2 hk:1 repeated:1 hi:5 encoded:2 dissipative:1 longer:3 made:1 up:2 ul:1 miguel:1 demonstrate:2 problem:2 called:1 cirac:1 certain:1 general:10 single:15 physical:2 functions:2 codes:4 no:4 rains:1 nonlinearities:1 ekert:1 generally:1 γll:2 setting:1 role:1 department:1 picture:1 kinds:2 conventionally:1 ustc:2 problems:1 includes:3 deriving:1 important:5 palma:1 dissipation:3 acknowledgment:1 independently:1 correlated:13 coupling:1 assume:1 physics:1 dτ:3 interval:3 together:1 time:7 firstorder:1 decoherence:26 having:1
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quant-ph9811059.txt |@word consider:12 maximum:1 interference:2 osi:6 continual:1 scalar:2 mile:1 rosales:5 grateful:1 expressions:2 causes:1 looking:1 hold:1 depend:1 calculate:1 4ns:1 young:1 tp:4 finally:2 those:6 stochastic:4 cm3:1 case:6 fax:1 amplitudes:2 straightforward:1 very:3 wave:3 witten:1 mξ0:1 experimentally:2 four:3 caesium:1 incoherent:3 vibrational:1 presented:2 evaluation:3 large:2 4t:4 vector:3 small:2 referred:1 optics:2 noted:1 programme:1 upper:2 squared:1 consistent:1 strunz:4 qmw:2 sign:2 approximation:7 likely:1 lines:1 traveling:1 7th:1 further:1 dynamics:2 odd:3 substitute:1 theory:13 even:1 what:1 nonlinear:2 apparatus:1 section:13 supplied:1 current:3 experiment:2 above:3 increasing:1 equivalent:1 contrast:4 gravitation:1 respectively:1 applies:1 component:1 here:4 atoms:1 localisation:3 objects:1 along:2 equations:2 appears:3 change:4 barchielli:2 study:1 studied:2 allows:1 through:2 leaving:1 suggests:2 amount:2 resulting:1 action:3 spacetime:14 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quant-ph9811060.txt |@word partial:1 consider:1 rev:16 results:3 entropy:15 doted:1 inverse:1 segments:1 umezawa:1 tr:1 ρs:1 nonlocal:4 fundamentally:1 breach:1 maryland:1 sent:1 conjecture:1 amplitudes:1 straightforward:1 far:2 continues:1 choice:1 sons:1 emphasized:1 difference:5 condition:4 tri:1 beam:1 hamiltonian:1 large:1 baltimore:2 coincidences:1 trs:1 optics:1 upper:1 unexpected:1 force:1 prediction:1 approximation:1 zero:8 pass:1 click:4 belief:1 spectral:6 what:3 nonlinear:4 plays:1 25mm:2 pinholes:1 agrees:1 experiment:6 above:1 new:5 paradoxical:1 respectively:2 even:2 experimentalist:1 address:1 directions:1 path:1 along:1 observing:1 sinc:2 cerf:2 naval:1 involved:2 study:4 completely:2 usually:2 fourier:1 studies:1 involves:1 mutual:2 transmittance:2 named:1 spatially:3 replace:1 county:1 herzog:2 total:2 select:1 use:1 figure:2 would:2 remains:1 positive:1 contains:1 negative:3 process:2 approach:1 therefore:1 spike:1 type:9 reflects:2 more:1 separated:4 operators:1 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quant-ph9811061.txt |@word represent:1 concept:1 consider:1 similarity:1 commute:1 generalize:1 spiridonov:2 edu:3 inverse:6 technique:1 th:4 under:1 norm:1 far:1 wave:1 eir:1 condition:4 hamiltonian:4 solution:2 math:2 originally:1 zn:2 zh:1 sukhatme:5 zb:2 integrability:1 further:1 zq:1 ˆq:1 ˆi:1 acknowledgments:1 eksp:1 here:2 explore:3 address:4 path:1 instituto:1 studied:3 useful:1 family:1 scaled:1 establish:1 takes:1 would:1 commun:2 e1:1 ca1:3 coordena:1 ψn:2 introducing:6 operators:5 ellinas:2 normalized:2 jˆ3:2 cases:3 iii:1 must:1 evolves:2 ma:1 deformed:2 science:1 equation:2 work:1 oscillator:4 ginocchio:1 barclay:2 states:7 uˆi:5 end:1 xˆ:1 write:2 ıvel:1 parameter:2 l873:1 algebra:10 amparo:1 mad:1 excited:4 short:2 dynamical:1 spectra:1 su:1 so:2 acknowledges:2 interpretation:1 dx:2 satisfied:1 paper:1 committee:1 satisfies:4 its:1 superior:1 le:1 fiz:1 permanent:1 deformation:1 them:1 janeiro:1 factorial:1 introduce:2 scaling:3 nov:1 easily:2 february:1 university:4 hermitian:2 2m:3 en:8 energy:2 reduce:1 related:5 investigated:1 obtains:1 quantum:4 our:1 eq:20 ep:1 special:1 shown:4 space:1 rep:1 since:1 rev:4 research:2 ref:6 rj:1 foundation:2 wisconsin:7 panigrahi:1 ısica:1 standard:3 khare:3 term:1 remainder:2 e0:2 hence:3 teor:1 already:1 number:2 set:1 relations:4 electronic:3 illustrate:1 given:5 rewritten:1 similarly:1 introduction:1 eqs:3 construct:2 ribeiro:1 shifted:1 relationship:1 exactly:3 part:2 translation:2 sˆ:7 conjugate:1 forced:1 latter:1 note:2 potential:3 take:1 most:1 considered:1 alumni:1 typeset:1 exp:4 physics:5 fukui:1 madison:2 show:7 supported:1 relation:3 substituting:1 ground:4 parameters:6 state:18 do:3 notation:2 dependent:1 de:7 closely:1 dt:1 evolution:2 qw:1 qx:5 arxiv:1 qa:1 qn:1 multiplying:1 observes:1 national:1 see:2 biedenharn:1 brazil:1 hilbert:1 commutation:4 federal:1 review:1 written:6 simplest:1 invariant:6 approach:3 macfarlane:1 shabat:2 nature:1 however:1 article:1 contract:2 context:1 point:1 simple:1 dutt:1 dimensional:3 pessoal:1 associated:4 reflectionless:1 described:1 aˆ:12 px:2 been:1 ph:1 algebras:5 supersymmetric:1 coherent:10 former:1 case:3 replaces:1 exponential:2 eigenstate:1 cast:1 pˆ:3 refs:1 ir:1 balantekin:3 ii:1 rio:1 grant:1 granted:1 l223:1 paulo:1 quant:1 emphasize:1 finite:2 independent:1 used:2 lie:5 hand:2 phy:1 potentials:10 infinite:5 invariance:4 uˆ:2 estado:1 recent:1 barut:2 self:7 left:2 detail:1 shape:10 immediately:1 alternative:1 eigenstates:1 conjugates:1 belongs:1 lett:3 easy:1 solvable:3 transformation:1 generalized:2 identical:1 eigenvalue:1 possible:1 harmonic:2 using:6 like:1 either:1 integrals:1 arbitrary:2 right:2 czech:1 some:1 atakishiyev:1 provided:1 cooper:2 does:5 prob:1 inserting:2 equivalent:1 revtex:1 between:1 chuan:1 usa:2 floreanini:2 prove:1 discussed:1 o:3 introduced:9 perelomov:1 previously:1 into:6 bound:1 down:1 appropriate:1 references:1 operator:6 hep:2 log:2 support:2 there:1 was:7 function:7 form:5 funds:1 but:2 funda:2 wisc:3 girardello:2 similar:7 called:1 mechanics:3 constant:1 defined:4 coincides:1 abstract:1 ao:4 general:3 tˆ:7 exist:1 aizawa:1 pis:1 universidade:1 functions:1 no:3 when:1 cˆ:6 department:2 nt:1 pesquisa:1 problems:1 a1:39 a0:6 a2:7 algebraic:4 vinet:1 equivalently:1 time:4 chaturvedi:1
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quant-ph9811062.txt |@word consider:2 rev:7 amplifier:21 resistance:2 commute:2 fout:1 consists:1 francesca:1 amplified:1 reynaud:5 amplification:8 paris:2 tr:1 braginsky:1 tp:3 finally:1 σcc:1 th:1 under:1 tf:1 tb:5 worth:2 sent:1 ta:4 case:3 advantage:1 far:1 2rf:1 implicitly:2 brossel:1 readout:8 rl:25 continued:1 2rp:1 level:1 solution:1 optica:1 large:2 optics:2 heidmann:1 mullen:1 zf:19 sign:2 zero:3 further:2 port:3 linear:7 spectral:1 aim:2 plays:2 appear:1 apparatus:5 sum:1 while:1 current:10 goes:1 sup:1 new:4 erieure:1 σii:2 viii:1 annalen:1 led:1 exchange:1 respectively:3 gathered:1 here:3 met:1 operating:3 2kb:1 directions:1 dissipated:1 equations:6 appears:1 change:1 deduced:2 obtained:2 incoming:1 involved:1 leaves:1 studied:2 allows:1 resulting:1 characterizing:1 commutators:1 usually:1 pathologies:1 helps:1 named:1 stabilization:2 extra:1 conditions:1 should:2 use:2 working:1 commun:1 positive:1 contains:1 negative:1 france:1 depicted:1 a29:1 butterworth:1 entails:1 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quant-ph9811063.txt |@word concept:3 consider:8 helstrom:1 global:1 results:2 four:2 rˆ:3 lkn:4 calculate:2 alamos:1 presents:1 finally:1 device:5 contours:1 under:1 tr1:2 breach:1 analogous:1 tr2:2 worth:1 norm:1 applied:2 straightforward:6 very:2 springer:1 formula:2 mixing:2 husimi:5 nieto:1 difference:1 al2:1 condition:1 splitter:19 presented:2 chains:1 notes:1 quadrature:3 convenience:1 indices:1 optics:1 setup:1 prudnikov:1 lecture:1 direct:1 further:3 port:7 subscripts:1 index:2 apparatus:2 specification:2 brief:1 m31:1 ˆa:1 ˆd:1 new:3 ˆk:1 ˆm:1 ˆn:6 edited:1 degree:1 respectively:2 component:4 here:3 behaviour:1 desired:1 objects:1 november:1 equations:8 obtained:4 study:1 studied:2 commonly:1 yˆ:31 action:4 suitable:1 plotted:2 composed:1 appropriately:2 buˇzek:1 via:1 useful:1 projection:1 hermite:1 summations:1 logical:1 addressed:1 summation:1 operational:1 use:1 commun:2 positive:1 grabowski:1 hilbert:3 comparing:1 noting:1 ψn:3 therefore:2 eϕ:1 type:4 theoretical:1 more:2 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quant-ph9811064.txt |@word inverse:1 emch:1 allowed:1 consider:19 subindices:2 strengthened:1 both:3 brownian:4 existing:1 kuleuven:3 commute:2 generalize:1 reinhold:1 go:2 homomorphism:1 expressions:1 contributions:6 nested:2 whose:1 c0:1 terms:6 violate:1 providence:1 γs:2 concerned:2 deterministic:1 ts:3 tq:1 tn:15 rightmost:1 tj:9 θt:4 excluded:1 under:5 stochastic:3 include:1 norm:1 certain:1 p2:2 labels:1 saying:1 presently:1 straightforward:1 sitting:1 very:3 assuming:1 translations:1 springer:1 subject:2 choice:2 corollary:6 p1:2 get:1 lecture:1 mixing:4 manageable:1 condition:16 partitions:11 randomness:5 narnhofer:2 level:2 irreducible:1 notes:1 tokyo:1 t2:48 t3:6 t1:65 large:9 discrete:5 proposition:20 rj:2 car:1 indices:7 eigenvalues:1 its:4 upper:1 strongly:11 smaller:1 version:1 zk:2 dealing:1 measurable:2 imply:4 lines:1 zu:1 dynamics:12 estimated:1 odd:6 canonical:1 subscripts:1 will:11 abb:1 developed:1 appear:7 incompatible:2 trivial:2 section:7 mf:2 kus:1 uniform:3 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quant-ph9811066.txt |@word magnetic:1 results:8 leads:1 roy:1 ge:1 tricomi:1 computation:1 types:1 cot2:1 faster:1 rigorously:1 whose:1 const:1 calculate:1 editors:1 presents:1 monotonically:2 present:4 hill:1 applied:1 amplitudes:1 straightforward:1 far:2 2ωe:1 rise:1 conditions:1 seemingly:1 choice:2 summarized:2 jacob:1 emphasized:1 difference:1 exact:8 condition:1 riemann:1 hamiltonian:3 turns:4 erratum:1 solution:4 damped:3 large:34 τrelax:3 convenience:1 dealt:1 small:33 eigenvalues:1 optics:1 upper:6 smaller:1 oscillation:5 10b:2 10c:1 consistent:1 10a:1 estimates:1 jump:32 elegant:1 zero:3 displays:1 theory:1 even:3 what:1 plays:1 appear:4 clock:2 near:2 above:6 values:15 increasing:2 method:2 contrast:1 respectively:2 never:3 equals:2 here:6 understanding:1 met:1 tangent:2 illustration:1 relaxation:21 ratio:2 along:1 equations:5 appears:1 extreme:1 box:1 remark:1 suitably:2 institute:1 studied:1 zener:9 usually:1 resonance:2 a4a:1 narrow:1 changes:2 plotted:4 followed:1 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