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quant-ph9907099.txt |@word represent:1 consider:1 remarkable:1 rev:8 four:1 per:4 computation:2 cerf:1 zone:1 program:1 worth:1 applied:1 amplitudes:1 federation:1 advantage:2 orthogonal:1 far:1 polarization:20 wave:18 figs:1 stays:1 experimentally:3 matrices:2 condition:2 joined:1 leave:1 vector:7 optics:2 inserting:1 sin2:3 second:1 what:1 nonlinear:1 appear:1 axes:1 experiment:4 3n:1 new:2 3a:3 d1:3 paradoxical:1 pinhole:2 degree:1 respectively:2 never:1 component:2 here:3 atoms:1 directions:1 path:6 along:2 digits:1 shift:1 leaves:3 larger:2 accomplished:1 schumacher:1 action:2 shifting:1 klyshko:3 diameter:1 via:6 spatially:1 explained:1 logical:1 eiφi:1 total:1 use:3 noncollinear:1 arms:2 noting:1 therefore:1 type:8 creates:1 more:1 separated:1 introducing:3 becomes:1 operators:1 visibility:2 reversible:1 normalized:1 particular:1 known:1 cases:1 high:2 join:1 mm:1 setup:4 work:2 spontaneous:2 deg:3 ions:1 figure:1 give:1 states:19 indicates:1 performed:4 degenerate:3 sense:1 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quant-ph9907100.txt |@word gans:1 monte:3 concept:2 managed:1 remarkable:2 brownian:15 four:2 known:6 go:1 localized:6 gh:1 whose:1 preserves:1 violate:2 ty:1 environment:5 finally:1 excluded:1 under:1 stochastic:16 resources:2 applied:2 g1:8 g0:10 far:1 rise:2 percival:6 wave:3 jack:1 exact:2 collett:1 condition:1 osi:7 hamiltonian:4 turns:3 solution:2 damped:3 large:1 vector:1 math:2 markov:5 optics:3 gnutzmann:1 smaller:6 force:2 strunz:7 jump:1 rate:3 zt:5 further:1 dynamics:7 chem:1 carlo:3 zs:1 even:4 established:1 nonlinear:4 zhang:1 version:2 new:4 method:2 edited:1 δzs:3 led:1 respectively:1 realizations:2 here:7 understanding:1 desired:2 plenio:1 address:2 represented:1 along:1 equations:5 obtained:3 great:1 institute:1 larger:2 allows:1 holmes:1 via:1 scales:2 castin:1 plenum:1 apply:1 total:2 imaginary:2 use:3 takes:2 would:1 remains:1 contains:1 ψt:20 classically:4 therefore:1 memory:8 taken:1 noisy:1 type:1 more:4 almost:5 guckenheimer:1 becomes:2 operators:1 apparent:1 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quant-ph9907101.txt |@word consider:1 rev:1 scalar:2 tr:2 infinitesimally:3 th:3 under:1 orthogonal:1 frequencies:1 rise:2 springer:2 hamiltonian:6 accidentally:1 discrete:5 vector:7 dealt:1 small:3 zero:6 arnold:1 even:1 apparatus:1 axes:1 possibilites:1 reconstruction:3 values:5 consisting:1 degree:1 here:2 desired:1 directions:2 along:1 obtained:1 technical:1 vectors:6 nationalfonds:1 uniquely:1 appropriately:2 projection:2 family:1 elaborated:1 iph:1 weigert:5 stern:1 linearly:1 working:1 dnn:1 therefore:1 associated:4 elliptic:1 hermitean:3 operators:7 berlin:1 known:1 keeping:1 mn:13 det:2 obvious:1 example:2 proof:2 leonhardt:1 give:1 expanding:1 states:9 sphere:2 numbers:2 occur:1 axis:1 information:1 provide:2 s2:2 means:1 product:2 algebra:1 may:1 variant:1 orbits:1 man:2 light:1 redundant:1 st:3 fictitious:2 acknowledges:1 hedgehog:2 restriction:1 indeed:2 over:1 move:1 symbols:1 including:1 statistical:2 its:3 la:1 chosen:2 tori:1 expectations:1 differently:1 weber:1 non:3 thereby:1 they:1 rotation:1 now:1 nor:1 2s:8 university:1 identified:1 each:1 accompanied:1 universit:1 side:1 schemes:1 financial:1 energy:3 related:1 measure:1 quantum:3 shown:4 matrix:7 space:9 gradient:1 restricted:1 since:3 parametrizing:1 looking:1 method:1 acting:1 performs:1 linear:5 york:1 put:1 greub:1 motion:1 turn:2 probability:2 symbolic:1 number:3 precisely:1 open:1 given:3 hyperbolic:1 system:3 brevity:1 statement:1 hedgehogs:3 gives:1 exactly:1 july:1 aims:1 determined:2 were:1 result:2 constellations:1 separatrices:2 seen:1 any:6 angle:1 physique:1 take:1 calculus:2 most:2 regular:1 phase:2 acknowledgements:1 class:1 invertible:1 flow:1 traditional:1 points:7 exp:1 typically:1 saying:1 thomas:1 particularly:1 show:1 implying:1 relation:1 gerlach:1 slov:1 based:1 parameters:1 only:1 integrable:1 do:2 quantph:1 exceptional:1 dependent:1 de:2 expectation:2 methods:1 words:1 new:1 dt:1 spikes:1 arxiv:1 summary:1 qa:4 gram:3 contain:1 switzerland:1 through:1 fixed:5 qn:6 set:2 relative:1 differentiable:1 close:5 constellation:12 satisfying:1 state:4 closed:2 invariant:1 neither:1 approach:1 ends:1 opening:1 visualise:1 job:1 unnormalized:2 come:1 infinitely:1 equal:1 passing:1 comes:1 arbitrarily:3 among:1 ch:2 co:3 point:2 reasons:1 corresponds:1 dimensional:3 polynomial:2 respect:2 considering:1 ps:1 described:1 basis:8 addition:2 three:2 been:3 describes:1 foliated:1 ph:3 ko:2 determinant:4 sufficient:1 coincides:1 coherent:11 curves:2 angles:1 spin:12 srivastava:1 value:1 choices:1 will:3 gnn:2 planar:1 ir3:2 almost:4 thus:1 according:1 itself:1 cone:1 vanish:1 agarwal:1 different:3 author:1 generic:1 same:1 quant:3 finite:2 independent:4 conceived:1 upon:1 hand:1 levels:1 purpose:1 nevertheless:1 well:1 components:3 dimension:1 just:1 distribute:1 uller:1 stratonovich:1 density:3 regarded:1 guaranteed:1 simple:1 other:4 real:2 possibly:1 press:1 using:1 theor:1 necessary:1 specific:1 either:1 spins:1 mathematical:1 right:1 cones:1 classical:3 happens:1 provided:1 measurements:1 does:1 unit:5 measuring:2 selfadjoint:1 stefan:2 rue:1 found:1 hilbert:2 about:3 freedom:1 o:1 act:1 consequently:2 projectors:6 cambridge:2 into:2 integral:1 down:1 appropriate:1 weyl:1 references:1 determine:3 operator:7 often:1 institut:1 support:1 there:3 appl:1 way:2 naturally:1 function:2 form:1 vanishing:1 hs:2 jul:1 ns2:1 quorum:2 made:1 variations:1 up:1 us:2 distribution:1 mechanics:1 constant:3 certain:1 abstract:1 proven:1 denote:1 kaufman:1 single:1 exist:1 nns:1 entirely:1 nn:28 unambiguously:2 spatial:1 ns:16 elements:1 symbol:5 generated:1 observables:1 equivalently:1 time:2 n0:4 n1:1 starting:1
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quant-ph9907102.txt |@word concept:3 partial:1 consider:8 remarkable:1 induces:1 magnetic:3 leads:1 eds:2 scalar:5 extrapolated:1 rebbi:1 computation:1 4e2:1 whose:1 certainly:1 boghosian:1 depend:1 finally:1 those:2 whatsoever:1 under:7 applied:1 amplitudes:9 far:1 deviates:1 wave:4 every:1 ishikawa:1 cellular:2 affect:1 difference:1 exact:1 four:1 immediately:1 hamiltonian:9 irreducible:1 large:1 discrete:3 vector:11 phase:2 small:1 relation:2 originally:1 consistent:1 plaquette:6 sign:6 zero:1 design:1 further:2 dynamics:3 canonical:3 even:1 reviews:1 what:1 christ:1 fine:1 sum:3 interactions:1 analogously:1 expressed:1 d3:3 version:3 above:1 ˆi:1 ˆj:4 except:1 contrast:1 coefficient:1 full:3 led:1 lee:1 reverses:2 spacing:3 preserves:1 here:6 desired:1 inversion:2 concluding:2 consideration:1 along:1 quite:1 equations:1 interpret:1 differential:1 obtained:1 remark:1 technical:1 shift:2 vectors:2 reason:3 action:1 changes:3 uniquely:1 emerge:1 via:1 useful:1 gluons:1 extra:2 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quant-ph9907104.txt |@word concept:1 alj:1 consider:3 pointing:1 magnetic:1 lack:1 δi1:1 scalar:2 entropy:11 computation:1 partial:1 contributions:1 whose:2 depend:1 violate:1 esf:1 knill:1 concerned:2 disturbances:1 tr:7 nonlocal:1 does:2 under:8 tr1:2 tr2:1 worth:1 straightforward:4 orthogonal:2 very:5 print:1 valued:1 matrices:1 condition:12 routledge:1 knight:1 fragile:1 ψ1j:3 large:4 vector:2 demonstrated:2 indices:1 chuang:1 mahler:1 vincenzo:1 neighborhood:1 disordered:2 hillery:2 second:1 design:4 perspective:1 implemented:1 selfadjointness:1 ues:2 theory:11 even:1 what:4 appear:2 sun:13 sum:1 expressed:1 new:3 ever:1 consisting:1 satisfy:1 αij:4 concepts:1 desired:1 iσy:2 plenio:1 ansatz:3 separation:1 represented:2 observing:1 appears:1 hansen:1 suitably:1 studied:1 amount:1 resulting:4 permutation:2 usually:1 resonance:1 changes:1 involves:2 uniquely:2 tasks:1 useful:1 vil:3 addressed:1 linearly:1 use:1 expresses:1 would:3 massar:1 covariant:8 negative:3 properties:3 spp:1 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quant-ph9908002.txt |@word represent:10 gt:2 consider:3 limited:1 results:4 four:5 generalize:1 computation:1 edu:1 row:2 whose:6 inverse:2 concerned:2 γi:4 ϕi2:1 γn:1 th:12 under:2 1p:4 case:2 belonging:1 supported:1 orthogonal:25 p0:20 denoted:1 σxs:1 difference:1 exact:2 condition:5 illustrated:2 level:1 guo:7 xih:1 σxp:2 vector:2 mn:3 deutsch:2 hillery:2 second:1 port:6 machines:3 linear:9 even:1 what:2 sub:1 giving:1 diag:11 section:5 realizing:1 expressed:1 networks:5 access:1 sequential:1 above:11 destroyed:1 new:8 net:1 method:6 contrast:1 satisfy:1 margolus:1 respectively:2 applies:2 here:4 china:3 others:1 represented:1 obtained:3 great:2 vectors:3 prior:3 products:3 schumacher:1 makes:1 uniquely:2 va:2 boolean:1 aimed:1 apply:1 total:1 circumvent:1 use:5 prove:1 remains:1 toffoli:2 tl:2 ψj:2 ψi:29 m1:3 iαk:2 m2:3 ineq:2 tell:1 marginally:1 more:2 introducing:2 successful:2 operators:3 about:3 normalized:1 cases:1 iii:2 must:5 science:2 equation:2 work:3 mi:11 acts:2 itself:2 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quant-ph9908003.txt |@word limited:1 consider:4 global:3 results:8 schatten:1 computation:1 edu:2 deterministic:9 tr:8 tween:1 efficiencies:1 under:1 norm:1 belonging:1 orthogonal:11 focus:1 matrices:1 categories:1 presented:1 guo:5 dis:1 upper:1 hillery:4 estimated:1 equation1:1 linear:1 even:1 what:2 nonlinear:1 giving:1 diag:3 above:6 method:3 satisfy:2 degree:1 respectively:1 realizations:1 here:2 met:1 china:3 address:2 represented:2 equations:1 obtained:4 completely:1 products:2 adopting:1 buˇzek:1 griffiths:1 natural:1 flexibility:1 linearly:1 massar:2 probabilities:4 positive:1 contains:1 ψj:3 ψi:7 therefore:1 ineq:1 more:1 optimizing:1 bennett:1 formally:1 operators:1 about:4 berlin:1 must:3 springer:1 fulfils:1 science:2 equation:4 work:1 following:2 strategies:1 proof:1 wang:1 figure:1 give:4 process:1 preserving:1 states:48 numbers:1 occur:1 verify:1 divided:1 means:3 machine:6 how:2 criterion:2 pure:2 optimal:19 ψim:4 ψin:15 product:1 may:8 max:5 clone:16 after:1 derived:3 produce:1 designed:1 attempt:2 resemble:2 interpolates:1 ones:1 allow:1 operate:1 acts:1 interpretation:1 produces:1 zek:4 vary:1 satisfied:1 fidelity:10 still:2 perfect:1 derive:2 chosen:2 exact:7 li:3 better:2 estimating:2 offers:1 choose:3 communication:2 main:1 them:1 greater:3 bruss:1 they:2 now:1 easily:1 always:4 university:1 identified:1 inequality:6 each:1 found:1 2n:1 macchiavello:2 mean:1 independent:3 ee:1 blank:2 extended:1 measure:1 quantum:17 laboratory:1 eq:8 special:1 divincenzo:1 shown:2 matrix:8 space:4 electronic:2 since:6 rev:17 performs:1 ref:5 correct:10 math:1 foundation:1 theory:3 diagonal:3 reason:1 jozsa:1 definition:1 could:1 omit:1 programming:1 explored:1 consequence:1 initial:3 probability:13 erroneous:4 enumerate:1 open:1 given:3 rewritten:1 unitarity:1 unknown:1 system:5 needed:1 compromise:1 perfectly:4 final:5 gives:2 exactly:2 part:1 opti:1 than:6 wootters:1 target:2 fuchs:1 require:3 were:1 result:5 remained:1 constrained:1 any:3 lie:2 note:1 potential:1 machines:3 continuous:1 fopt:4 though:2 jun:1 reach:2 most:3 errors:1 letter:1 device:1 probabilistic:5 why:1 considered:1 average:9 later:1 implications:1 braunstein:1 physics:1 χj:2 χi:5 supported:1 merit:1 find:2 principal:1 feng:1 popescu:1 parameters:1 92a:1 should:6 only:3 bases:1 do:2 cryptography:1 get:1 dependent:7 inconclusive:5 zurek:1 cannot:3 closely:2 evolution:3 arxiv:1 yield:1 summary:1 ψjm:1 ψjn:3 set:6 exists:2 achieved:1 national:1 bounds:1 see:1 cloning:13 fail:1 close:1 violates:1 statedependent:1 error:2 ways:2 hybrid:2 please:1 state:15 identification:2 between:7 αi:19 αj:2 approach:1 notice:1 nature:1 however:5 hefei:1 come:1 σn:3 according:1 connection:4 interesting:1 estimation:16 among:1 cn:2 simple:1 dimensional:1 pati:1 werner:2 maximize:1 lagrange:1 respect:1 basis:1 discrimination:3 copies:10 been:3 strategy:2 describes:3 ph:1 ariano:1 cerf:1 corresponding:1 linearity:1 subspace:4 uqcm:1 determination:1 those:5 case:1 intriguing:1 pacs:1 value:2 will:2 while:1 suppose:1 aij:2 situation:2 property:1 unitary:6 thus:4 non:6 probabilistically:1 equal:1 characterize:1 duan:2 zhang:3 technology:1 acknowledgments:1 make:2 quant:1 φi:4 φj:2 finite:1 φn:2 difficult:1 fairly:1 used:1 hand:1 keyl:1 infinite:2 niu:1 prescribed:1 lower:7 maximizing:1 nevertheless:1 obviously:1 without:1 solve:1 prescribes:1 sets:1 guang:1 just:1 less:1 generally:1 obtain:5 identify:1 λi:9 λn:2 wei:1 priori:1 lett:13 theorem:2 input:1 transformation:3 opt:2 bij:2 increased:1 optimality:3 possible:4 spanned:3 know:1 using:1 mod:2 success:3 follows:1 either:2 arbitrary:2 output:5 inter:2 fulfil:1 because:1 people:1 some:2 ideals:1 provided:1 eiν:1 best:1 does:2 unit:1 refer:1 dieks:1 equivalent:1 bu:4 prohibited:1 yuen:2 hilbert:1 bz:1 chuan:2 eavesdropper:1 freedom:1 discussed:1 o:11 introduced:1 op:1 h2:1 ηn:1 into:1 chefles:1 bound:16 ηi:9 determine:2 operator:1 span:2 measured:1 there:4 question:1 approximate:2 inner:3 was:1 function:3 barnett:1 smolin:1 denoting:1 but:1 cloned:5 clones:3 cloner:3 applying:2 cij:4 cii:3 maximum:10 below:1 limit:5 problem:3 similar:1 called:1 gisin:1 constant:1 defined:2 universal:3 describe:2 condition:3 general:1 satisfies:1 exist:1 our:4 physical:1 incorrect:2 discriminate:4 no:3 ekert:3 when:3 multipliers:1 tight:2 other:1 republic:1 department:1 conclusion:1 elements:3 generates:1 ustc:2 meaning:1 important:3 transfers:1 auxiliary:1 fact:2 time:1 recalled:1 original:3
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quant-ph9908004.txt |@word limited:1 depends:1 comparatively:1 switches:1 ceased:1 ρt2:2 computation:1 consists:1 follow:1 feeding:1 depend:1 including:1 tj:4 under:4 td:18 include:1 amplitudes:2 continues:1 print:3 hewlett:1 difference:1 splitter:4 level:8 knight:3 proposals:3 large:2 vector:1 phase:3 small:1 entropy:1 optics:1 programme:2 upper:1 direct:1 jump:3 second:1 uk:1 concludes:2 implemented:1 leakage:1 theory:1 even:1 established:1 sub:1 section:1 experiment:1 above:3 increasing:4 satisfy:1 supporting:1 exchange:1 respectively:3 realizations:1 lange:1 teleportation:19 here:3 atoms:7 plenio:5 κt:2 consideration:3 convert:1 institute:1 shift:3 studied:1 amount:1 procedure:2 action:2 portions:1 implement:1 makes:1 via:2 extra:1 requiring:1 outcomes:2 total:2 estimate:1 unit:1 plot:1 use:1 takes:2 would:1 briegel:1 distinct:2 next:1 noting:1 call:1 noisy:1 type:1 prep:3 more:1 lowering:1 initiated:1 successful:8 initial:6 operators:3 ti:2 proceed:1 known:1 cases:5 must:2 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quant-ph9908005.txt |@word partial:2 consider:3 separates:3 results:1 mnw:1 ge:2 research:2 whose:2 depend:5 calculate:2 aug:1 mwc:1 quasi:2 program:1 γn:8 under:11 case:2 2γn:1 hibbs:2 song:4 rise:1 differently:1 choice:4 wishes:1 hannay:3 exact:1 condition:1 hamiltonian:10 turns:1 solution:5 t0:2 quasiperiodicity:2 noted:2 force:13 periodicity:3 zero:3 value:2 further:1 even:3 axes:1 uniform:1 pulsating:1 values:1 method:1 satisfy:1 lee:3 respectively:1 equals:1 here:1 address:2 path:2 along:2 change:8 obtained:2 divisor:1 periodic:17 action:2 adopting:1 fourier:2 winkler:1 classification:1 requiring:1 unit:1 use:2 additive:2 asymptotic:1 would:2 remains:1 positive:1 depicted:1 ψn:4 therefore:1 more:1 odinger:1 carrying:1 particular:2 known:3 cases:4 must:2 equation:6 oscillator:17 mw:6 obvious:1 already:1 making:1 example:3 compare:2 figure:5 give:2 sense:1 states:2 minimum:1 numbers:1 allowed:1 absolute:2 needs:1 rather:1 parameter:1 sin:4 irrational:1 algebra:1 may:10 after:1 fd:1 coming:1 representations:4 horizontal:1 wave:18 fn:6 short:1 dynamical:4 so:4 representation:25 acknowledges:1 order:5 indeed:2 pointed:1 satisfied:2 perceptive:1 through:1 motions:3 mentioned:1 still:1 its:1 acknowledge:1 τf:8 interesting:1 choose:2 mail:2 might:1 dae:1 non:1 they:2 half:2 now:1 above:1 eigenvalue:1 finite:5 2p:3 university:3 2c:6 found:2 2n:2 en:2 financial:2 gaussian:1 related:1 frequency:7 year:1 quantum:3 special:5 out:2 shown:6 driving:10 space:1 rep:1 since:4 rev:10 denotes:1 hill:2 dxdt:1 formula:3 hψn:1 math:5 foundation:1 theory:1 free:1 york:2 care:1 could:1 motion:6 view:2 origin:1 there:9 probability:2 number:4 construct:2 says:1 xp:15 angular:6 aharonov:3 given:10 introduction:1 leading:1 system:22 least:2 needed:1 floquet:2 gives:7 park:1 part:2 authors:1 x2:1 anandan:3 than:1 coefficients:2 distance:1 cyclic:1 finiteness:1 submitted:1 determined:2 undriven:4 w2:2 generality:1 curves:3 need:2 nτ0:6 any:10 depict:2 angle:2 magnus:1 take:3 korean:1 formulas:1 though:1 who:1 iwt:1 formulae:1 phase:59 observation:1 considered:3 clear:1 feynman:3 exp:6 χn:3 physics:1 fact:6 dover:1 pandey:2 show:2 lewis:3 relation:7 solutions:20 find:5 subtracting:1 parameters:5 title:1 only:3 explicitly:1 circle:2 over:6 continuity:1 do:1 goes:1 dependent:3 overall:1 dys:1 dz:1 closely:1 new:2 dt:5 gen:3 adiabatically:1 evolution:19 arxiv:1 cycled:1 acknowledgments:1 paper:2 common:1 london:1 sho:20 kernel:3 ser:1 exists:5 national:2 packet:2 observed:1 naturalness:1 depends:6 radius:1 result:2 phases:2 satisfying:1 mechanically:1 ways:1 circulating:1 written:9 closed:3 between:1 invariant:2 geometric:2 approach:1 wf:2 korea:3 terms:6 vertical:1 however:1 wt:9 ji:3 both:1 cos:15 enables:1 many:1 berry:51 contribution:4 comes:1 point:1 simple:4 ca:1 period:13 simply:1 moreover:1 pp:1 described:1 transformations:1 equivalent:1 due:2 been:6 ph:2 systems:1 corresponding:5 george:2 fund:1 external:3 child:2 mcw:1 c2:2 general:16 those:1 p2:2 defining:1 evaluated:2 will:9 while:5 property:1 unitary:1 almost:1 thus:6 iv:3 im:3 ic:1 different:5 suggest:1 make:1 same:1 shorter:1 complex:1 quant:2 several:1 independent:5 used:4 infinity:1 nγn:1 trajectories:1 driven:6 kim:6 recent:1 mρ2:1 schr:1 no:2 well:4 without:2 sets:1 coordinate:1 being:1 obtain:1 alternative:1 multiples:1 infinitely:1 except:1 lett:3 theorem:2 iπ:1 eigenstate:3 generalized:1 real:1 around:1 khandekar:1 possible:3 harmonic:13 adiabatic:1 δn:5 integrals:1 arbitrary:1 become:1 stationary:10 classical:28 some:6 choosing:2 nonzero:1 kwangju:1 does:5 linearly:5 proc:1 kruskal:2 agreement:2 2m:2 losing:1 analyses:3 bz:1 yeon:2 integers:1 carried:1 mcgraw:1 recognized:1 compatible:1 soc:2 presence:5 soh:1 into:3 integral:2 references:1 determine:1 operator:2 conceptually:1 additional:3 assumed:1 support:2 initial:1 u2:1 quadratic:3 way:2 was:3 propagator:1 function:6 complete:1 hw:1 but:1 hn:3 pp4:1 line:3 directed:1 made:3 applying:1 circulation:1 uv:1 up:2 um:2 distribution:2 define:2 calculated:1 mechanics:1 ac:2 diverges:1 constant:8 moore:2 defined:20 abstract:1 describe:1 denote:1 exist:4 inc:1 again:1 functions:10 kr:2 dashed:2 detail:1 application:1 department:2 mathematics:1 conclusion:1 velocity:1 curve:2 mass:9 time:11 n2:2
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quant-ph9908013.txt |@word camacho:8 concept:1 consider:6 lagrangian:3 results:4 eds:2 generalize:1 controversial:1 follow:1 gm:12 contributions:1 forget:1 particles:6 aug:1 i2:5 equivalence:4 γt:30 finally:4 present:3 under:5 include:3 case:22 lrb:1 hibbs:1 very:8 frequencies:1 continues:1 springer:1 wave:2 2γt:14 experimentally:1 difference:5 condition:7 school:1 level:7 positions:1 proposals:2 try:1 phase:2 equation:2 employing:1 says:1 b29:1 cosh:38 approximation:3 second:2 qualitatively:1 dynamics:2 expressions:7 even:4 plays:1 appear:2 current:2 experiment:8 goes:1 new:12 falling:1 acknowledgments:1 movement:1 justification:1 whose:5 mω:1 here:13 atoms:1 sinh:46 path:10 appears:6 change:3 deduced:3 obtained:2 remark:2 dehmelt:1 institute:1 involved:2 feasibility:2 allows:3 controversy:2 shall:1 resulting:1 sternwarte:1 action:1 hospitality:1 devices:2 changes:1 projection:1 polonica:1 neutrons:1 resolutions:3 use:1 would:3 contains:2 predictions:6 process:8 going:2 therefore:4 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quant-ph9908014.txt |@word ibid:1 dewitt:1 consider:11 crucial:1 magnetic:1 global:2 results:7 produce:1 illustrated:2 obstruction:2 rˆ:4 commute:1 overlap:1 gˆαβ:2 expressions:1 excluded:2 once:1 hole:1 issues:5 whose:20 certainly:5 inverse:1 depend:1 patches:2 regularization:1 gˆ:2 eigenbasis:16 equivalence:1 undetermined:1 removal:1 supported:1 eigenspectrum:1 finally:6 pˆr:5 alvarez:1 those:7 whatsoever:1 umich:1 tf:6 connecting:1 include:1 presentation:1 applied:2 belonging:2 lack:1 amplitudes:1 risk:1 g1:19 far:3 2rf:2 translations:2 induce:1 qˆα:11 redefinition:4 ui:2 emphasized:2 difference:1 exact:1 condition:3 explanatory:1 entire:5 annihilated:2 immediately:1 hamiltonian:34 ref:12 scalar:12 correct:7 leave:1 discrete:6 vector:15 louvain:2 fnrs:1 generalises:1 manifestly:3 relation:2 programme:1 application:4 periodicity:1 oscillator:5 consistent:7 profs:1 direct:6 literature:1 sign:2 helicities:1 second:7 fiber:1 value:2 zz:1 incidentally:1 further:8 dynamics:16 q0α:1 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quant-ph9908017.txt |@word discards:1 ui:2 consider:1 results:1 four:2 roy:1 commute:1 follow:1 whose:1 depend:1 aug:1 deterministic:4 tr:1 send:4 under:2 resources:1 p2:1 belonging:1 kent:2 orthogonal:7 novel:3 affect:1 exact:14 iut:1 condition:2 generalised:1 leads:1 trb:1 guo:3 herbert:2 bangor:1 optics:1 vincenzo:1 says:1 consistent:1 direct:1 hillery:1 past:1 rate:3 street:1 further:1 machines:2 linear:3 even:4 index:1 what:4 abc:1 experiment:1 above:2 shared:2 consisting:1 chose:1 ρab:1 here:2 them:2 address:1 pati:3 along:2 sending:1 antisymmetric:1 involved:1 changed:1 allows:3 resulting:1 action:1 implement:1 buˇzek:1 via:1 useful:3 projection:1 explained:1 outcomes:2 hardy:4 total:1 unit:4 use:1 takes:1 would:4 distinct:2 ψi:15 call:2 more:2 separated:1 successful:2 becomes:1 operators:1 known:3 producing:4 must:1 kumar:1 ρb:2 postselection:2 equation:1 remain:1 sent:1 following:2 averages:1 example:1 abcd:2 give:3 process:2 states:31 allowed:1 axis:1 information:3 holds:1 machine:14 criterion:1 optimal:2 sin:6 product:1 superluminal:18 ancilla:1 clone:3 after:4 collection:1 povms:1 produce:4 joint:1 light:1 acknowledged:1 cosmology:1 keeps:1 subsequently:1 bipartite:2 operations:2 help:4 produces:2 amplifying:1 years:1 through:1 statistical:4 fidelity:1 still:1 write:2 derive:1 group:1 thank:2 chosen:3 ll:1 relativity:2 systems:2 wales:1 hidden:1 might:2 weber:1 correspondence:1 non:15 yj:2 evolution:3 they:4 party:3 now:2 february:1 university:2 orthonormal:1 iff:1 inequality:1 transmitted:2 each:1 found:2 macchiavello:1 subsystem:1 financial:1 barnett:3 idea:1 deterministically:1 measurement:12 quantum:23 operation:3 eq:2 special:2 out:5 secretly:2 shown:6 matrix:3 space:7 furthermore:1 since:4 rev:8 particles:1 performs:1 get:2 shows:2 theory:9 kok:1 possibility:3 quite:1 approaches:1 put:3 simplifying:1 hand:1 generate:1 could:1 times:1 place:1 hence:2 onto:1 βk:1 xj:3 xi:7 probability:12 number:5 infinite:1 multiplying:1 done:4 blank:2 carry:1 impossible:2 message:1 given:7 unitarity:2 unknown:1 system:14 their:1 passed:1 wootters:1 asymmetric:1 doomed:1 exactly:6 speakable:1 part:4 copy:1 than:5 distance:1 kind:2 zero:6 preparation:1 arun:1 outcome:3 result:5 say:1 need:1 seen:1 tells:1 able:1 multiple:3 though:2 singlet:1 kar:1 letter:1 device:2 cloned:8 measured:1 ekert:1 observation:1 clear:1 dimension:1 braunstein:1 definitely:1 principle:1 fact:1 show:4 hb:3 stringent:1 find:2 based:2 should:1 only:5 going:1 local:6 do:3 his:3 means:2 dependent:2 zurek:2 famous:1 cannot:11 processes:1 podolsky:2 arxiv:1 yield:1 investigate:1 view:1 set:6 correlations:1 maximum:1 ancillas:2 namely:1 cloning:31 discussions:1 satisfying:1 state:18 smallest:1 various:1 between:2 invariant:2 αk:1 recently:1 nature:3 however:4 gratefully:1 distinguish:4 suggested:1 observable:2 cos:6 stages:1 many:2 taking:1 against:1 admit:1 context:1 qubit:2 finds:2 ck:1 bruß:1 bell:2 had:1 dimensional:1 probing:1 exploit:1 described:2 basis:10 discrimination:2 due:2 been:4 pa:4 combined:1 pj:4 pk:3 ph:4 pi:13 abstract:1 define:1 ariano:1 photon:1 spin:2 case:3 p0:12 p1:7 choices:1 will:2 suppose:2 aij:1 situation:1 procedure:1 unitary:7 vi:5 vj:1 vk:3 thus:5 site:2 probabilistically:4 ij:1 duan:4 ib:2 different:2 make:1 belong:1 lett:8 same:2 any:3 quant:4 copying:1 mixtures:4 φi:5 φj:1 φk:1 interpolation:1 independent:11 used:5 conceived:1 possible:2 entanglement:1 bob:17 recent:2 epr:1 thought:1 contact:1 nb:3 know:2 ρbc:2 protocol:1 proposed:2 less:3 being:1 when:2 distant:2 inference:1 speed:2 density:3 regarded:1 seems:1 signals:6 location:2 theorem:1 input:3 transformation:2 depends:2 rules:1 term:1 entangled:5 press:2 using:5 ruled:1 like:2 success:7 performing:1 alice:11 wooters:1 yields:1 arbitrary:4 evolutions:1 conclusion:1 reduced:2 dean:1 classical:3 some:3 measurements:1 overlap:2 decomposition:1 linearly:12 provides:1 demonstrated:1 measuring:1 inaccurate:3 bc:5 dieks:2 communicate:1 agreement:1 yuen:2 refers:1 hilbert:6 about:1 actual:1 carried:1 constraint:2 instantaneously:3 mutually:1 projectors:1 cambridge:2 communication:2 chefles:4 bound:5 copies:2 references:1 einstein:2 operator:1 her:2 interacted:1 probabilistic:18 support:1 there:6 question:2 doubt:1 inner:1 way:1 forward:2 was:5 rimini:1 form:1 smolin:1 but:5 principles:1 failure:1 neutral:1 larger:1 clones:14 ha:2 true:1 proposal:1 he:2 whether:2 prevents:1 particle:8 us:7 limit:3 uk:5 attaches:1 ua:2 gisin:2 mechanics:3 possession:2 ab:6 proved:2 certain:4 universal:2 measure:1 linearity:1 general:1 single:3 exist:1 check:1 again:1 cim:2 no:11 na:3 whereas:1 rosen:2 composite:7 other:6 polarisations:1 superposition:2 allowing:1 studied:2 variable:1 song:3 network:1 remote:2 longer:1 eberhard:1 together:1 time:1 signalling:19 ghosh:1 nuovo:2 unspeakable:1
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quant-ph9908018.txt |@word restates:1 consider:12 φn1:10 φn0:3 forbidden:1 varying:1 desirable:1 results:14 integration:2 illustrated:5 roy:4 scalar:1 signatures:1 concerning:1 during:1 consists:1 expressions:3 contributions:5 localized:1 φn2:6 whose:1 certainly:1 inverse:2 const:1 calculate:3 aug:1 concerned:1 switched:1 bl:2 orthonormalized:1 simplify:2 finally:2 does:3 contours:1 th:2 under:2 analogous:2 include:2 worth:1 indicating:1 divergent:4 summarizes:1 applied:5 g4:1 amplitudes:2 expressing:1 orthogonal:2 very:5 listed:1 connects:1 choice:2 grid:1 p1:1 every:1 interpreting:1 intersecting:2 got:1 affect:1 snk:1 difference:10 exact:9 fourth:1 switches:1 propagating:2 exponential:2 ed:1 hamiltonian:51 positions:3 presumably:1 permits:1 michael:2 solution:46 t0:30 occurs:5 large:15 discrete:2 differential:1 phase:15 enclosing:2 small:13 eigenvalues:15 heading:17 proof:1 degeneracy:3 upper:3 χn0:1 smaller:3 neighborhood:8 renormalized:17 consistent:5 os:1 direct:2 sign:3 past:2 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quant-ph9908019.txt |@word limited:3 interference:3 desirable:1 gillespie:2 γt:1 under:6 ontological:2 spec:1 every:7 affect:1 cause:2 solution:2 vector:18 guiding:1 markov:2 ups:1 degeneracy:1 osmotic:3 force:1 concise:2 consistent:2 approximation:4 second:4 rigorous:1 even:7 established:1 incompatible:1 selected:1 above:2 new:11 increasing:3 coefficient:1 evolving:1 notions:1 never:7 equals:1 here:14 represented:2 path:1 interpret:1 obtained:4 rigorously:1 study:1 completely:8 changes:4 buˇzek:1 projection:2 discontinuous:2 explained:1 objectively:5 santini:1 total:3 unit:1 derivatives:1 would:37 negative:1 jaekel:1 call:5 therefore:32 type:5 tell:1 separated:1 odinger:15 berlin:1 reversible:1 physically:1 hold:1 must:19 springer:1 leavens:1 arndt:3 ml:1 work:4 mi:4 theories:1 mu:2 macroscopically:2 concepts:1 appraisal:1 transition:16 renormalization:1 give:1 relativistic:4 degenerate:4 feasible:1 cushing:2 hoc:1 healey:2 provide:2 how:6 answer:4 classify:1 description:1 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quant-ph9908021.txt |@word consider:2 grateful:1 sch:1 aug:1 charge:10 program:1 those:1 th:5 under:1 include:2 applied:1 advantage:2 capacitances:4 electron:1 sons:1 difference:3 matrices:1 level:3 positions:1 guo:1 large:1 discrete:1 small:4 oscillation:1 estimated:1 nonlinear:1 section:2 current:6 new:1 ǫsi:2 acknowledgments:1 nakamura:2 full:1 here:3 asymmetry:1 mev:1 q10:2 excess:2 q5:2 capacitively:4 change:3 shift:1 changed:1 studies:1 fujita:1 mobility:1 semiconductors:1 analyzing:1 total:2 conventional:2 commun:1 coupled:18 predictions:1 next:1 few:1 fet:1 vi:3 more:2 flat:1 odinger:1 vi2:1 appendix:2 vn:1 known:1 iii:1 crosses:1 science:2 equation:2 values:1 following:1 example:1 control:1 weaker:1 calculation:1 states:2 junctions:1 disappear:1 pure:1 gate:9 charging:3 wiley:1 derived:2 realized:3 short:3 dynamical:1 succeeded:1 blockade:1 σzj:1 si:4 so:2 σzb:1 σza:1 order:4 gershenfeld:1 john:1 mainly:1 paper:3 differs:1 japan:1 its:1 hackenbroich:1 constituted:1 bottleneck:1 longitudinal:1 ln:1 vth:12 lateral:1 solving:1 li:2 detected:3 fig:5 insulator:1 deformation:1 junction:3 ye:1 toshiba:1 band:1 effects:5 realize:1 easily:1 february:1 hamiltonian:2 l2:1 each:2 crossing:1 2ec:1 series:1 energy:15 related:1 constitute:1 investigated:3 measurement:2 quantum:33 approximated:2 eq:2 out:1 shown:4 since:1 rev:8 research:1 semiconductor:4 shows:2 linear:1 sio2:1 reason:1 formation:1 york:1 detecting:4 jozsa:1 interaction:1 r2:1 motion:1 length:1 transfer:1 first:1 ichimura:1 mosfets:1 array:4 size:1 given:5 temperature:1 width:2 introduction:1 behaves:1 system:8 assumption:1 leggett:2 n2b:1 asymmetric:1 continuous:1 environmental:1 than:1 detection:1 polarized:1 electrostatic:7 amplitude:1 were:2 toward:1 distinguished:1 zanardi:2 lowest:1 seen:2 relatively:1 livermore:1 vgi:2 depending:2 efficient:1 c72:1 mechanism:5 potential:2 take:1 negligible:1 channel:9 averin:4 electric:2 normal:2 connected:1 intrinsic:1 why:1 considered:4 ku:1 physics:1 vg1:4 vg2:4 shor:1 show:4 sze:1 minimizing:1 relation:1 threshold:1 q1:2 q3:2 q2:2 based:4 q4:2 q7:2 q6:1 q9:2 q8:1 state:17 viewpoint:1 di:2 dependent:1 cannot:1 ϕb:1 substrate:1 arxiv:1 factorization:1 circuits:2 qb:2 qi:2 fixed:1 set:3 electrodes:1 observed:3 see:1 computer:4 radius:1 discussions:1 recently:1 electrode:2 interacting:1 phonons:1 dipole:2 enough:1 between:6 tens:2 conditions:1 terms:2 nature:1 qubits:14 configuration:1 enables:1 many:1 region:7 σz:1 σx:1 qubit:9 estimation:1 comment:1 ci:1 point:1 cc:7 cb:10 ca:13 period:1 environments:1 cd:4 simply:1 moreover:1 fruitful:1 described:2 due:1 been:2 expected:2 ph:2 lett:4 dots:22 direction:2 corresponding:1 gemma:1 gar:1 c9:2 c8:2 c3:21 c2:2 c1:2 c0:3 c7:34 c6:25 c5:27 case:5 ǫb:2 ǫa:2 josephson:4 solid:3 ǫj:1 originate:1 will:2 behavior:1 σxj:1 tunneling:2 procedure:1 va:7 vb:6 larger:1 vd:6 vg:7 almost:1 characteristics:1 thus:2 surface:1 iv:1 ii:1 superconducting:1 bias:1 id:8 currents:1 author:1 shifts:1 quant:3 pauli:1 higher:1 development:1 used:1 hand:1 moment:1 levels:4 nanocrystals:1 expand:1 4ca:1 zµ0:1 drain:3 schr:1 center:1 largely:1 changes:1 well:1 analysis:1 contact:1 corporation:1 model:4 corporate:1 ekert:1 charged:2 gates:4 proposed:3 being:1 when:4 obtain:1 voltage:6 macroscopic:1 previous:1 mosfet:13 vd2:1 preprint:2 conclusions:1 source:2 attractive:1 c10:2 excited:1 b54:1 b55:1 increases:1 using:1 mod:2 vds:1 sizes:2 signal:1 tsukada:1 kawasaki:1 reduced:1 therein:1 because:1 some:1 koga:1 2c4:2 2c5:5 2c3:2 gurvitz:1 depletion:3 nmr:2 l1:1 oscillating:1 use:1 carried:1 2ci:1 andez:1 bloch:1 within:1 ferm:1 bath:1 references:1 rossi:1 theoretically:1 c52:1 assumed:3 there:1 long:2 capacitance:4 appl:2 was:3 function:1 2vg:1 fore:1 ec:5 cia:1 embedded:1 whether:2 attached:1 devices:2 ωj:2 fermi:2 distribution:5 similar:3 detailed:2 computing:1 devise:1 single:1 exist:1 controlled:3 operation:2 inc:1 nj:2 compared:1 nm:1 na:11 nb:12 nc:3 nd:5 field:2 other:1 tiwari:1 a1:2 generated:1 dissipation:1 n2:2 structure:7 qi2:1 individual:1 coupling:2 coulomb:1 assume:3 expands:1 coherent:1 phonon:3 dot:8 time:8 decoherence:8 shnirman:5
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quant-ph9908022.txt |@word monte:1 partial:1 rev:1 bull:1 results:2 roy:1 computation:6 foundations:1 consists:1 sci:2 primes:1 gk:12 devoted:1 superpositions:1 aug:1 producing:4 certification:2 cess:1 factoring:1 tn:16 finally:11 tk:5 th:5 under:2 eprint:1 norm:3 conjecture:3 supported:2 amplitudes:1 straightforward:2 far:2 kco:10 choice:2 unstructured:1 print:2 every:3 summarized:1 condition:8 subroutine:3 level:1 ref:15 large:1 convenience:1 undone:1 wagstaff:3 programme:1 upper:3 smaller:6 periodicity:3 zk:13 miller:1 α2k:1 sin2:1 go:1 design:2 further:6 estimated:1 odd:1 gm:3 even:2 errors:1 suc:1 sub:3 section:9 3p:2 find:1 witnesses:2 above:1 replaced:1 boost:1 method:2 sli:2 satisfy:5 full:1 respectively:4 error:4 here:2 behaviour:1 superpolynomial:1 b2k:5 undo:2 directions:1 change:2 obtained:2 search:2 institute:3 larger:3 periodic:1 alamos:3 usually:1 hospitality:1 fourier:6 makes:1 followed:1 extra:2 inducing:1 baillie:1 apply:1 counts:3 total:1 select:2 use:12 asymptotic:4 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quant-ph9908023.txt |@word represent:3 2nπ:1 sci:2 interference:4 particular:1 results:1 integration:1 gf:1 comments:1 contributions:3 reasoning:2 terms:1 aug:1 tn:1 efficiencies:1 device:1 preserved:1 under:2 exit:1 presentation:1 indicating:1 amplitudes:3 advantage:7 very:8 rise:1 wave:13 untenable:2 interpreting:1 decide:2 refractive:1 cook:1 emphasized:1 difference:2 condition:3 splitter:3 progression:2 presented:2 supports:1 proposals:1 integrated:1 large:1 harry:1 small:3 optics:1 round:30 upper:2 sin2:1 pulse:6 cosh:2 surrounding:1 second:5 doubt:1 traveling:1 further:1 click:5 even:3 aim:2 appear:1 opaque:2 sum:2 analogously:1 cell:11 experiment:23 above:3 new:3 paviˇci:3 contributes:1 bn:5 filled:1 coefficient:1 condensed:1 full:1 reverses:1 exchange:2 respectively:3 never:3 modify:1 here:1 atoms:1 ranges:1 objects:1 possibility:1 sinh:1 path:15 principle:2 wait:1 obtained:4 great:2 ref:1 incoming:14 receive:2 shift:5 changed:2 allows:2 approaches:3 leaving:1 amount:1 m3k:1 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quant-ph9908024.txt |@word secondly:3 companions:1 partial:2 sch:1 rx:4 demand:2 results:3 existing:1 four:11 gf:1 grateful:1 consists:1 consider:6 whose:5 aug:1 ty:5 equal:7 tu:2 nonlocal:3 containing:1 compensate:1 tj:3 present:3 under:2 presentation:1 p2:12 conjecture:1 emerged:1 orthogonal:5 very:1 frequencies:4 quadruples:2 none:2 wave:2 every:1 sidebands:1 experimentally:2 difference:4 exact:2 wipe:1 condition:1 splitter:55 modulator:2 presented:3 did:2 turns:2 brendel:1 t2:9 cascading:2 t1:9 leave:1 coincidences:3 phase:3 independence:1 resorting:1 realization:1 ups:2 upper:3 unexpected:1 force:1 foundation:1 appearance:1 sin2:5 direct:1 unpolarized:10 past:1 second:8 compensates:1 catching:1 enhancement:3 annihilation:1 pass:2 zu:1 estimated:1 click:2 eik1:2 linear:1 even:7 what:3 nonlinear:2 adds:1 appear:8 rate:1 invoking:1 section:6 selected:1 analogously:1 expressed:1 t2x:1 experiment:28 above:2 ˆi:1 paviˇci:9 connected:1 method:2 counters:6 body:1 outgoing:4 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quant-ph9908025.txt |@word grobe:1 consider:1 crucial:1 results:1 gy:1 leads:1 generalize:2 overlap:1 bergmann:2 consists:2 anggi:1 research:1 gk:1 localized:17 aug:1 finally:2 under:2 applied:1 belonging:1 amplitudes:1 2re:1 stroud:2 wave:8 condition:8 lalo:1 immediately:1 level:1 knight:5 list:1 damped:1 leave:1 diu:1 optics:2 upper:7 sin2:2 pulse:1 approximation:2 dalton:1 substitute:1 theory:1 even:2 appear:1 imamo:1 section:2 localization:8 above:4 new:2 consisting:1 edited:2 degree:1 respectively:1 here:5 tracks:1 selective:1 cos2:2 separation:2 others:1 strong:2 equations:2 obtained:1 antisymmetric:1 studied:2 eberly:3 resonance:2 glu:1 eiδt:2 via:1 regardless:2 explained:1 electromagnetically:1 analyzing:2 condensates:1 quenching:1 manipulate:1 eiωt:1 use:3 hegerfeldt:1 superpositions:1 would:1 commun:1 probabilities:3 lasing:1 coupled:3 few:1 therefore:5 type:4 today:1 more:1 stable:1 odinger:1 berlin:1 transient:1 known:2 cases:2 springer:2 tunnel:1 recall:1 equation:1 work:1 london:1 theories:1 remain:5 transparency:2 closing:1 spontaneous:2 example:5 stated:1 process:4 pons:1 states:21 assumptions:3 council:1 r28:1 occur:9 verlag:1 united:2 decaying:1 xxxv:1 revisit:1 how:1 numerous:1 opt:3 sin:2 transforming:1 after:3 epsrc:1 dynamical:7 whitley:1 element:1 shore:3 so:4 interpretation:1 emmanuel:1 satisfied:1 swain:1 pulses:2 statistical:1 its:2 before:1 thank:1 decay:4 interesting:2 scully:2 fig:4 tors:1 rabi:2 dxφ:2 combination:1 ya:2 evolution:1 walls:1 they:2 now:6 matched:2 eigenvalue:1 february:1 hamiltonian:6 magnitude:1 each:2 found:1 interfering:1 side:3 energy:3 idea:1 related:1 vansteenkiste:1 frequency:4 quantum:24 our:2 ev:1 eq:2 out:2 ultimately:1 matrix:1 rep:3 rev:22 denotes:1 re:1 induced:5 ref:3 occurs:1 hioe:2 wiley:2 linear:1 barrier:2 state:40 approaches:1 york:2 starts:1 could:2 transition:2 times:1 ohler:1 transfer:1 hence:2 first:1 origin:1 initial:2 features:1 probability:2 grifoni:1 another:2 angular:2 given:4 iω1:1 iω3:2 iω2:1 introduction:1 leading:3 system:33 their:2 cooling:1 assumption:2 too:2 molecular:1 asymmetric:5 part:3 oscillate:3 iωt:1 showed:1 double:9 approximations:1 depends:1 amplitude:1 bare:1 function:5 cohen:2 modern:1 manuscript:1 elsevier:1 orders:1 note:4 sciences:1 potential:23 tannoudji:2 begin:1 added:2 electric:2 systems:2 wells:7 most:1 intrinsic:1 chap:1 trapping:3 soliton:1 considered:2 optical:1 velocity:1 physics:2 phenomenon:2 show:4 nπ:1 text:1 supported:1 contemporary:1 rotating:1 bright:4 relation:1 fleischhauer:2 ground:7 2bz:1 outside:1 should:1 only:10 population:2 dependent:1 words:1 gray:1 processes:1 continuum:2 textbooks:1 fields:2 arxiv:1 predicted:1 through:1 parkins:1 phenomenologically:1 arimondo:2 see:7 college:1 discussions:1 exploited:1 review:1 dipole:1 symmetric:6 written:4 between:4 µe:5 progress:1 conditions:2 compliment:1 luo:1 terms:1 initially:10 however:2 jr:2 j2i:1 article:4 iδt:2 both:2 cos:2 fulfilled:1 propagation:2 plenio:1 period:1 simply:2 bose:1 kocharovskaya:1 pr:8 basis:2 addition:2 been:4 detuning:1 khanin:1 ph:1 prototype:1 pl:7 define:1 suppress:1 formed:1 photon:2 coherent:4 coherently:1 c2:10 c1:11 presented:1 present:1 case:6 multi:1 laser:12 pacs:1 expanded:1 appearance:1 engineering:1 transformation:1 will:19 contemp:1 suppose:2 tunneling:18 sw7:1 real:2 larger:1 ve:3 vg:3 vol:4 characteristics:1 surface:2 couples:2 examined:1 ib:4 agarwal:3 media:1 belong:1 radiation:1 same:1 any:2 quant:2 wavepacket:13 units:1 several:1 used:3 interscience:2 possible:4 driven:3 harris:4 potentials:2 recent:1 lower:4 schr:1 well:22 analysis:3 obviously:1 without:1 model:3 left:10 being:3 obtain:1 shape:1 atomic:3 aspect:1 integer:1 useful:1 belongs:1 lett:16 haq:1 mod:1 excited:12 kingdom:2 couple:3 inversion:1 dark:19 moi:1 using:3 helpful:1 like:3 δt:8 adiabatic:1 niels:1 either:1 δi:1 kilin:7 reduces:1 right:9 creation:2 phenomena:2 b1:4 b2:4 b3:4 oscillations:3 peter:1 kaiser:1 zhou:1 lead:2 comments:1 does:7 theuer:1 arbitrary:1 step:1 prepared:1 properties:2 discussed:1 o:3 2i:1 a2:1 wolf:1 j1i:1 into:1 bound:1 because:2 determine:1 einstein:1 amsterdam:1 giv:1 statistics:1 assumed:4 there:2 gases:1 imperial:1 width:1 was:1 hz:1 metastable:2 but:2 properly:1 hb:1 dissipative:1 zhu:2 fluorescence:1 cim:1 ωi:4 decays:2 problem:3 ωb:1 similar:1 blackett:1 mechanics:2 associated:1 ai:1 certain:2 general:1 single:1 exist:1 laboratory:1 eigenstate:1 physical:2 functions:2 transitions:1 no:1 wavefunction:1 when:2 field:7 other:4 conclusion:1 may:1 superposition:3 excitation:1 berman:1 shown:4 emission:2 a1:1 a3:1 important:2 suppression:13 structure:1 uncoupled:1 required:1 having:1 time:2 nuovo:1
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quant-ph9908026.txt |@word consider:1 similarity:1 rev:23 results:2 gy:1 leads:2 lewenstein:4 consists:1 research:1 gk:3 inverse:1 aug:1 re:2 rostovtsev:1 finally:2 those:1 under:1 supported:1 very:1 wave:1 print:1 bhatt:1 resonant:2 condition:3 level:3 knight:3 solution:1 solid:2 pbg:18 vector:2 small:1 optics:2 upper:1 pulse:2 approximation:1 go:1 second:1 enhancement:1 chen:1 dynamics:4 situated:1 linear:8 even:3 aim:1 nonlinear:2 trapping:1 imamo:2 brackets:1 section:1 near:8 current:1 above:1 contrast:1 respectively:1 here:5 atoms:6 behaviour:3 zibrov:1 groups:1 consideration:1 strong:1 ωa1:1 ωa0:1 obtained:2 root:4 study:3 vectors:1 through:1 eberly:1 microcavities:1 resonance:3 studies:3 cancellation:1 via:1 vapors:1 electromagnetically:1 welch:1 apply:1 unit:2 wang:1 plot:1 use:1 proceed:1 waveguides:1 lasing:1 therefore:3 taken:2 type:5 today:1 becomes:2 odinger:1 labelled:1 particular:1 known:1 cases:1 account:1 quantized:1 equation:2 work:1 modified:4 values:1 thin:1 transparency:11 hollberg:1 spontaneous:3 example:2 r29:1 figure:5 expanding:1 states:3 application:1 council:1 r27:1 occur:1 united:2 decaying:1 far:2 opt:1 βa:2 profile:3 epsrc:1 date:1 effective:1 light:1 spectra:2 element:1 so:5 reservoir:3 swain:1 london:1 roots:1 group:4 kofman:2 decay:8 interesting:2 j1i:1 scully:2 systems:1 rabi:2 derivative:2 schmidt:1 non:1 mølmer:2 material:1 processes:3 band:6 effects:3 singularity:2 now:1 transparent:4 susceptibility:9 february:1 university:1 presented:1 sufficiently:1 mode:1 2c:1 found:1 lorentzian:1 l9:1 square:4 ei:1 energy:1 related:1 decays:2 obtains:1 quantum:6 laboratory:1 transitions:2 eq:4 shown:2 matrix:1 space:3 since:1 interference:4 rz:2 denotes:6 attracted:1 glu:2 denoted:1 induced:1 occurs:7 shows:1 theory:1 localization:1 ewski:2 free:3 formation:1 interaction:2 could:1 transition:10 times:1 motion:1 harris:5 isotropic:7 hussein:1 probability:1 omitted:1 channels:1 thick:1 angular:1 given:5 perturbation:1 introduction:1 leading:1 eqs:2 bay:2 system:11 1a:1 their:1 1b:1 2ωg:1 john:6 final:1 asymmetric:1 part:3 below:1 population:2 critically:1 rate:2 annihilation:1 amplitude:4 bare:1 treated:3 displays:1 exhibit:1 spectrum:2 cumbersome:1 any:1 strength:1 zero:1 lim:1 polarization:2 sciences:1 k0:3 evaluated:1 electric:2 sherman:1 impurities:1 involving:1 phase:1 sa1:1 intrinsic:2 ka:1 especially:1 surprising:1 steady:2 optical:2 velocity:2 physics:1 review:1 phenomenon:2 show:2 probe:10 rotating:1 purely:1 relation:3 threshold:6 substituting:1 slow:1 2bz:1 parameters:2 kleppner:1 only:1 µnm:1 quantph:1 means:1 dependent:2 photodetachment:1 closely:1 kurizki:2 dt:1 steepness:1 reveal:1 qs:1 heaviside:1 fields:2 arxiv:1 summary:1 investigate:2 predicted:2 4πn:1 behroozi:1 kernel:3 observed:1 depends:1 college:1 result:1 eliminating:1 recently:2 3c3:1 away:1 dipole:1 materials:2 state:9 between:1 αk:2 terms:2 nature:1 initially:1 attention:1 weak:5 however:2 j2i:1 huang:1 iδt:1 originates:1 concentrated:1 both:2 many:2 equal:1 quantization:1 connection:1 blackett:1 addition:2 radiative:3 due:2 been:4 commission:1 detuning:7 much:1 interest:1 anisotropic:3 ph:1 fig:2 j0i:1 photoionization:1 coherence:2 photon:3 gap:4 present:1 case:7 laser:16 eit:4 ǫe:1 pacs:1 ǫk:2 value:2 spontaneously:3 will:1 while:3 shift:1 yablonovitch:1 sw7:1 real:3 mostowski:1 vg:3 couples:1 ik:2 im:1 ia:2 mod:1 demolition:1 agarwal:1 different:1 az:2 quang:3 suggest:1 zakrzewski:2 complex:1 quant:1 units:2 several:1 european:1 used:3 see:4 effect:1 lambropoulos:2 driven:1 levels:1 schr:1 modes:7 mention:1 well:2 without:1 ωnm:1 approached:1 edge:9 model:8 being:4 obtain:3 photonic:4 shape:1 atomic:10 previous:1 note:4 rapid:1 density:7 absorption:9 zubairy:1 lett:13 theorem:1 iπ:1 formal:1 hau:1 kingdom:2 easily:1 iγ:4 iβ:1 inversion:2 reads:1 kash:1 background:4 vacuum:4 press:1 using:3 occurring:3 velocities:2 extremely:1 specific:1 arbitrary:1 become:2 qed:1 phenomena:4 examples:1 tmr:1 cavity:1 measurements:1 does:2 each:1 step:1 δg:17 imaginary:1 properties:3 chapter:1 discussed:1 o:3 carrier:1 dutton:1 cambridge:2 markovian:2 presence:2 communication:1 into:1 bound:1 three:3 operator:1 assumed:3 there:2 transform:1 long:2 imperial:1 dispersion:11 describes:1 function:1 medium:1 complete:1 regard:1 volume:1 atom:11 line:3 dissipative:1 fry:1 piraux:1 zhu:1 embedded:2 lukin:1 inside:1 up:1 meschede:1 ωk:5 frequency:6 ωm:1 ωn:2 unusually:1 similar:3 laplace:2 ωg:9 diverges:1 associated:2 ak:2 engineering:1 reservoirs:1 our:6 hamiltonian:1 physical:1 dashed:3 wavefunction:1 when:3 field:14 other:4 picture:1 zhou:1 models:1 emission:3 a1:9 a0:3 a3:1 suppression:1 variable:1 network:1 coupling:5 assume:1 lanl:1 curve:3 mass:1 time:3
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quant-ph9908027.txt |@word gv:1 consider:1 pointing:1 rx:2 desirable:2 results:5 leads:4 edu:1 iu0:1 inverse:2 depend:1 calculate:1 aug:1 program:1 stable:2 must:2 summarizes:1 p2:8 unrenormalized:1 amplitudes:2 g2:2 straightforward:1 g0:14 translations:2 wave:2 exact:1 condition:3 presented:2 suffices:1 singularly:1 evy:2 annihilates:1 relation:2 noted:6 renormalized:2 consistent:2 direct:1 sign:2 past:1 zero:1 insertion:1 further:1 residue:1 will:3 what:1 section:11 expressed:1 henceforth:1 version:2 above:1 new:1 consisting:1 satisfy:2 outgoing:2 lee:5 respectively:4 here:5 agreement:1 desired:1 galilean:16 separation:1 address:1 consideration:1 equations:2 appears:2 obtained:11 remark:1 incoming:1 study:1 allows:1 resulting:1 resonance:1 adopting:1 makes:1 cancellation:1 requiring:1 ask:1 total:1 renormalization:7 conventional:1 dpdq:1 would:1 commun:1 covariant:3 contains:1 properties:1 calculation:6 noting:1 bender:2 taken:8 type:2 theoretical:1 more:1 becomes:2 operators:1 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quant-ph9908028.txt |@word measurements:1 partial:2 consider:2 rev:14 rob:1 results:1 schatten:1 commute:1 entropy:1 lewenstein:2 edu:2 go:1 violate:3 aug:1 tr:9 nonlocal:3 environment:1 thapliyal:1 finally:3 norm:11 conjecture:4 straightforward:1 orthogonal:2 very:2 induce:1 every:4 mixing:1 emphasized:1 difference:1 condition:2 dim:1 level:2 turns:1 applicable:1 large:2 vector:11 recall:2 small:2 application:1 neighborhood:6 direct:1 consists:1 zero:2 further:2 canonical:1 even:4 what:1 appear:2 d3:4 reminiscent:1 new:1 increasing:1 acknowledgments:1 simultaneously:1 degree:1 teleportation:1 here:1 desired:1 plenio:1 represented:2 obtained:1 remark:1 larger:1 recently:1 schumacher:2 usually:1 suitable:1 uniquely:1 schack:2 useful:2 projection:1 family:2 replace:1 brought:1 pxi:2 limn:1 establish:1 unit:5 use:1 usa:2 prove:1 distinct:1 positive:3 contains:1 next:1 few:1 noting:1 therefore:2 themselves:1 theoretical:1 more:7 linden:6 composite:5 initial:1 operators:16 odinger:2 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quant-ph9908029.txt |@word represent:2 consider:8 rev:9 comparatively:1 brownian:6 focus:1 illustrated:1 eds:1 settle:1 mile:1 entropy:1 consists:3 follow:3 expressions:4 cases:1 causes:2 rd:1 certainly:2 const:5 calculate:7 4ns:1 re:2 respectively:3 pˆn:1 environment:13 quasi:6 present:1 under:1 tegmark:1 tc:14 γe:6 p2:1 expressing:1 straightforward:3 zhang:6 very:6 desirable:1 rise:2 mg:2 tacitly:1 wave:3 print:6 every:3 reversibility:1 husimi:1 difference:3 exact:4 condition:3 osi:1 gov:5 y1:2 level:2 t6:1 positions:3 integrating:1 t2:3 solution:4 correct:4 pˆ1:1 discrete:2 pˆ2:2 phase:4 small:5 noted:2 averaged:2 det:8 direct:1 qmw:2 mh:5 approximation:11 rate:1 timescales:1 j22:2 substituting:3 further:5 copenhagen:1 choices:2 mπ:1 spectral:4 index:2 what:2 plays:3 invertible:1 giving:2 fine:1 section:13 expressed:4 tσ0:2 localized:1 3m:4 obvious:1 order:6 consisting:1 contrast:1 krs:1 body:6 eω0:6 integrated:1 lee:1 degree:3 whose:1 mω:14 γkb:1 here:2 behaviour:9 smearing:1 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quant-ph9908030.txt |@word barone:1 partial:1 consider:2 interference:1 magnetic:3 both:5 results:3 dϕ2:1 a45:1 localized:2 whose:1 referring:1 aug:1 spin:5 environment:1 monotonically:1 under:3 analogous:3 tb:10 tc:4 discriminates:1 ta:8 applied:1 amplitudes:1 provides:1 far:2 splitting:1 sons:1 resonant:1 experimentally:3 difference:2 matrices:1 condition:3 squids:1 quartic:1 level:6 turns:1 proposals:2 damped:1 large:2 discrete:1 vector:1 min:1 pbc:4 small:1 eigenvalues:2 setup:1 configurations:2 limitations:1 sapienza:1 oscillation:1 dealing:1 prediction:1 sign:1 tex:1 located:1 zero:1 value:8 further:1 dynamics:3 canonical:1 even:1 what:1 abc:6 plays:1 barrier:4 incompatible:1 ˆx:2 uniform:1 current:1 experiment:1 above:2 shared:1 increasing:2 satisfy:1 edited:1 full:1 newyork:1 respectively:1 component:1 here:1 atoms:1 behaviour:1 favourable:2 represented:3 consideration:1 along:1 observing:1 galilei:1 simulating:1 obtained:3 paterno:1 tunneling:3 suitably:1 institute:1 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quant-ph9908032.txt |@word secondly:1 concept:6 evidence:1 consider:4 similarity:1 induces:1 lack:1 ciudad:1 emch:1 go:2 sci:1 compact:3 hold:3 aug:1 concerned:1 deterministic:1 tr:1 contained:1 under:1 atlas:1 decomposition:1 include:1 applied:1 orthogonal:1 very:12 wave:1 every:9 remarks:1 experimentally:5 difference:1 condition:2 heaven:1 level:9 turns:3 applicable:1 try:1 sand:1 small:1 challenge:1 consistent:1 approximation:2 consists:3 second:1 qualitatively:1 dynamics:2 linear:3 even:1 aim:1 what:3 appear:1 deeply:1 http:1 version:1 above:4 new:5 consisting:2 contrast:2 satisfy:1 justification:2 simultaneously:2 proper:1 never:1 here:2 understanding:1 objects:1 address:1 represented:1 based:5 strong:1 equations:1 appears:1 knowledge:2 obtained:3 instituto:1 ultra:1 commutant:2 study:4 vectors:3 approaches:1 ignoring:2 commutators:1 studies:1 family:1 extra:1 namely:2 outcomes:2 ask:2 boolean:2 logically:1 apply:1 establish:1 causal:2 unit:3 use:1 projector:1 would:1 prove:2 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quant-ph9908035.txt |@word sci:1 consider:1 chain:2 results:1 leads:1 executing:1 computation:22 consists:2 perturbations:3 localized:1 row:13 certainly:1 number:2 pointing:1 aug:1 ac03:1 irrelevant:1 subjected:1 contained:1 factoring:1 environment:1 th:1 under:2 analogous:1 division:2 amplitudes:1 straightforward:1 orthogonal:1 far:2 choice:1 electron:3 exact:1 disturb:1 hamiltonian:23 leave:1 small:1 chuang:3 optics:1 degeneracy:1 sign:5 zero:1 design:2 pass:1 nmr:1 implemented:4 will:4 what:1 errors:1 appear:1 fine:1 section:1 lawrence:1 while:5 expressed:1 subspaces:1 designing:1 supplies:1 construction:2 method:1 satisfy:2 quenched:1 full:3 obviating:1 respectively:3 component:1 here:3 desired:4 berkeley:4 directions:1 change:1 box:3 search:2 property:2 accomplishes:1 technical:1 involved:1 changed:1 accomplished:2 simultaneous:1 products:4 suggestion:1 complicated:1 implement:2 suitable:1 changes:1 york:2 via:1 projection:1 castagnoli:1 total:2 proceed:1 would:9 positive:1 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