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quant-ph0703201.txt |@word limited:2 gt:1 partial:7 consider:2 crucial:1 forbidden:1 lack:1 dynamic:1 results:7 leads:3 scalar:3 concept:2 generalize:3 bohm:1 ptk:2 expressions:1 conservative:1 contributions:6 localized:3 increase:1 const:1 calculate:1 segments:1 deterministic:2 lnr:1 acting:1 environment:1 quasi:3 permanently:1 present:1 under:2 tf:13 stochastic:1 analogous:2 include:2 tb:10 tc:3 ta:13 belonging:4 global:1 straightforward:1 far:1 account:1 wave:11 electron:1 novel:2 every:1 trough:1 difference:1 matrices:1 condition:9 hamiltonian:7 did:1 issue:1 developing:3 proposals:1 t0:1 large:2 vector:2 small:2 relation:1 equation:13 version:2 inevitably:1 consistent:4 sign:1 approximation:9 elegant:1 zero:5 pass:1 chen:1 further:1 dynamics:1 odd:1 linear:1 even:3 employ:3 sub:1 charges:1 trivial:1 sum:2 localization:1 xtk:2 brief:1 expressed:3 d3:5 3h:1 above:2 new:7 method:1 x0µ:8 movement:3 satisfy:4 simultaneously:3 ibid:1 whose:1 respectively:2 never:1 component:4 here:11 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quant-ph0703204.txt |@word consider:2 chinese:1 rev:1 magnetic:1 dynamic:2 results:3 leads:1 ge:1 proposition:1 entropy:4 grateful:1 whose:1 preserves:1 tr:5 those:2 under:2 applied:1 hibbs:1 orthogonal:3 far:1 2re:1 wave:71 electron:5 fan:2 level:7 solution:1 large:1 solved:1 science:1 eigenvalues:1 concluded:4 concludes:2 chen:1 dynamics:1 giving:1 wavelike:1 agrees:1 experiment:4 establishes:2 lifshitz:1 satisfy:4 schilpp:1 respectively:3 here:1 operˆ:1 wuhan:2 reported:1 china:2 address:1 path:2 equations:2 change:3 box:1 institute:2 larger:1 formalism:5 suggests:2 simultaneous:6 resonance:1 suitable:1 changes:1 involves:2 useful:1 explained:1 heiblum:1 vivid:1 would:1 distinct:1 positive:1 ψp:5 visit:1 ψw:4 partite:1 ψn:20 therefore:2 ψm:11 theoretical:1 more:4 introducing:1 duality:9 operators:4 odinger:29 correspondingly:1 normalized:3 particular:3 known:2 foundations:1 cases:1 iii:1 me:1 nonn:1 equation:38 work:1 unknowns:3 values:2 following:2 relativistic:1 bennett:1 states:3 slit:5 numbers:3 sense:1 conversely:1 united:1 numerous:1 fourth:1 product:3 after:1 hong:1 physik:2 waves:2 natural:1 dynamical:1 third:1 correspond:2 ϕn:4 so:4 every:7 bipartite:16 interpretation:1 eigen:2 scientist:1 through:3 satisfies:3 its:2 derive:1 chosen:1 solving:1 coordinates:1 li:2 forms:3 systems:2 covered:2 schmidt:2 lx:6 non:1 landau:9 mention:1 they:1 oxford:3 eigenvalue:1 february:1 dirac:1 characterizes:2 university:3 presented:2 l2:2 bonn:1 2m:2 em:8 differential:2 ed:1 energy:10 principles:1 interferometer:1 gaps:4 ex:1 measure:5 quantum:12 laboratory:2 eq:23 special:2 try:1 shown:2 matrix:2 trx:1 umansky:1 furthermore:2 since:4 interference:3 research:1 particles:4 hill:1 integrated:1 math:1 foundation:1 theory:1 free:1 imagine:1 r3:1 determining:1 transition:7 times:1 motion:2 hence:7 there:4 probability:2 number:1 electronic:1 given:2 rempe:1 district:1 introduction:1 behaves:2 system:12 their:1 assumption:1 molecular:1 gives:1 collapse:4 academy:1 explanation:1 albert:1 x2:3 x3:1 x1:1 than:1 wootters:1 showed:1 princeton:2 determined:3 contrary:2 amplitude:1 were:1 behaviors:4 ann:2 any:1 responsible:1 note:2 sciences:1 potential:1 detector:1 heisenberg:7 formulas:1 sequel:2 most:1 quantitative:4 probabilistic:1 considered:1 average:1 behaviour:2 periment:1 feynman:1 electrons:1 principle:3 urr:1 mechanical:1 physics:3 fact:1 show:6 supported:1 mahalu:1 relation:1 expressed:1 d3:7 based:1 explain:1 entities:1 only:1 hamiltonians:1 means:1 beams:1 express:1 expectation:2 cannot:1 dr:1 x21:1 µ2n:4 arxiv:1 paper:1 schuster:1 view:1 set:3 tation:1 exists:1 sep:1 national:1 correlations:1 edition:2 quantitatively:2 satisfying:2 subsequent:1 definite:3 state:11 µn:3 various:1 between:5 invariant:2 conditions:1 x23:1 x22:1 recently:1 ability:1 nature:2 screen:1 however:2 key:2 article:1 both:2 instant:1 many:5 uncertainty:2 ln:4 dated:1 divincenzo:1 expression:4 cn:11 point:2 corresponds:1 instants:1 moreover:3 described:6 basis:1 west:1 been:1 basic:2 living:1 ph:1 xd3:3 define:2 obtained:1 corresponding:4 observable:4 gap:2 external:2 albeverio:1 denote:1 present:1 case:2 conception:1 pacs:1 value:3 will:4 while:5 behavior:1 a21:2 a22:2 unitary:1 lx2:4 vi:1 von:16 thus:2 xiao:1 iv:1 ii:1 different:2 ing:1 grant:1 perhaps:2 suggest:1 make:1 quant:1 inc:1 shan:1 difficult:2 used:4 hand:2 levels:8 entanglement:2 task:1 schr:29 well:2 bohr:2 sets:1 position:2 usual:2 buks:1 just:3 λt:1 being:2 when:1 atomic:2 cut:1 density:5 regarded:4 conclude:1 seems:2 evanston:1 mathematically:1 slits:2 lett:1 easy:4 theorem:1 momentum:1 evaluate:2 press:3 unique:1 loss:2 like:13 particle:31 follows:1 reduces:1 manifest:1 integrals:1 january:1 mcgraw:1 stationary:3 reduced:1 mathematical:7 because:1 neumann:16 sequence:1 some:4 library:1 deduce:1 respect:2 complementarity:5 provided:1 describing:1 calculating:1 philosopher:1 behave:1 decomposition:1 provides:2 prof:1 demonstrated:1 equivalent:1 illustration:1 refers:1 properties:1 extension:7 getting:1 inviting:1 o:7 practical:1 deserves:1 consequently:1 pergamon:1 lies:1 en:8 determine:5 einstein:1 operator:5 initial:1 accordingly:1 way:5 was:1 function:12 complete:2 form:8 ator:1 forming:1 smolin:1 regard:1 but:1 philosophers:1 atom:1 collapses:4 partially:1 made:1 us:1 ud:1 problem:1 pm:2 similar:1 mechanics:8 ac:1 associated:5 defined:1 measurement:5 am:2 general:2 single:10 exist:1 our:3 hamiltonian:3 check:3 physical:1 impermeable:1 functions:28 no:3 generally:1 field:2 other:3 mathematics:2 conclusion:2 a11:2 superposition:1 ly2:1 a12:2 problems:1 meaning:1 important:1 variable:1 implies:1 equivalently:1 time:3 once:1 representative:1
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quant-ph0703206.txt |@word represent:1 consider:2 show:2 being:1 indeed:1 delta:2 results:2 interpreted:1 four:1 via:1 relation:1 looks:1 anticorrelated:1 go:2 label:1 eigenstates:1 make:1 define:1 derive:1 calculate:1 bram:2 decay:11 chosen:1 irrelevant:1 actually:1 only:2 going:2 lett:1 easy:2 pair:2 total:1 bramon:1 hidden:6 mod:1 local:6 into:2 ruiz:1 opt:1 alberto:1 them:1 kπ:1 march:1 comments:1 straightforward:1 means:4 dependent:1 propose:1 dλ1:2 garbarino:2 sooner:1 choice:1 joint:3 ones:1 putting:1 they:1 during:2 dt:2 difference:1 xdx:2 insert:1 term:2 exhibiting:1 dirac:2 densities:5 particle:10 always:1 arxiv:1 t2:30 modulated:1 t1:32 specific:1 inequality:1 either:1 integrals:1 each:1 2n:1 assignement:1 ql:10 realism:3 i21:1 right:1 namely:2 due:1 physically:3 conditional:2 prediction:2 plausible:1 rate:1 decays:8 quantum:3 our:4 eq:4 quite:1 will:2 errors:1 giving:1 sum:1 2nπ:2 commented:1 finally:1 agrees:2 particles:7 similarly:1 enough:1 experiment:5 dλ2:2 provides:1 between:2 new:1 get:4 ri:3 measuring:1 particular:1 performing:1 terms:1 respectively:2 predicting:1 obtain:1 agreement:1 standard:1 lack:1 reported:1 reproduces:1 flavours:1 dx:3 cosinus:1 symmetry:1 ikl:3 obtained:2 both:1 cos:14 property:1 involved:2 density:1 according:1 times:3 compatible:2 mt2:2 periodic:2 period:2 produced:1 emilio:1 hence:1 symmetrical:1 exhibited:1 experimental:1 first:7 mt1:2 useful:1 probability:7 bell:3 variables:6 within:1 integral:2 corresponds:1 perform:1 variable:2 appropriate:1 references:1 another:1 rkl:7 should:5 bertlmann:1 given:1 prove:2 probabilities:1 positive:2 eqs:4 initial:2 predictions:1 attach:1 explicitly:1 assuming:1 way:1 taken:1 pk:10 ph:3 type:2 until:1 gives:1 function:2 introducing:1 corresponding:1 said:1 definition:1 becomes:2 duration:1 albert:1 but:3 argument:1 lives:1 normalized:3 somewhat:1 dt2:1 known:1 cases:1 removed:1 true:1 dt1:1 oscillate:1 case:2 account:1 flavour:5 exponential:1 fulfilling:1 was:1 second:6 different:1 aim:1 mt:2 below:1 archiv:1 values:1 following:1 distribution:3 more:3 similar:1 interval:3 proved:1 defined:1 i11:2 abstract:1 contribute:1 thus:4 purposes:1 equal:2 states:2 proper:3 say:2 proves:2 equality:1 dλ:3 sense:2 any:4 defines:1 0b:1 santos:1 decaying:2 depending:1 rather:1 convenient:1 i22:2 holds:1 note:1 necessary:1 other:1 quant:3 opposite:1 test:1 so:2 ensemble:1 paper1:1 hiesmayr:1 mar:1 see:3 shall:1 may:4 after:1 2ti:1 functions:11 important:1 purpose:1 saying:1 entanglement:2 law:1 measured:1 compatibility:2 normalization:2 recent:2 contrived:1 independently:1 escribano:1 using:1 acknowledge:1 random:1 later:1 epr:2 4s:4 i12:1 lhv:4 cannot:1 mass:2 does:1 exp:10 time:8 exponentials:1 model:10 oscillates:1 physics:1 order:1 left:1
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quant-ph0703207.txt |@word represent:3 consider:6 chain:28 a23:2 rev:18 magnetic:32 varying:2 desirable:1 results:5 sketching:1 leads:2 ge:2 generalize:1 during:1 expressions:1 faster:1 targeted:1 viceversa:1 increase:3 preserves:1 depend:3 remarkable:2 show:2 a19:3 corrections:1 ωa2:4 environment:1 finally:3 does:1 christandl:2 dφ:1 th:6 under:2 alternating:1 case:22 amplitudes:1 orthogonal:4 very:2 frequencies:9 rise:1 noncommuting:1 ρth:1 choice:1 pn:4 electron:27 verd:1 summarized:1 resonant:1 experimentally:3 difference:1 cool:2 evi:1 swapping:4 hamiltonian:33 transmission:11 tex:6 proposals:1 integrated:1 large:5 vector:2 small:2 optics:1 enforce:1 leibfried:1 smaller:4 illustrating:1 zi:17 oscillation:2 ψi:1 estimates:1 direct:1 sign:1 approximation:1 rate:4 insertion:1 zt:1 further:2 dynamics:7 estimated:4 canonical:3 even:5 will:6 errors:4 plays:1 trapping:4 sum:1 brief:1 uniform:1 current:1 below:1 axial:21 above:1 new:2 occupation:2 consisting:3 iσj:2 full:1 evaluating:1 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quant-ph0703208.txt |@word katz:1 gt:1 sch:1 rx:2 leads:1 martinis:3 expressions:1 gh:1 equivalence:1 finally:1 under:2 nori:1 applied:2 zhang:3 frequencies:2 differently:1 wave:2 resonant:2 experimentally:1 emphasized:1 hamiltonian:5 michael:1 t1:11 cms:1 upper:1 pulse:4 sign:1 approximation:2 likely:1 design:3 leakage:1 canonical:1 giving:1 above:1 emily:1 acknowledgments:1 vala:1 here:5 november:1 sine:1 larger:1 steffen:2 simultaneous:2 g2n:1 implement:1 suitable:1 appropriately:1 family:1 total:1 use:2 would:1 dermott:1 athens:1 steering:3 chu:2 robertson:2 w911nf:1 today:1 becomes:1 varying:1 known:1 high:1 none:1 quartic:4 sastry:1 science:6 work:1 dragt:2 values:1 averages:1 sinusoidal:3 wang:1 preserving:1 implementations:1 states:1 performed:2 junctions:1 information:1 varied:1 discussion:1 how:1 gate:8 parameter:1 profile:3 mar:1 mat:1 wu:2 derived:1 different:1 constants:1 johnson:2 su:3 simmonds:1 so:1 order:2 office:1 paper:1 pulses:2 fidelity:1 rapidly:1 thank:1 wilhelm:1 systems:1 rabi:2 lx:1 non:1 rotations:3 inductively:1 landau:4 rotation:2 now:2 yu:2 2t:2 february:1 corners:1 university:1 lucero:1 gt1:3 2g:1 found:1 2n:2 b70:1 weyl:5 ei:3 generation:1 σ2x:2 σ2y:2 related:1 inverted:6 quantum:3 our:4 transitions:1 out:1 ansmann:1 shown:1 matrix:1 rev:6 ry:2 rf:1 ref:3 shows:1 foundation:1 theory:1 ramos:1 plourde:2 inductive:3 generate:1 interaction:2 times:2 turn:1 neglect:1 first:1 number:1 urbina:1 neglects:1 xu:1 given:2 construct:1 quadratic:2 john:2 national:1 part:1 authors:1 than:2 accordance:1 approximations:1 see:1 tunable:7 doubly:1 minus:1 turned:4 pritchett:1 any:1 strength:4 angle:1 convenient:1 mechanism:1 ramping:1 switching:7 track:2 most:1 phase:7 class:2 later:1 physics:2 lying:1 show:1 supported:1 rotating:3 slow:1 based:2 implementation:2 capacitive:1 candidates:1 factor:1 local:4 his:1 dependent:3 overall:2 scalable:1 a71:1 lobb:2 famous:1 σ1y:2 σ1x:2 dt:2 evolution:2 arxiv:1 summary:1 fixed:2 valid:2 frame:1 depends:1 individual:1 discussions:1 recently:1 cleland:1 state:1 trapezoidal:6 approach:2 terms:1 qubits:9 vanishing:1 both:1 σi:1 according:1 logic:3 qubit:6 expression:1 simple:2 sequences:1 cp:1 considering:2 tuning:1 three:2 been:2 detuning:1 describes:1 ph:1 choose:1 controlled:1 strauch:2 commutes:1 andrew:1 ustinov:1 andrei:1 disruptive:1 present:1 case:1 georgia:2 reichardt:2 josephson:2 pacs:1 solid:1 rectangular:1 kσ1:1 promising:1 sornborger:1 vectors:1 coupled:1 thus:1 middle:1 superconducting:3 bias:1 cond:1 technology:1 containing:1 grant:2 mcdermott:2 unity:1 parts:1 quant:1 higher:2 used:3 berkley:1 architectures:1 infinite:1 identity:2 relies:1 tracking:1 off:4 itself:1 analysis:1 accurate:1 geller:1 λi:3 han:1 mathematically:1 belongs:1 lett:2 theorem:2 hat:3 real:1 using:2 makhlin:2 mod:1 like:1 follows:2 chamber:5 characterizes:1 soft:3 a67:1 some:2 examples:1 bialczak:1 cooper:1 flux:2 moderate:1 proc:1 demonstrated:1 oscillating:1 broken:1 weig:1 cnot:10 actual:1 oh:1 dependence:2 hime:2 slightly:1 osborn:1 22n:1 presence:1 into:1 integral:1 down:1 references:1 operator:1 prefactors:1 whaley:3 area:3 assumed:1 fast:2 σ2z:2 anderson:2 cosine:1 fraction:1 was:1 form:2 triangular:1 construction:2 coupling:11 made:1 applying:1 circuits:2 smooth:1 up:1 ωi:4 2πt:1 demonstrate:1 clarke:2 constant:1 computing:1 defined:1 abstract:1 describe:1 corresponding:1 inf:1 proceeds:1 ideally:1 cos:1 when:1 nam:1 other:1 department:1 you:1 neely:1 helpful:1 generated:1 suited:1 astronomy:1 aumentado:1 faster:1 curve:1 wellstood:2 fact:1 cicak:1 time:11 shnirman:1
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quant-ph0703209.txt |@word sector:1 consider:1 chain:15 rev:10 magnetic:2 desirable:1 results:4 interpret:1 entropy:5 computation:1 follow:1 whose:4 inverse:1 terms:2 calculate:1 nonlocal:1 containing:1 summarised:1 compensate:1 under:2 must:1 norm:1 p2:1 conjecture:5 straightforward:1 very:1 dynamic:1 rise:1 account:1 unitaries:1 ultraviolet:1 bounding:3 tridiagonal:1 exact:2 partitions:3 hamiltonian:4 notes:1 large:6 solved:1 small:5 upper:1 disordered:14 approximation:2 second:1 further:1 dynamics:7 canonical:1 even:1 errors:1 giving:1 supplied:1 networks:3 access:3 version:1 above:2 lri:1 new:2 method:2 contrast:1 satisfy:4 evolving:2 christian:1 respectively:4 applies:1 here:1 localisation:9 condmat:2 along:1 strong:1 logarithmic:8 wait:1 obtained:2 study:4 allows:1 completely:1 amount:3 bob:6 appropriately:1 via:3 regardless:2 highly:1 send:3 org:1 apply:2 linearly:1 fr:1 nuffield:1 use:4 proceed:1 would:1 prove:3 contains:1 tail:1 anticommutation:1 linear:1 call:1 therefore:1 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quant-ph0703210.txt |@word represent:1 logarithms:2 partial:9 consider:9 gp:1 varying:2 results:5 gx:2 leads:1 proposition:2 computation:2 rephrased:1 consists:3 follow:1 expressions:1 gl:2 row:1 compact:3 whose:1 preserves:1 eu:1 terms:7 calculate:1 leung:1 technique:2 arbitary:2 acting:2 cλµν:3 finally:4 according:2 christandl:2 γn:1 th:5 under:2 analogous:2 include:4 norm:1 combinatorics:1 subtleties:1 applied:2 worse:1 straightforward:8 orthogonal:2 far:1 implicitly:1 eiλt:2 choice:2 corollary:23 every:14 commute:1 entries:1 bounding:1 difference:2 matrices:5 condition:1 wa:5 dim:12 annihilated:1 unlike:1 immediately:1 presented:1 irreducible:42 trb:9 fewer:1 integrated:1 deals:2 vector:39 rν:19 small:4 eigenvalues:1 trr:1 programme:1 upper:2 smaller:2 says:1 carter:1 haar:7 direct:4 literature:1 approximation:27 fold:4 zero:6 concludes:2 further:5 oneto:1 ρn:2 gm:1 canonical:3 even:1 koenig:1 what:2 sud:2 plays:1 ψn:4 giving:1 section:14 expressed:1 henceforth:1 version:3 speedy:1 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quant-ph0703211.txt |@word neighbors:5 limited:1 positions:1 code:2 skeleton:19 chain:3 represent:1 magnetic:1 reversibility:1 focus:1 existing:2 illustrated:11 executing:3 proposition:1 computation:12 lll:1 consists:2 gn:5 faster:1 gi:1 consider:3 whose:2 aligned:1 depend:1 graph:5 technique:5 nonlocal:1 long:1 helps:1 analogous:1 include:2 swap:22 applied:17 amplitudes:1 g1:1 g0:1 very:4 pages:2 results:3 every:15 updates:1 jacob:1 affect:1 1s:4 matrices:1 entire:2 grover:1 swapping:10 level:12 turns:1 proposals:4 make:6 fewer:2 large:3 discrete:3 commute:4 science:1 small:2 markov:1 round:1 upper:13 smaller:3 10n:5 mosca:1 direct:6 l2n:2 approximation:1 surrounding:1 likely:2 cost:1 go:1 concludes:1 run:3 implemented:3 odd:1 targets:1 diagonal:3 theory:2 even:3 what:3 indicator:3 sub:1 advantageous:1 brackets:1 section:6 selected:1 decoding:1 version:1 3n:8 above:4 3l:4 values:6 unrestricted:6 ever:1 acknowledgments:1 satisfy:1 lessons:2 simultaneously:1 degree:6 becher:1 vala:1 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quant-ph0703214.txt |@word gr:5 results:9 leads:3 entropy:8 computation:1 expressions:1 contributions:1 preserves:1 calculate:2 petersburg:1 td:4 include:1 case:4 very:2 frequencies:3 aarseth:2 electron:4 kittel:1 emphasized:2 condition:4 presented:2 applicable:2 small:1 force:2 grateful:1 consistent:1 literature:1 zero:12 street:2 linear:1 even:2 established:1 what:1 appear:1 goes:2 lifshitz:2 new:2 acknowledgments:1 contrast:1 publications:1 satisfy:2 condensed:1 bezerra:4 residual:3 here:1 mev:9 relaxation:8 alone:1 violate:1 obtained:2 rigorously:1 technical:1 larger:1 approaches:1 contradiction:5 makes:1 explained:2 bostr:1 decrease:1 use:2 takes:1 would:1 prove:1 negative:1 m2:3 høye:2 more:1 formally:1 clearly:2 becomes:1 hold:1 must:6 account:1 room:3 recall:1 values:6 temperatures:7 following:2 proof:2 claim:1 numbers:1 requirements:1 provide:1 holds:1 instead:1 mar:1 description:1 thermodynamic:1 wiley:1 ζm:9 uneisen:6 wrong:1 deviates:1 demonstrating:1 law:8 constants:1 dynamical:1 liquid:1 computations:2 acknowledged:1 st:1 decreasing:2 order:2 typical:4 unacceptable:1 course:1 thermal:4 including:1 statistical:3 mentioned:2 perfect:17 rapidly:1 decreases:3 gen:1 mohideen:2 pergamon:1 them:1 landau:1 framework:1 they:1 oxford:1 dielectric:2 easily:1 term:3 university:1 realistic:1 inequality:11 found:3 energy:4 principles:1 frequency:11 ellingsen:2 quantum:2 our:1 drude:13 satisfied:3 rev:3 collisions:1 contained:1 ref:27 correct:2 math:2 theory:2 interactions:1 given:1 reason:3 york:1 derivation:4 omits:1 first:2 opez:4 number:1 least:2 inapplicable:1 temperature:14 their:3 introduction:2 eqs:2 system:1 approximately:2 indicate:1 assumption:1 imperfect:1 moscow:1 exactly:1 proving:1 transverse:2 part:1 authors:5 than:2 coefficients:7 wide:1 accordance:3 matter:1 determined:2 were:2 russia:2 bordag:1 lowest:1 nernst:12 correction:4 partnership:1 argument:1 seen:2 concentration:1 orders:1 depending:1 note:2 k2:3 electric:2 opposite:3 impurities:12 most:1 boltzmann:1 inconsistency:1 calculated:1 metal:1 physica:1 brevik:2 physics:5 fact:2 particularly:1 violation:2 based:1 should:4 analytic:1 only:3 employed:1 equilibrium:1 do:1 above:5 truly:1 cannot:1 lattices:16 ds:1 arxiv:1 analytical:3 explanations:1 ignored:1 reference:2 violated:3 see:2 result:4 discussions:1 close:1 violates:2 best:4 subject:1 fails:1 inequalities:1 nondegenerate:1 state:2 various:1 correctly:2 between:2 approach:7 recently:1 however:5 configuration:1 abruptly:1 both:2 many:1 taking:1 equal:2 casimir:12 contribution:1 expression:2 finds:1 comment:1 co:1 conclude:1 simple:1 simply:1 applicability:1 proved:1 thermodynamics:2 west:1 romero:4 due:3 been:1 much:1 basic:2 ph:5 ann:1 sufficient:1 krause:4 metals:8 c2:7 c1:7 present:1 applied:2 pacs:1 solid:1 value:2 behavior:2 region:1 refs:5 thus:6 according:5 claimed:1 helium:1 containing:1 formulations:1 same:2 any:2 quant:5 incorrectly:3 plates:2 conflict:1 independent:1 used:5 numerical:4 uses:4 noncommercial:1 lower:3 solve:1 model:14 just:2 less:1 being:1 obtain:1 mistakes:1 scattering:1 previous:1 field:1 mostepanenko:8 lattice:4 valid:4 samples:8 theorem:12 plasma:1 real:1 around:1 using:3 formal:1 helpful:1 index:1 works:1 permittivity:1 because:1 decca:4 deal:1 some:1 debye:1 nonzero:5 lead:1 klimchitskaya:6 does:2 provides:1 run:1 scientific:1 jumps:1 agreement:3 although:3 permitted:1 asymptotic:3 om:1 actual:1 dependence:2 range:1 misleading:1 recognizes:1 consequently:1 bloch:3 lowtemperature:1 presence:1 previously:1 instruments:1 into:2 within:1 numerically:1 references:1 theoretically:1 there:3 dispersion:1 low:4 fraction:1 was:4 function:2 north:1 heat:4 magnitude:2 impedance:1 up:2 theoretical:1 crystal:16 verification:1 demonstrate:1 problem:1 matsubara:4 constant:1 800k:1 abstract:1 contribute:1 fischbach:4 geyer:3 proven:1 au:14 physical:1 compared:1 nn:1 no:5 eq:4 whereas:1 when:5 invalid:1 application:2 other:1 theor:1 concerning:1 conclusion:1 sernelius:2 important:1 additionally:1 phonon:2 starting:1 having:2
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quant-ph0703215.txt |@word neighbors:1 limited:2 partial:4 consider:10 chain:1 informally:1 results:3 leads:8 gf:5 proposition:3 entropy:3 comments:1 computation:2 rephrased:1 consists:1 disj:8 rectangles:8 whose:1 simon:2 depend:1 calculate:1 graph:2 concerned:1 deterministic:7 tr:9 quasi:1 those:5 under:3 suite:1 must:3 presentation:1 started:1 applied:4 conjecture:3 string:2 advantage:1 very:2 implicitly:3 r99:4 choice:2 me:2 every:8 anonymous:1 fall:1 instantiations:1 proba:1 condition:5 partitions:1 four:1 randomness:8 exponential:5 solves:9 level:1 r92:3 having:1 solution:5 occurs:19 try:1 solved:9 harry:1 small:1 markov:2 upper:4 zn:1 smaller:1 restated:1 za:4 elegant:1 likely:2 cost:24 perspective:1 equal:4 rigorous:2 further:1 αi0:4 even:4 established:2 what:3 appear:1 richard:1 section:4 selected:1 nec:1 lexicographic:1 experiment:1 absolute:4 watrous:2 relational:5 public:9 satisfy:1 pose:1 simultaneously:5 degree:1 exchange:1 respectively:6 applies:3 answers:1 desired:1 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quant-ph0703216.txt |@word represent:2 consider:17 pointing:1 limited:1 magnetic:5 global:3 results:6 eds:1 generalize:1 computation:1 edu:2 go:1 expressions:3 contributions:1 localized:1 whose:1 γx:4 tx:1 ρst:3 γs:1 subjected:3 environment:8 γi:2 under:36 γc:12 stochastic:4 γa:45 include:2 concurrences:1 indicating:2 ta:1 division:1 labels:3 rise:1 conditions:1 choice:2 implicit:1 γabc:3 bounding:1 em:2 parameter:1 matrices:28 encounter:1 paz:1 bxy:3 beginning:4 retaining:1 level:9 tra:1 who:1 fragile:10 solution:1 large:4 solid:1 vector:2 science:1 further:5 eigenvalues:1 markov:2 shows:1 noted:1 dis:2 privman:2 miquel:1 rate:10 timescales:11 qualitatively:1 dynamics:1 canonical:1 subscripts:1 eia:2 what:1 abc:28 appear:3 giving:1 trivial:1 sum:3 jaeger:3 labeled:3 d3:1 3k:1 ρr:5 en:1 above:24 new:1 d1:1 method:1 contrast:7 satisfy:1 full:2 ρw:15 degree:1 ρab:9 respectively:4 ficek:1 component:2 teleportation:1 here:23 atoms:2 lack:3 cac:5 possibility:1 address:4 alone:2 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quant-ph0703217.txt |@word ωr:15 a2:1 cn:3 jº:1 2a2:1 16d:1 2md2:2 eº:1 cathode:1 τsp:1 quiet:1 2πx:1 mdx:1 en:2 anode:1 3a:2 ad:2 ev:6 dc2:3 cv:1 reflector:1 dc1:2 iω1:3 pt:2 iω2:3 d2:1 radiation:1 γt:1 t2:2 µo:1 quant:1 ψm:2 ψn:8 ph:1 γc2:1 sin:3 τp:11 dcn:2 mar:1 p3:1 ω2r:10 x¹:4 dµ:6 xd:1 dx:8 2m:5 c2:18 dt:25 dr:4 πx:1 dp:1 e2:1 p2:4 iωt:2 cos:13 2r:1 iωr:1 sr:6 arxiv:1 ǫo:3 ωt:12 t1:3 evx:2 2g:1 exp:19 ωn:2 dº:1 x12:2 iωn:2 c1:9 sd:4
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quant-ph0703218.txt |@word argues:1 gda:4 scalar:1 paper:3 expressions:1 teoretycznej:1 true:1 theorem:6 hidden:1 save:2 local:3 get:1 showing:1 unveil:1 they:1 now:1 like:1 fizyki:1 arxiv:1 bivectors:1 realistic:1 inequality:1 works:1 uniwersytet:1 programme:1 eh:1 ec:1 namely:1 eu:1 out:1 marcin:1 since:1 between:1 confusion:1 clifford:2 christian:4 bb:4 respectively:1 disproof:2 institute:1 equal:1 v3:1 mentions:1 comes:1 comment:1 nsk:2 bell:6 variables:4 qed:1 use:1 there:1 physics:1 statement:1 astrophysics:1 ph:2 theoretical:1 pl:2 flaw:1 form:1 scalars:2 acceptable:1 but:1 part:1 irrelevant:1 valued:5 nska:1 clifford:3 equation:5 work:1 nski:1 us:1 values:1 proof:2 aa:4 proved:1 rewrite:1 argument:1 pawlowski:1 qap:1 quant:2 mar:1 algebra:5 rhs:1 wrong:1 important:1 recent:1 requires:1 correspond:1 dρ:2 observables:2 chsh:1
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quant-ph0703220.txt |@word represent:3 since:4 homomorphism:1 results:2 four:8 scalar:1 generalize:1 partial:1 contributions:1 compact:1 whose:1 calculate:1 bivector:2 graph:1 tr:3 intensive:1 glaser:1 those:3 excluded:1 case:6 amplitudes:2 orthogonal:2 wave:4 every:2 summarized:2 matrices:5 condition:5 leads:1 level:10 pacs:1 fewer:2 bivectors:10 convenience:1 small:2 noted:1 e35:2 upper:1 smaller:5 ten:3 pulse:1 elegant:1 second:1 design:1 pass:2 iσ3:1 dynamics:1 implemented:1 odd:1 even:8 expressed:3 sequential:1 nonuniversal:1 new:2 connected:1 method:3 full:2 αkj:2 here:2 operating:1 possibility:1 groups:5 represented:6 along:2 fifteen:1 change:1 obtained:2 study:3 vectors:6 eberly:2 akj:16 products:5 uniquely:1 stockton:1 e15:5 offset:4 e14:4 unit:6 clifford:11 use:1 projector:2 distinct:1 contains:1 ψj:12 ψk:4 therefore:2 usp:1 taken:1 themselves:1 rabitz:3 until:1 diagrams:2 more:5 mineola:1 anticommuting:1 operators:4 odinger:1 everywhere:1 known:2 projective:1 cases:1 iii:3 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quant-ph0703221.txt |@word secondly:1 monte:3 code:1 sci:1 consider:1 switched:1 induces:1 results:9 leads:4 latter:3 lewenstein:1 go:2 follow:1 amplified:1 faster:1 phenomenon:1 ρss:2 increase:2 object:1 gases:2 immanuel:1 rayleigh:1 finally:1 monotonically:1 those:1 th:1 under:2 stochastic:2 analogous:2 worth:1 apparatus:1 applied:1 evolves:1 very:8 springer:1 wave:5 electron:2 every:3 resonant:1 experimentally:4 difference:4 exact:1 condition:6 dominate:1 olaf:1 vibrational:3 level:4 did:1 positions:1 solution:2 supersolid:1 damped:2 large:4 solved:1 vector:1 quick:4 entropy:1 equation:4 configurations:12 application:2 damski:1 slower:2 oscillation:11 sin2:2 direct:3 literature:1 sign:2 jump:15 consists:1 second:9 noise:1 plenum:1 sustaining:2 further:2 dynamics:22 carlo:3 remarkably:1 quite:3 even:6 trapping:2 rate:1 specification:1 dephasing:1 experiment:1 bernhard:1 above:17 flowing:1 new:2 increasing:8 consisting:1 contrast:1 body:1 full:4 escaping:2 adiabatically:2 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quant-ph0703222.txt |@word represent:1 hampton:2 concept:9 semantic:1 consider:22 riccardo:2 crucial:1 results:9 leads:7 eds:3 commute:2 anticorrelated:2 expressions:1 decisions:4 reasoning:2 causes:1 maximally:1 depend:1 violate:1 tu:1 contained:1 finally:7 daniel:1 helps:1 under:1 resources:1 case:10 orthogonal:2 very:10 misunderstanding:1 focus:2 every:1 rationality:30 experimentally:1 difference:3 framing:2 perceived:1 incoherent:1 presented:6 try:2 discrete:2 vector:14 cognition:1 eigenvalues:3 busemeyer:3 measuring:2 occurrence:2 consistent:1 sin2:1 measurable:1 sign:1 second:4 perspective:1 further:1 repetition:1 theory:10 even:3 asin:2 what:4 errors:3 appear:2 rate:1 incompatible:1 giving:1 sun:1 section:6 interactions:1 brief:1 expressed:1 aerts:3 version:1 jerome:1 above:1 new:7 kahneman:4 paradoxical:2 hastie:1 collateral:1 simultaneously:6 measurements:1 respectively:7 human:3 answers:9 diagonal:1 objects:1 operating:1 cos2:1 directions:1 standard:1 equations:3 change:2 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quant-ph0703223.txt |@word childs:1 homomorphism:4 consider:1 results:2 computation:2 consists:1 query:1 primes:1 simon:2 calculate:4 xtp:18 present:4 p2:18 g2:2 g1:2 very:1 worst:1 decide:2 høyer:2 xt2:2 xt1:6 presented:5 proc:1 notes:1 list:3 solution:4 t1:3 solved:2 zn:10 employing:7 bacon:1 direct:9 literature:1 second:1 concludes:1 odd:6 employ:2 appear:1 sum:1 above:1 new:1 method:4 lee:1 respectively:1 mula:1 mathe:1 groups:17 address:11 magniez:1 funded:1 step:1 fourier:4 quotient:1 useful:1 divide:5 classification:2 apr:1 vii:2 addressed:3 apply:3 counts:1 use:7 proceed:5 distinct:1 positive:1 properties:1 therefore:6 minor:1 foundations:4 cases:6 iii:8 must:1 isomorphism:2 science:4 work:3 remain:1 values:16 following:10 root:2 proof:2 employs:1 give:1 organized:1 states:1 numbers:1 hides:4 sense:1 guarantee:2 information:4 end:1 gcd:2 provide:1 verify:2 holds:1 how:3 symposium:2 parameter:2 fp:3 product:5 fx:3 fy:3 after:1 mal:1 efficiently:4 attempt:1 third:4 register:4 secs:1 ones:2 algorithms:19 fp3:1 fp2:4 order:3 over:2 paper:2 left:1 ieee:5 le:3 group:30 thank:1 solving:1 decreases:1 forms:11 parts:1 choose:1 hidden:6 main:1 lx:1 maximal:1 eventually:1 non:4 greater:1 dam:1 disregarded:1 they:2 yp:1 now:9 discuss:1 february:1 2s:1 fully:1 applied:1 each:6 found:3 characterized:4 t2:1 reduce:1 society:2 extended:1 yield:1 measure:4 quantum:24 our:1 operation:1 avoided:1 special:2 gon:1 restricted:2 since:1 may:3 formula:7 ref:11 occurs:3 rj:1 semidirect:2 possibility:1 completely:4 advance:2 r1:1 determining:1 exponentially:2 first:3 initial:3 probability:3 xa:4 number:3 oracles:1 done:1 directly:1 xp:40 electronic:2 xt:9 given:4 introduction:1 unknown:1 their:1 too:1 siam:2 eliminates:2 part:1 somewhat:1 authors:1 calves:1 than:3 kind:1 determines:2 showed:1 cyclic:9 was:3 see:1 determined:3 opolis:1 addressing:1 generality:3 argument:1 generalization:1 randomly:2 say:2 gall:3 any:10 relatively:1 zero:1 min:1 efficient:5 zp:7 latter:1 complexity:4 take:3 normal:7 cient:1 santha:2 simplify:1 satisfying:1 probabilistic:1 class:14 considered:1 tpm:1 laborat:1 proceedings:3 usual:2 physics:1 shor:2 show:3 reductions:2 obtains:1 keywords:1 trivial:3 parameters:10 distributed:2 lemma:1 only:4 generators:8 factor:2 employed:2 abelian:32 get:3 de:1 overall:1 cannot:1 international:1 prime:9 runs:1 querying:1 arxiv:6 factorization:2 acknowledgments:1 contain:1 set:2 depends:2 computer:8 sec:10 result:8 discussions:1 close:1 techniques:1 brazil:1 learns:1 currently:1 state:8 classes:3 petr:1 recently:1 restricting:1 both:2 last:1 ıfica:1 many:1 annual:2 faperj:1 dated:1 finds:1 otherwise:3 among:1 point:1 poly:2 orio:1 polynomial:1 pr:3 most:1 described:8 basis:4 zps:1 zpr:33 three:1 strategy:5 reduction:15 pj:1 ph:6 pi:3 pn:1 partial:2 pm:1 restrictions:1 kitaev:1 irrelevant:1 those:5 case:26 p3:3 p1:1 pacs:1 xa1:4 xa2:2 zp2:40 value:4 will:4 cast:1 inui:3 suppose:5 viii:2 applies:1 35th:2 procedure:1 portugal:1 vi:4 them:1 iv:3 ii:7 same:5 orders:1 unity:1 complex:1 quant:6 split:1 finite:3 development:1 independent:1 used:1 stacs:1 sym:1 running:2 purpose:1 kim:1 subgroups:16 relies:1 depending:1 analysis:2 46th:1 solve:2 paradigm:1 subgroup:19 obtain:2 integer:6 alternative:1 conclusions:2 conclude:1 seems:1 nacional:1 easy:1 theorem:1 reason:1 solvable:3 remaining:5 build:1 advances:1 possible:11 know:3 press:2 using:10 intersection:1 mod:13 loss:3 success:3 follows:2 reduces:3 yields:1 either:13 characterizes:1 works:1 reduced:1 because:4 methods:2 classical:1 some:9 constructively:1 b0:3 examples:1 b2:6 proper:1 leal:1 does:6 provides:4 straightforward:2 measuring:1 considering:1 run:2 bb:1 journal:3 hsp:36 br:2 between:3 simpler:1 integers:1 about:3 a0:6 o:3 chi:1 primitive:1 computational:7 letters:1 into:4 isomorphic:4 determine:6 operator:4 reducing:1 van:1 log:4 prepare:2 there:7 transform:4 fast:1 ωp2:1 way:2 sections:1 function:7 hx:5 hy:5 complete:1 form:11 differences:2 but:1 cnpq:1 faster:1 computa:1 coset:1 whether:2 ωp:1 us:1 pr11:4 pl:1 problem:6 similar:5 b1:9 computing:2 defined:2 describe:1 ao:1 general:1 no:3 when:12 elements:2 a1:2 commutator:1 generated:2 a2:4 bounded:1 focs:1 structure:2 factorized:3 algorithm:14 time:1 oracle:1
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quant-ph0703224.txt |@word ibid:2 childs:2 consider:6 switched:1 hint:1 invoke:1 varying:5 results:15 illustrated:1 arranging:1 scalar:2 disappears:1 lewenstein:2 dalton:7 follow:2 expressions:5 contributions:9 cases:34 restrictions:2 whose:3 b10:1 dimensionality:1 depend:2 d18:1 transferred:2 eα:16 involve:11 editors:1 finally:5 restriction:3 those:5 excluded:1 breach:1 γa:1 characterised:2 raimond:1 b5:1 r1:60 applied:2 rsr:12 amplitudes:4 g2:53 straightforward:1 linked:1 frequencies:37 ρc:20 splitting:5 explanation:1 k0:1 approximate:1 resonant:14 little:1 matrices:13 condition:3 treating:1 four:2 brisbane:1 level:18 altering:1 positions:3 notes:1 developing:1 t2:122 solution:10 quasimode:21 large:3 discrete:14 pbg:10 vector:6 pba:1 small:5 zhu:1 becker:1 optics:9 noted:1 maali:1 upper:35 iht:1 smaller:2 nikolopoulos:1 computation:1 dealing:1 direct:3 pulse:1 sign:1 approximation:6 zero:41 displays:1 d7:1 qualitatively:5 dynamics:2 choices:1 situated:5 linear:4 spectral:57 aim:1 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quant-ph0703225.txt |@word capacities:2 partial:1 consider:8 chain:1 similarity:2 alg:1 global:14 desirable:1 results:4 eds:1 mild:1 entropy:5 comments:1 2n2:1 expressions:1 research:1 c1:62 compact:4 increase:1 hold:1 remarkable:1 tr:4 γt:2 γk:3 finally:7 program:1 squeezing:1 those:2 th:2 under:6 alberta:1 stochastic:1 presentation:1 spec:2 norm:5 applied:3 orthogonal:1 very:4 rise:5 springer:1 4ef:1 corollary:7 every:1 entries:1 matrices:22 condition:8 basics:1 beam:1 hamiltonian:1 induction:5 guo:1 solution:6 leave:1 solved:3 vector:4 phase:3 small:1 eigenvalues:27 anal:1 shows:2 optics:1 ciar:1 upper:5 abbreviated:1 ρj:1 disordered:1 findings:1 zk:2 consistent:9 literature:1 horn:3 second:8 perspective:1 substituting:1 qma:1 further:3 remarkably:1 canonical:2 even:3 established:2 what:10 plays:1 stands:1 t2n:1 qip:1 diag:15 sum:1 celebrated:1 2c21:1 higuchi:4 networks:1 witnesses:1 version:1 en:1 above:12 sup:1 obvious:1 ground:1 consisting:2 satisfy:5 condensed:2 full:7 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quant-ph0703227.txt |@word neighbors:2 since:1 partial:1 consider:13 global:1 results:6 leads:2 roy:1 scalar:1 concept:1 entropy:2 computation:2 intricate:1 covalent:1 faster:1 reasoning:1 excludes:3 gases:1 terms:2 tr:1 finally:1 spain:1 under:2 sent:1 applied:2 belonging:1 chennai:1 very:3 regional:1 wave:1 every:2 matrices:2 four:4 school:1 presented:1 turns:1 trb:1 qudit:2 small:2 eigenvalues:1 noted:1 dimer:2 configurations:1 upper:4 findings:1 insignificant:1 trebst:1 liang:1 mediterranean:1 direct:1 sign:2 zero:4 infimum:1 further:1 odd:5 cfs:1 even:5 what:2 ferromagnetic:1 sub:12 3r:1 sum:1 3p:1 brief:2 expressed:2 indian:1 3n:1 above:4 shared:6 increasing:2 method:2 body:6 condensed:5 lee:1 mec:1 teleportation:2 here:4 understanding:1 leeds:2 mckenzie:1 boron:1 represented:1 consideration:1 along:1 strong:2 observing:1 superconductor:1 extreme:2 obtained:4 sending:1 institute:1 elaborate:1 amount:7 periodic:1 resulting:2 monogamous:1 action:1 resonance:1 genuinely:2 via:1 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quant-ph0703232.txt |@word semantic:3 results:5 rebbi:3 controversial:2 whose:1 aug:1 subjected:1 summarised:1 those:2 under:1 amplitudes:4 very:1 rise:2 misunderstanding:1 focus:1 electron:13 affect:1 bubbles:11 purely:1 vector:1 surrounding:1 even:1 incompatible:1 giving:1 experiment:3 above:3 fractional:10 relational:6 jumps:1 full:2 exchange:1 here:2 understanding:1 condmat:1 objects:2 others:1 implicit:1 vectors:1 ignoring:1 resulting:2 bob:7 changes:1 involves:1 jackiw:1 appropriately:1 regardless:1 addresses:1 ions:1 outcomes:7 aimed:1 spawned:1 would:1 remains:1 charge:7 examination:1 more:1 constructs:1 carrying:1 objections:1 schrieffer:1 account:1 recall:1 work:1 del:1 claim:1 process:3 vicolo:1 cited:1 assumptions:1 arise:1 sharp:1 information:3 rather:1 verify:1 holds:1 feature:1 dismissed:2 mat:1 superluminal:2 may:2 wave:2 data:1 liquid:5 light:1 correspond:1 so:1 order:1 interpretation:1 pointed:1 argues:1 paper:1 through:1 argued:3 actually:2 detected:2 systems:1 hidden:1 correspondence:1 them:2 evolution:1 they:4 now:1 handy:1 nor:1 matched:2 verifying:1 presented:1 each:2 found:4 constraints:2 formulate:1 series:1 energy:5 related:1 measurement:18 quantum:5 our:3 out:1 contend:2 furthermore:1 since:1 particles:5 induced:2 correct:1 theory:1 enforcing:2 free:1 put:1 interaction:1 reexamined:1 exhibited:1 exotic:1 instances:2 directly:2 toy:1 temperature:2 similarly:1 system:1 their:3 assumption:1 statement:1 speaking:1 gives:1 collapse:1 releases:1 relative:1 smerlak:2 optical:1 authors:2 july:1 than:1 observed:2 require:2 aims:1 amplitude:4 falsification:1 outcome:1 epr:2 measure:1 argument:9 any:2 viewed:1 note:1 forming:1 detector:1 play:1 arguing:1 object:2 maris:11 but:3 device:1 coin:1 measured:4 clear:1 electrons:9 ferrara:1 notion:2 fact:1 bring:1 based:3 knowledge:2 rovelli:2 should:1 only:5 surveyed:1 local:3 zeh:2 probabilities:1 exchanged:2 his:1 quantph:1 dependent:1 cannot:1 words:2 regarding:1 arxiv:5 experiments:1 common:1 contain:1 release:2 erroneous:2 observer:3 detection:1 see:2 nonlocality:2 inappropriate:2 subsequent:2 fission:1 state:5 disprove:1 between:4 approach:1 email:1 preserve:1 terms:2 nature:3 suggested:1 triggers:1 according:1 against:1 distinction:1 argue:4 com:1 experimental:4 relevant:3 point:2 cf:2 dimensional:1 rightly:1 pp:1 described:1 basis:2 locally:7 due:1 been:1 appears:2 minimise:1 ph:3 enable:3 corresponding:1 observers:1 spin:2 present:1 case:1 vecchi:4 will:12 while:4 superposed:2 property:4 unitary:1 examines:1 vol:1 surface:1 cluster:1 examined:2 cond:1 helium:5 capture:1 different:3 italy:1 make:1 same:1 quant:3 split:1 upon:3 entanglement:14 recent:1 disappears:1 well:1 analysis:1 person:1 comes:1 position:1 model:11 arising:2 just:1 being:2 underlying:1 shorthand:1 photons:3 discuss:1 setting:3 location:1 relevance:1 nos:1 excited:1 around:3 famously:1 entangled:8 spawns:1 like:1 particle:2 follows:1 alice:10 altschul:2 sized:1 arbitrary:1 page:1 classical:2 phenomena:2 affects:1 measurements:8 does:1 refer:1 measuring:2 core:2 minimization:1 journal:2 properties:3 simpler:1 about:4 concretely:1 constraint:1 discussed:1 distinct:3 carries:1 carrier:1 raised:1 referenced:1 letters:1 flawed:1 into:3 splitting:3 predictions:1 down:1 remarks:1 appropriate:1 references:2 elementary:1 uncertainties:1 intrinsic:1 strictly:1 there:3 long:2 conservation:1 low:2 fraction:1 decisive:1 bubble:6 function:2 steers:1 some:3 sequel:1 encodes:1 subjective:1 failure:1 encoded:1 he:1 absent:2 whether:1 up:1 us:1 verification:1 problem:1 similar:1 agree:1 mechanics:1 associated:2 certain:1 abstract:1 sketched:2 evidence:1 single:1 relates:1 physical:2 no:3 when:7 other:5 papers:1 optically:1 briefly:1 superposition:1 excitation:1 models:1 critiques:1 stay:1 accounts:1 physics:3 proposed:1 together:1 observables:4 signalling:2
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quant-ph0703233.txt |@word limited:1 sci:1 consider:1 switched:1 magnetic:1 particular:1 splitting:3 entropy:2 computation:1 anggi:1 localized:1 calculate:2 re:6 stably:1 factoring:1 environment:7 investigation:1 presentation:1 norm:1 very:5 frequencies:3 results:5 electron:2 affect:3 difference:1 exact:1 trk:1 level:2 large:5 kondo:1 fourier:1 small:2 biological:3 grifoni:3 smaller:3 force:1 broader:3 oscillation:5 trend:1 mi:14 approximation:12 zero:1 design:1 dynamics:14 estimated:1 linear:1 spectral:6 established:1 expressed:1 cell:1 en:1 cheng:2 letter:2 3a:1 appeal:1 method:8 coefficient:2 condensed:1 lee:1 here:10 κc:1 shortened:1 believed:1 china:2 relaxation:34 path:4 strong:1 equations:1 obtained:6 great:2 spite:1 institute:1 study:1 larger:2 mx:1 resonance:2 suitable:4 studies:1 plotted:2 tasks:1 useful:2 makri:7 namely:5 logical:1 zwerger:1 flexibility:1 decrease:3 total:1 shiokawa:1 plot:3 use:7 rugar:1 call:2 memory:10 taken:1 theoretical:3 more:4 introducing:1 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quant-ph0703234.txt |@word limited:1 consider:1 remarkable:1 holman:1 rev:4 kanai:1 existing:1 ge:1 edu:1 whose:1 ambjorn:1 technique:1 tr:1 under:5 applied:1 string:3 orthogonal:1 very:2 activation:2 connects:1 wave:13 exact:2 condition:4 hamiltonian:7 solution:9 discrete:4 small:1 eigenvalues:9 configurations:1 jhep:1 miller:1 direct:1 surrounding:1 zero:6 dynamics:2 odd:3 substitute:1 canonical:3 even:2 plays:3 richard:1 above:1 new:5 increasing:1 3d:1 lee:1 respectively:1 here:1 understanding:1 l20:1 separation:1 address:1 directions:1 path:1 strong:1 equations:4 interpret:1 box:5 great:1 study:3 studied:2 hermite:1 namely:1 explained:1 addressed:1 analyzing:1 apply:1 linearly:1 silva:1 would:1 negative:1 nucl:1 introducing:1 becomes:2 stable:1 hofmann:1 normalized:3 varying:1 known:3 states:3 equation:14 work:1 oscillator:39 theories:2 values:2 following:2 spontaneous:1 example:3 sinusoidal:1 expanding:2 involve:1 effectively:1 numbers:3 occur:1 normalize:1 fortunately:1 breaking:1 instead:1 parameter:2 sin:1 simplicity:1 mar:1 description:1 inflationary:1 derived:1 applications:1 plane:2 law:1 constants:1 branches:2 dynamical:1 effective:1 attracts:1 so:4 decreasing:1 janik:1 words:1 thermal:2 statistical:4 satisfies:1 castagnino:1 before:1 decay:6 interesting:3 solving:1 writing:1 systems:1 derivative:1 non:3 scaling:1 front:1 now:5 february:1 gets:1 university:2 level:2 barton:1 theory:6 l0:5 each:3 2m:2 square:2 directly:1 energy:25 gaussian:2 related:2 inverted:31 frequency:1 quantum:14 our:1 operation:1 special:1 shown:5 pedrosa:1 space:2 furthermore:2 since:7 crucial:1 may:4 contained:1 daniel:1 ra:1 get:1 occurs:2 math:3 linear:1 barrier:1 found:3 free:8 standard:5 admits:2 reason:1 khare:2 besides:1 temperature:3 hψ1:1 starts:1 transition:3 used:5 motion:3 length:2 exponentially:3 quadratically:1 first:1 origin:2 initial:3 symmetry:1 tachyon:1 variables:1 number:3 another:2 precisely:1 electronic:1 given:6 toy:1 sates:1 introduction:1 2ωt:3 system:4 expand:1 recovered:1 fermions:1 centered:1 continuous:1 authors:2 x2:3 wide:1 determines:1 approximations:1 tree:1 rate:3 contrary:3 perturbative:1 rewrite:1 ann:2 modern:1 spectrum:5 say:2 seen:2 note:2 high:2 potential:11 take:1 analogy:1 finding:1 coincide:2 begin:1 exactly:7 phase:2 analytically:1 observation:1 inferred:1 exp:4 mechanical:1 link:1 physics:12 laws:1 show:1 nπ:1 iǫ:2 relation:1 solutions:3 substituting:1 find:2 d0:2 resemblance:1 only:1 factor:1 parabolic:2 integrable:2 hamiltonians:1 equilibrium:1 goes:1 means:1 dependent:1 simplest:1 mignani:2 da:1 reversal:3 during:3 gen:2 evolution:1 arxiv:1 investigate:1 mapped:1 view:1 set:3 constructing:2 achieved:1 ωt:3 see:1 individual:1 mechanically:1 interacting:1 fission:1 diverge:1 state:4 between:5 invariant:2 boundary:4 statistically:1 attention:1 however:4 joo:1 both:1 reinterpreted:1 many:3 contract:1 dated:1 context:1 safely:1 point:4 wall:4 harmonic:22 reimann:1 lagrange:2 associated:3 turkey:2 guth:2 second:2 due:1 interest:1 expected:1 ph:1 pi:2 lett:2 obtained:3 direction:1 corresponding:2 gas:3 observe:2 understand:1 decreased:2 those:2 case:6 pacs:1 solid:1 cremonini:1 replaced:1 bhaduri:2 loop:1 chaotic:2 surface:1 ii:1 ik:2 vanish:1 fermion:1 increased:2 different:1 same:1 unity:1 complex:1 quant:1 physical:1 investigated:1 infinity:1 receives:1 levels:2 moving:1 potentials:1 normalization:3 well:1 solve:1 coordinate:1 position:4 model:4 just:4 being:1 newton:1 obtain:2 transforms:1 paul:1 speed:2 eigenstates:1 application:5 conclude:1 character:1 except:1 iω:2 transformed:2 treatment:1 solvable:4 transformation:5 around:2 depends:1 early:1 inflation:1 rescales:1 vacuum:1 confined:5 using:5 mod:1 theor:1 like:1 particle:14 cooler:1 follows:3 unstable:2 stationary:1 reduced:1 replacement:4 mathematical:1 parity:5 classical:4 kilic:1 provides:1 equivalent:1 expansion:3 instability:2 properties:1 rare:1 choi:1 dependence:1 range:1 guedes:1 introduced:2 h2:1 into:3 hermitian:1 en:1 operator:5 schrodinger:2 there:6 was:5 function:10 complete:1 metastable:1 brane:2 but:3 idea:1 volume:3 hn:1 atom:1 coupling:1 made:2 compute:1 characteristic:1 maximum:1 us:4 record:1 below:1 fermi:2 fluctuations:2 problem:9 mechanics:5 constant:7 classic:1 int:2 describe:1 doesn:2 single:1 formalism:1 distributions:1 sarkar:1 constructed:2 functions:4 dx:2 no:7 when:2 field:1 other:3 role:3 department:2 shin:1 massless:1 models:1 problems:1 polynomials:1 important:3 additionally:1 boyanovsky:1 longer:1 assume:1 expands:1 interval:1 confinement:1 mass:3 time:8 n2:1 starting:1 having:2
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quant-ph0703235.txt |@word consider:1 primed:1 ge:1 edu:1 depend:2 calculate:2 tr:1 finally:1 program:1 under:8 analogous:1 p2:2 far:1 wave:6 difference:1 exact:6 condition:14 hamiltonian:32 t4:2 t5:1 t2:8 solution:2 eigenvalues:19 noted:1 concluded:2 dutra:1 measurable:1 second:1 concludes:1 odd:4 even:4 appear:1 section:5 d3:1 above:3 suppose:3 contrast:1 satisfy:3 simultaneously:1 respectively:2 following:4 separation:1 address:1 change:1 obtained:1 great:1 study:3 allows:1 tial:1 simultaneous:1 usually:1 symmetrical:1 useful:1 hermite:2 substitution:2 replace:1 readily:1 use:2 prove:1 positive:1 next:3 ψn:3 bender:1 f02:3 taken:1 more:3 successful:1 becomes:1 backwards:1 known:1 cases:2 hold:1 eα:1 dunning:2 valued:3 equation:8 work:1 oscillator:1 remain:2 believed:1 spontaneous:1 example:6 f0:6 4t3:1 4t2:2 cited:1 organized:1 states:4 numbers:1 japaridze:1 conversely:1 guarantee:3 discussion:1 breaking:1 explains:1 simplicity:1 product:1 mar:1 transforming:1 derived:2 excited:4 constants:1 realized:1 introduced:1 spectra:3 so:9 fundamental:1 integrand:1 operations:1 words:1 over:1 expects:1 paper:1 existence:3 its:4 if0:1 lj:1 gen:3 better:1 parts:1 choose:2 derivative:1 h0:1 non:13 introduce:1 they:5 souza:1 now:2 nor:1 eigenvalue:2 february:1 always:1 university:1 2f:8 2g:2 found:2 2n:1 2i:3 en:4 energy:31 idea:1 t3:2 sinha:1 quantum:3 our:2 special:1 conjectures:1 shown:3 space:2 furthermore:1 since:7 rev:1 denotes:1 may:3 investigation:1 conjectured:1 math:3 linear:2 standard:1 reason:3 hott:1 dx:5 hψ0:1 derivation:1 hence:1 first:6 simplifies:1 symmetry:22 timeindependent:1 electronic:1 given:11 necessarily:1 introduction:1 system:1 unbroken:7 boettcher:1 shifted:1 exactly:2 part:4 x2:7 eliminated:1 than:1 zero:8 determined:1 contrary:1 unchanged:1 spectrum:20 7t:1 need:1 seen:4 any:3 latter:2 note:1 potential:8 unless:1 analytically:1 why:2 exd:1 don:1 surprising:1 considered:1 later:1 coincides:1 exp:4 mechanical:1 dos:1 physics:1 sum:1 dot:1 show:1 relation:1 substituting:1 trivial:1 find:2 ground:4 postulates:1 boundaries:1 e11:2 explain:3 should:1 analytic:2 only:1 explicitly:4 ien:2 hamiltonians:6 do:1 get:5 dependent:7 de:1 expectation:2 satisfied:3 ones:1 dz:1 reversal:2 dt:2 neither:1 fields:1 arxiv:1 investigate:2 europhys:1 requirement:2 set:1 computed:1 physically:1 depends:2 result:1 fail:1 techniques:1 said:1 eigenfunctions:5 symmetric:12 case:8 state:3 between:1 invariant:7 boundary:1 conditions:2 preserve:1 importance:1 however:2 2αx:1 suggested:1 both:2 region:1 equal:6 tateo:2 dated:1 finds:1 conclude:1 harmonic:2 maintained:1 associated:2 considers:1 turkey:1 transformations:6 pt:18 due:1 been:2 ph:2 systems:1 arises:1 corresponding:4 commutes:1 sufficient:3 2if:2 former:1 applied:1 pacs:1 value:2 spontaneously:9 will:4 replaced:1 property:3 ix:1 iu:1 them:1 reads:3 claimed:1 vanish:1 ig:13 santos:1 make:1 unity:1 complex:9 quant:2 hermiticity:4 independent:2 trivially:1 appearances:1 effect:1 reflection:1 well:1 solve:2 coordinate:4 parametric:1 obtain:3 transforms:1 eigenstates:3 regarded:1 character:1 lett:3 theorem:1 guarantees:2 solvable:1 transformation:2 real:27 eigenfunction:3 showing:1 using:3 lost:1 follows:1 serves:1 yields:2 either:1 works:1 reduced:2 parity:2 because:4 czech:1 successfully:1 some:1 examples:1 provided:1 integration:1 does:4 run:1 broken:9 shifting:1 although:1 2m:2 imaginary:2 getting:1 numerator:1 discusses:1 dorey:2 h2:1 into:3 h1:1 integral:6 hermitian:17 operator:8 schrodinger:2 there:3 question:1 was:5 eg:1 function:14 but:1 hn:8 true:1 whether:1 up:1 us:9 below:1 problem:1 mechanics:1 constant:4 general:3 exist:1 formalism:1 nonhermitian:2 functions:1 mathematica:1 when:11 vanishes:2 reality:7 other:1 department:1 conclusion:1 time:18 polynomials:2 variable:2 4t:1 interval:3 4i:1 antilinear:1 having:1
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quant-ph0703236.txt |@word partial:1 consider:3 chinese:1 focus:3 four:2 abelian:1 gb:1 computation:1 edu:1 gn:15 totient:1 research:1 row:2 whose:5 certainly:1 graph:49 quadruple:1 finally:1 monotonically:1 christandl:1 th:1 undirected:1 bipartiteness:3 p2:2 straightforward:1 very:1 results:1 fak:1 every:9 mixing:1 2rt:3 exact:2 vast:1 leads:1 hamiltonian:4 irreducible:2 list:1 solution:8 noiseless:1 discrete:1 proposition:1 math:1 harry:1 eigenvalues:10 upper:4 zn:14 smaller:1 periodicity:2 second:1 design:1 perspective:1 further:1 dynamics:6 odd:14 primes:4 substitute:1 telecommunication:1 residue:2 index:3 diam:8 section:7 networks:2 above:10 values:1 increasing:1 method:1 satisfy:1 degree:13 respectively:1 doing:1 here:1 desired:1 groups:1 path:2 equations:1 box:1 divisor:2 institute:1 shift:1 studied:1 contradiction:2 periodic:8 survey:3 hospitality:1 fourier:1 sci:1 york:2 diameter:10 classification:2 replace:1 hardy:1 sachs:1 sloane:1 univ:1 use:1 additive:5 vlsi:1 prove:5 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quant-ph0703237.txt |@word consider:9 similarity:1 caused:3 results:1 scalar:6 generalize:2 computation:7 edu:1 go:2 query:33 gj:2 causes:1 seemed:1 whose:2 careful:1 depend:1 reformulate:1 tt:11 technique:2 tr:7 γv:1 tn:13 finally:1 program:1 tj:12 th:2 norm:7 πs1:1 random:2 string:1 straightforward:1 evolves:1 bulletin:1 ρti:11 tradeoffs:3 corollary:15 worst:2 interpreting:2 fall:1 bounding:5 difference:2 matrices:8 høyer:4 tri:4 dim:1 conjugating:1 swapping:1 presented:1 turns:1 having:1 large:3 item:2 convenience:1 vector:1 minimal:1 science:1 small:10 eigenvalues:9 upper:21 smaller:3 says:2 consistent:1 direct:8 10e:3 fold:3 zero:1 design:1 initialized:2 zv:1 eigenspaces:6 goes:1 even:6 index:5 what:1 appear:1 complexities:1 fact:1 section:9 zhang:1 uniform:2 access:2 19th:1 version:11 subspaces:22 conduct:1 new:14 construction:1 increasing:1 method:27 beals:1 ρt:3 full:1 simultaneously:4 lee:2 degree:1 d1:6 respectively:2 applies:1 here:5 diagonal:17 berkeley:2 ratio:2 πji:1 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quant-ph0703238.txt |@word partial:1 consider:5 fitch:2 results:4 edu:2 calculate:1 technique:2 finally:1 include:1 division:2 presently:1 rise:1 focus:2 mixing:1 large:1 optics:2 upper:1 findings:1 rate:5 port:7 even:1 what:1 ˆs:1 diamanti:1 sum:1 current:1 goes:1 sup:1 acknowledgments:1 here:5 desired:3 appears:1 drops:2 funded:1 commonly:1 imaging:1 via:4 app:2 banaszek:3 visible:1 achievable:1 counts:3 plot:4 conventional:1 projector:1 rohde:3 distinct:1 distributing:1 australian:1 w911nf:1 more:2 outputs:1 silberhorn:2 particular:2 known:1 high:1 equation:1 work:2 values:2 caveat:1 making:2 arrive:1 give:1 process:1 confused:1 states:1 contradicts:1 numbers:1 council:1 counting:1 axis:1 information:1 optimal:1 mar:1 description:2 use:1 applications:1 improving:1 realized:1 undesired:1 light:3 ordinarily:1 element:2 ones:1 so:4 order:2 help:1 office:1 produces:3 over:1 paper:2 including:1 fidelity:16 jacobs:2 rapidly:1 thank:1 acknowledge:1 detected:2 fig:6 overcome:1 pittman:2 non:5 reflected:1 effects:2 they:1 arriving:2 now:2 discuss:1 represents:1 february:1 james:1 university:1 magnitude:1 mode:4 each:2 2n:1 ports:2 characterized:1 schemes:2 generation:1 idea:1 used:1 measurement:8 quantum:4 our:5 huntington:1 beyond:1 out:2 factors:1 rev:3 research:2 increase:1 ref:1 occurs:1 earlier:2 linear:1 kok:1 free:1 approaches:1 orm:1 conditioning:1 χ2n:1 detecting:2 pairs:2 benefits:1 could:1 routed:1 turn:1 signature:8 first:7 intuition:1 probability:11 number:14 timothy:1 given:4 introduction:1 jex:1 indicate:1 rates:1 scheme:4 asymmetric:5 qld:1 observed:1 perfectly:1 dto:1 measured:4 second:1 preparation:6 beneficial:2 were:1 modern:2 unlikely:1 sliwa:2 apparently:1 conversion:5 strength:1 zero:1 depending:1 able:1 click:1 ideal:3 causing:1 take:1 detector:4 begin:1 multiple:2 centre:1 most:2 significant:1 multiply:1 achilles:2 extremely:2 url:1 vlpc:1 detectors:5 takeuchi:2 braunstein:1 proceedings:1 χn:1 physics:3 fact:1 signatures:1 show:2 registers:1 networks:1 ratio:11 just:1 distributed:1 behind:1 only:1 mixture:1 between:1 remedy:1 cannot:1 timing:1 processes:1 resolve:1 arxiv:1 summary:1 experiments:1 architecture:1 set:1 bucket:1 detection:8 namely:2 computer:1 result:3 discussions:1 techniques:2 detect:1 registering:1 ways:1 currently:1 ralph:1 label:1 state:8 simplest:2 approach:2 across:2 notice:4 terms:4 confusion:1 attention:1 however:2 incident:3 distinguish:1 configuration:1 both:4 improved:3 region:1 equal:1 against:6 asym:1 dated:1 franson:2 expense:3 comes:3 applicability:1 considering:1 ps:8 three:1 been:2 ph:1 define:1 sanders:1 photon:19 resultant:1 present:3 case:5 multi:1 laser:2 pacs:1 value:1 will:8 determinism:1 metric:1 thus:2 downconversion:1 walmsley:3 ii:1 contract:1 technology:1 different:2 same:3 unity:1 quant:1 filtered:1 several:2 events:1 higher:3 arrives:1 http:1 see:1 possible:1 uses:1 kim:2 bartlett:1 modes:2 well:1 roughly:1 analysis:1 components:1 inability:1 model:1 parametric:4 protocol:1 kiss:1 proposed:3 brisbane:1 photo:5 obtain:1 paul:1 yamamoto:3 field:2 photons:13 day:1 source:1 other:3 lett:5 mod:1 opt:4 multiplexing:2 australia:1 government:1 multiport:2 term:3 dark:6 increases:2 entangled:2 using:6 helpful:1 desire:1 loss:5 like:1 success:2 follows:1 reduces:3 zoom:1 facing:1 benefit:1 arbitrary:1 popular:1 become:1 reduced:2 webb:1 www:1 because:2 people:1 conditional:6 some:1 peter:1 δn:1 ported:1 demonstrates:1 when:4 does:1 tdm:1 reaching:1 processing:1 confidence:1 ratios:1 output:8 plots:1 approximating:1 includes:1 tracing:1 army:1 discussed:1 practical:1 beamsplitter:7 presence:1 communication:1 splitting:9 bound:1 due:1 down:7 device:2 operator:1 proportional:1 prepare:1 assumed:1 support:1 there:8 approximate:1 specifically:1 low:2 was:2 form:2 but:2 count:3 applying:1 converter:2 places:1 uq:2 us:2 considered:1 limit:1 problem:2 associated:1 povm:4 resolving:5 general:1 single:9 au:2 regime:1 no:2 generally:1 application:2 interested:1 department:1 realize:1 elements:1 variation:1 prepared:4 important:1 queensland:2 independently:1 coupling:1 assume:1 space:1 modules:1 inset:2 time:2
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quant-ph0703239.txt |@word represent:1 consider:2 chinese:2 switched:4 caused:1 magnetic:3 global:2 splitting:1 four:2 commute:5 computation:7 edu:2 4e2:2 involved:1 layers:3 chain:5 tu:3 charge:33 tm:2 present:5 excluded:1 under:1 include:1 indicating:1 lack:1 zhang:3 very:1 springer:1 fabricated:2 blockade:1 electron:8 every:1 affect:3 randomness:3 hamiltonian:4 dodd:1 guo:9 t3:3 t0:17 t1:3 large:1 small:2 relation:1 gossard:4 noted:3 upper:1 mn:12 stepanenko:1 dealing:1 10a:4 zero:4 initialized:2 dynamics:1 mnb:1 folk:1 even:1 diag:8 section:1 while:1 experiment:1 above:7 new:2 satisfy:1 respectively:2 promising:1 residual:2 here:8 diagonal:2 following:4 explore:1 focused:1 address:2 based:1 tunneling:1 bremner:1 shift:1 changed:2 funded:1 leaving:1 usually:1 resonance:3 composed:1 technique:1 useful:1 apr:1 eiφ:2 total:8 gaas:1 use:3 remains:1 positive:8 negative:11 generate:3 comparing:2 program:1 andy:1 therefore:2 theoretical:2 more:6 separated:3 xian:1 berlin:1 qds:3 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quant-ph0703243.txt |@word consider:6 caused:1 global:1 eckert:1 results:7 chaos:3 leads:1 tripartite:1 proposition:2 entropy:14 mnm:1 computation:1 constants:1 follow:1 expressions:2 sega:1 reasoning:1 row:6 naudts:4 calculate:13 technique:2 tr:18 ts:2 tn:1 finally:4 program:1 tj:3 analogous:1 applied:3 random:1 worse:1 straightforward:4 orthogonal:10 far:1 rod:1 multi:1 choice:2 electron:3 entries:5 li:1 simplify:1 matrices:18 condition:1 generalised:6 four:1 squares:1 swapping:1 vibrational:2 hamiltonian:12 did:1 erratum:1 solution:2 t0:1 large:3 vector:1 math:1 indices:2 eigenvalues:10 noted:1 dimer:2 degeneracy:12 oliveira:1 mn:6 lewenstein:1 zj:2 horn:1 fold:3 imply:1 zx:1 castro:1 concludes:1 chen:3 dynamics:3 chem:1 odd:1 eigenspaces:1 theory:1 even:2 multiqubit:1 sum:3 localization:2 fortschritte:1 above:5 obvious:2 subtracting:1 method:4 buscemi:2 satisfy:3 kicked:3 bifurcation:1 diagonalises:2 here:5 reported:1 field:1 plenio:4 ansatz:1 others:1 represented:1 diagonalised:1 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quant-ph0703245.txt |@word represent:1 concept:1 consider:5 funct:1 holevo:2 proposition:3 entropy:41 compact:2 choquet:1 calculate:1 ohya:21 tr:20 tn:2 uniqueness:1 tk:2 ti:3 cm2:3 norm:5 accardi:1 orthogonal:1 springer:2 ieice:1 print:1 every:14 anonymous:1 matrices:1 trh:13 transmission:9 t4:1 t2:5 t3:2 t0:3 t1:4 deals:1 discrete:2 vector:2 math:6 science:1 eigenvalues:1 anal:4 dimens:2 second:1 further:2 dynamics:1 theories:1 linear:6 spectral:2 stands:2 xσ:1 associate:3 expressed:3 subspaces:1 sup:3 new:1 net:3 increasing:2 bn:1 fujiwara:1 here:12 fisica:1 address:2 represented:1 xα:5 extreme:1 obtained:1 remark:2 ekl:6 ekk:1 ekj:2 study:1 studied:5 amount:2 action:1 uniquely:2 named:1 useful:1 projection:1 classification:1 kossakowski:2 apply:1 use:1 prove:2 positive:15 hilbert:5 therefore:6 m2:4 taken:2 ua:1 operators:1 relat:2 berlin:2 normalized:1 fan:1 keeping:1 ers:4 recall:4 ρk:5 extremum:1 itself:3 obvious:2 ρt:11 following:9 trans:1 example:3 proof:8 continuity:1 suggestions:1 states:1 numbers:1 sense:1 occur:1 verlag:2 information:5 get:4 maps:9 instead:2 map:20 algebra:4 may:3 max:1 mapping:2 collection:1 coming:1 bratteli:1 natural:3 dynamical:5 e22:1 grant:1 element:4 extremal:2 si:1 ones:1 so:3 fundamental:1 representation:2 holds:6 ϕk:6 indeed:2 over:4 paper:3 through:2 yandex:2 statistical:1 differs:2 milman:2 its:2 fis:1 ln:9 lj:1 lk:1 forms:2 systems:4 ours:1 h0:8 non:1 h1:5 combination:2 gets:1 introduce:1 framework:2 now:8 finite:1 equality:6 extr:10 always:1 2x:1 orthonormal:2 inequality:3 each:3 mean:1 subset:1 arbitrariness:2 used:1 measure:3 quantum:23 ru:2 shown:1 matrix:2 unital:5 furthermore:2 since:4 rev:2 chaos:2 denotes:1 denoted:5 rj:1 shows:1 theory:6 state:22 infin:2 departamento:1 completely:8 york:1 besides:1 put:1 publ:1 log:12 definition:3 δij:1 wehrl:1 hence:4 probab:4 onto:1 separable:2 probability:2 faculty:1 powerful:1 channels:7 xy:1 another:2 takesaki:1 open:2 given:3 introduction:2 top:2 system:3 relations:1 1i:21 speaking:1 dt4:1 tashkent:1 continuous:2 representing:1 completes:1 kind:1 depends:1 determined:1 were:3 decompose:1 result:2 generality:2 rewrite:1 tϕ:6 mind:1 generalization:2 any:7 generalizes:1 jour:1 mappings:2 min:2 lim:1 mechanism:1 note:3 take:5 channel:6 play:1 fct:1 trace:4 normal:5 measures:2 algebraic:2 acknowledgements:1 tν:4 dordrecht:1 clear:2 coincides:2 kl:20 kq:1 points:1 mechanical:4 physics:1 notion:2 farrukh:7 show:6 converge:1 ki:3 spaces:1 relation:1 decompositions:3 find:3 e11:1 assertion:2 appreciated:1 lemma:7 only:1 going:2 araki:2 preliminaries:1 hope:1 meant:1 mixture:2 µk:10 means:1 ϕt:4 de:3 ϕq:3 ϕs:1 ϕr:1 ϕm:4 ϕl:3 dyn:1 ϕn:2 ϕi:11 words:1 ϕj:7 closure:2 arxiv:1 modern:1 implication:1 krein:2 thanks:3 set:16 exists:1 δjm:1 box:1 λk:15 see:17 projections:1 ieee:1 subject:1 said:2 capacity:2 supα:2 positivity:2 functionals:1 enough:1 closed:1 between:1 approach:1 petz:2 publishers:1 receivers:1 weak:5 ji:1 key:1 universitario:1 topology:3 both:1 many:1 conclusions:1 according:8 passing:1 finds:1 ck:1 cj:3 ci:1 ucp:28 reasons:1 dimensional:5 written:1 assertions:1 associated:3 commutative:1 pt:1 pu:1 due:1 been:2 defined:10 ph:2 algebras:2 abstract:1 empty:1 define:5 sfrh:1 referee:1 subspace:2 θx:1 representative:1 mail:2 c2:1 denote:10 present:1 c4:1 applied:1 kodai:1 will:4 compactness:1 behavior:1 eii:1 investigating:1 eij:14 λt1:1 a21:2 a22:2 portugal:2 von:3 thus:2 them:1 σf:2 ii:4 ij:18 im:1 property:2 hdµ:1 author:1 campus:1 complex:1 quant:2 units:2 several:2 φn:5 extended:1 nasir:7 hand:1 sys:1 infinite:3 identity:1 eigenvectors:1 weakly:1 yx:1 weapon:1 well:1 roughly:1 academic:1 without:2 usual:1 just:1 less:2 obtain:3 atomic:2 using:5 facts:1 λn:10 kluwer:1 density:1 conclude:1 had:1 other:1 collections:1 easy:1 theorem:15 input:1 heidelberg:1 seminorms:1 decomposed:1 possible:2 know:1 immediately:1 unique:2 moreover:1 loss:2 bpd:1 follows:4 δk:1 output:1 because:1 neumann:2 classical:1 pϕ:1 conditional:2 some:4 santiago:1 malaysia:1 b1:6 convex:3 2d:1 dense:2 decomposition:1 bb:5 bl:4 equivalent:2 bi:2 bj:8 bk:3 properties:3 extension:4 basis:3 o:2 mutually:1 whence:1 introduced:12 consequently:1 lieb:1 inclusion:1 into:5 within:3 functional:2 mukhamedov:8 references:1 operator:17 methods:1 uncertainties:1 formulate:1 there:5 strict:1 appl:2 physicists:1 way:1 was:3 function:1 complete:2 form:1 δkj:2 convergence:1 commun:2 extremity:1 us:4 limit:1 similar:1 called:9 barycenter:1 mechanics:1 proved:3 ai:13 certain:1 ak:4 aj:3 general:1 chap:1 proves:1 inf:10 universidade:1 physical:1 ni:6 mutual:1 nk:2 faithful:1 no:3 when:1 rs:5 field:1 valid:4 role:1 mathematics:1 stat:1 elements:5 a11:2 a12:2 symbol:1 semin:1 a1:1 generated:3 important:1 bounded:3 sides:1 watanabe:3 implies:3 auxiliary:1 assume:5 aveiro:2 space:4 resolution:2 rep:1
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