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quant-ph9607028.txt |@word holmes:1 semiclass:1 feedback:4 proposed:1 less:1 indeed:1 supported:1 destroyed:1 illustrated:1 kurizki:1 quadrature:2 already:1 human:1 still:1 macroscopic:1 find:1 causes:1 rev:9 ratio:1 thank:1 zoller:1 acknowledge:1 chosen:1 interesting:1 mobility:1 seems:1 should:2 recurrence:1 quasi:1 fig:7 easy:1 factor:3 anharmonic:3 versus:1 case:2 advantage:1 very:1 capital:1 evolution:1 number:1 february:1 dv:1 ys:3 difference:1 apart:1 term:1 fox:1 stated:1 like:2 only:1 presented:1 turns:1 university:1 adiabatic:1 kerr:1 thermal:1 large:3 convenience:1 mode:3 alternatively:1 small:1 universit:1 european:1 optics:2 equation:3 programme:1 arxiv:1 just:1 occurrence:1 generation:2 some:1 related:1 manifests:1 zero:2 dissipation:1 result:2 quantum:3 dynamics:1 ur:1 eq:3 out:4 ignore:1 shown:2 nonlinear:2 tombesi:1 interacting:1 bottom:1 cavity:2 washed:1 quantenphysik:1 state:4 daniel:1 between:1 prof:1 increasing:1 ref:5 brune:1 bz:1 sherman:1 parkins:1 creating:1 interactions:1 presence:2 use:1 here:1 however:1 davidovich:1 formation:2 possibility:2 although:1 alone:1 plots:1 coupling:1 milburn:7 lc:1 both:1 about:1 interaction:1 central:1 could:1 decay:2 allows:1 times:1 sensitive:1 atom:1 raimond:1 variance:3 ture:1 makes:1 support:1 first:2 comment:2 considerations:1 initial:2 computes:1 point:1 previously:1 within:1 visible:1 homodyne:1 community:1 bath:3 phase:1 schemes:1 abteilung:1 fast:1 knight:1 moreover:1 schleich:2 plot:1 given:1 temperature:2 would:2 similarly:1 top:1 rewrite:1 due:1 been:1 whereas:1 master:2 damping:4 way:1 recognize:1 var:1 ph:1 scheme:1 type:1 garraway:1 more:2 function:1 media:1 generating:1 medium:1 received:1 metastable:1 photon:1 odinger:3 jul:1 marte:1 coherent:2 optical:1 gain:1 authors:2 elimination:1 yurke:2 line:2 than:1 present:1 longer:1 diffusion:1 high:1 kind:1 zagury:1 moya:1 pacs:1 solid:1 inside:1 oscillator:3 rate:1 value:4 cat:3 crystal:1 contrary:1 ulm:3 contrasted:1 similar:2 stoler:2 claim:1 larger:1 approximate:3 vogel:1 coupled:2 well:1 thus:1 haroche:1 states:4 kimble:1 itself:1 numbers:1 any:1 mauro:1 ariano:1 fortunato:2 turn:1 rather:1 dashed:1 make:1 utilize:1 mechanism:2 lett:6 field:1 other:1 quant:1 instead:1 effectiveness:1 difficult:1 independent:1 used:1 superposition:1 cessa:1 normal:1 models:1 after:1 reach:1 effect:1 possible:1 helping:1 moment:1 produce:1 germany:1 letter:1 hospitality:1 included:1 cases:1 model:2 recent:1 schr:3 modes:1 nonlinearity:1 considered:1 values:3 later:1 curve:2 ky:1 exp:2 time:4 decoherence:1 plotted:1 order:1 fact:1
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quant-ph9607029.txt |@word 8d:3 partial:2 consider:4 switched:1 rev:10 lack:1 leads:3 grateful:1 γr:66 undistorted:2 charge:2 those:1 γl:60 very:4 distort:3 electron:19 resonant:11 difference:1 entire:7 level:2 large:1 small:1 der:2 upper:9 direct:1 prager:2 zero:2 even:1 rate:6 sum:1 current:22 experiment:2 above:3 flowing:2 3c:1 3b:1 3a:1 method:1 3d:1 mea:1 ibid:1 respectively:6 possibility:4 relaxation:1 σaa:9 strong:2 observing:2 appears:1 obtained:2 lipkin:1 great:1 institute:1 study:1 studied:2 contradiction:1 usually:1 hospitality:1 studies:1 via:1 followed:1 projection:2 triumf:1 decrease:1 total:3 hegerfeldt:1 takes:4 would:4 remains:2 weizmann:1 negative:11 a53:1 therefore:4 today:1 more:1 israel:1 rehovot:1 odinger:4 berlin:1 varying:1 springer:1 science:1 equation:6 work:2 ρm:2 modified:3 ρr:2 following:2 modifies:1 compare:1 indicated:1 process:10 relativistic:4 states:19 numbers:1 arise:1 information:1 kwiat:2 rather:2 off:3 stayed:1 how:4 vancouver:1 adjacent:2 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quant-ph9607030.txt |@word code:34 saturating:1 consider:3 interference:1 illustrated:1 commute:3 computation:4 edu:1 consists:3 gj:1 gi:5 row:1 whose:5 number:6 aug:1 producing:2 finally:1 those:4 under:1 alberta:1 include:1 applied:1 conjecture:1 g4:1 g3:1 g2:1 g1:6 orthogonal:2 very:1 keeping:1 choice:1 every:1 reordering:2 decide:1 entries:1 affect:4 matrices:17 condition:3 paz:1 four:4 basics:1 presented:2 positions:2 large:4 gd:5 recall:3 eigenvalues:1 inspection:1 grateful:1 ten:2 zg:4 direct:1 imply:1 implemented:2 linear:1 even:1 what:3 errors:2 adds:1 richard:1 t2n:1 section:7 decoding:1 version:1 above:1 new:3 method:2 evolving:1 full:4 respectively:1 error:29 here:3 operating:1 represented:1 equations:1 change:3 obtained:1 convert:3 institute:2 shift:3 vectors:8 unitarily:1 products:3 knill:1 action:2 suitable:2 useful:3 explained:1 private:1 sloane:1 apply:5 total:3 linearly:8 readily:1 use:3 takes:1 would:3 codewords:20 distinct:1 contains:1 calt:1 next:3 explicitly:2 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quant-ph9608001.txt |@word allowed:1 consider:4 induces:2 magnetic:1 reversibility:1 results:10 leads:1 generalize:2 l12:3 computation:1 edu:1 consists:1 partial:2 research:1 worked:1 equivalences:1 whose:12 preserves:1 maximally:8 depend:1 aug:1 spin:1 deterministic:10 tr:27 environment:1 finally:1 swap:3 under:3 tr1:1 circumstances:1 ingredient:1 summarizes:1 case:12 supported:1 proved:1 advantage:1 orthogonal:6 implicitly:1 readout:1 suggesting:1 ρb:1 putting:1 should:3 condition:34 four:2 obvious:2 hamiltonian:1 tra:2 turns:1 ri:2 convenience:1 vector:3 section:10 indices:1 eigenvalues:6 a123:2 barbara:2 noted:3 mn:1 aρa:2 occurrence:1 α2j:1 zero:1 dordrecht:1 incidentally:1 further:2 dynamics:2 canonical:1 even:2 index:2 what:3 appear:2 apparatus:1 trivial:1 sum:1 axes:1 brief:1 henceforth:1 3j:4 subspaces:1 overcomplete:1 new:2 consisting:2 satisfy:6 transportation:1 respectively:2 never:1 teleportation:42 here:5 understanding:2 explore:1 address:1 concluding:1 along:2 quite:1 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quant-ph9608017.txt |@word since:1 aforementioned:1 mielnik:3 similarity:1 supported:1 results:1 leads:1 commute:1 relation:1 statements:1 scattering:1 find:1 previous:1 inverse:1 group:1 thank:1 aug:1 la:1 interesting:1 gto:1 only:1 conjugated:1 judged:1 versa:1 under:1 rosu:2 hamiltonians:1 local:1 transformation:1 correspondence:1 do:2 non:1 good:1 infinite:2 therefore:1 means:2 very:1 de:3 possible:1 bound:3 mention:1 cannot:1 they:5 mixing:1 using:1 nieto:3 postal:1 regarding:1 hussin:1 continuum:1 hamiltonian:1 did:1 arxiv:1 proposals:1 factorization:2 discrete:2 common:1 found:1 commented:1 terminology:1 bucharest:1 hλ:2 old:3 methods:1 creation:1 some:2 related:3 relative:1 decided:1 merits:1 connect:1 avoided:1 linear:1 nonlinear:3 unbound:1 though:1 comments:1 yet:1 between:3 construction:2 solitonic:1 issue:3 math:1 recently:2 theory:1 nature:1 ısica:1 however:1 quite:1 reason:1 khare:5 address:1 depend:1 relating:1 appears:1 instituto:1 o:1 suggests:1 connection:2 universidad:1 apdo:1 comment:2 romania:1 useful:1 mail:1 family:1 merely:1 number:1 andrianov:2 pair:1 directly:1 consideration:1 isospectral:8 open:1 additional:1 guanajuato:1 strictly:1 negative:2 their:1 too:1 conacyt:1 ph:4 isospectrality:1 type:1 more:1 reduce:1 operators:8 continuous:2 odinger:1 but:1 coherent:1 part:5 particular:1 schr:1 true:1 case:1 kumar:4 pacs:1 deformed:1 was:1 equation:1 work:2 oscillator:1 annihilation:1 fock:2 limit:3 problem:1 ugto:1 mx:1 fernandez:2 manner:1 magurele:1 unitary:1 thus:1 spectrum:4 general:1 states:2 itself:1 numbers:1 constructed:1 incorrect:1 different:1 perhaps:1 self:1 lett:3 write:1 mix:1 without:1 quant:4 parameter:4 product:1 cubic:2 may:2 oscillators:1 laa:1 questioning:1 reflect:1 applications:1 a2:1 remarks:1 representations:1 why:2 identity:1 exico:1 natural:1 vice:1 clear:1 spectra:1 eon:1 concrete:1 ones:2 original:1 fact:2
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quant-ph9608018.txt |@word sergei:1 consider:1 rev:1 invariable:1 leads:3 scalar:6 commute:1 gc:2 gb:1 ga:8 go:1 follow:1 contributions:1 compact:1 compose:1 depend:4 aug:1 tr:2 quasi:1 ac0:1 semenov:1 tg:16 analogous:1 case:1 orthogonal:4 wave:1 matrices:3 condition:6 hamiltonian:4 tra:1 turns:2 t0:1 solved:1 vector:6 manifestly:2 relation:1 grateful:1 haar:1 ators:1 incidentally:1 further:1 canonical:6 index:2 plays:1 iterating:1 brackets:2 sum:2 subspaces:1 new:3 ˆj:6 method:3 degree:3 respectively:2 component:1 here:7 path:6 change:3 obtained:3 sending:1 remark:2 antisymmetric:3 changed:2 poisson:1 usually:1 symmetrical:1 involves:1 jackiw:1 iδab:1 useful:1 projection:2 ipj:1 unitary:1 summation:1 apply:1 total:7 establish:2 select:1 use:4 projector:3 would:1 prove:1 remains:2 positive:2 contains:2 negative:1 properties:1 nucl:1 explicitly:1 therefore:2 theoretical:2 operators:6 labelled:1 known:1 projective:2 cases:1 must:2 me:1 equation:4 work:1 modified:1 theories:2 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quant-ph9608019.txt |@word horne:1 since:1 jα:3 consider:2 sentence:1 violation:5 random:3 results:2 valuable:1 argues:1 course:1 experiments:6 through:1 filters:3 existence:1 consists:2 regardless:1 still:2 depend:1 violate:2 aug:1 density:1 eigenspace:1 spin:2 regarded:1 muenchen:2 tr:2 expectations:6 presents:2 xb:13 only:1 nor:1 under:3 mail:1 hidden:9 he:1 local:11 theresienstraße:1 arguments:1 his:1 university:1 easily:1 subensembles:3 de:2 possible:2 unchen:2 joint:3 cannot:1 they:2 press:1 measured:1 outcomes:2 moreover:1 pov:4 eigenvalue:1 goldstein:2 preclude:1 arxiv:1 yield:1 sin:4 theory:1 inequality:5 careless:1 each:1 references:1 universit:1 refer:1 dip:1 setup:3 reproducing:1 because:1 xa:13 tells:1 conditional:6 some:1 related:1 observed:1 carefully:1 depends:2 ie:7 expect:1 measurement:3 quantum:12 our:1 satisfied:1 nonlocality:3 special:1 concern:1 even:3 will:1 clauser:1 matrix:1 lead:1 space:3 giving:1 apparently:1 section:2 measurements:7 rev:1 analogously:1 rz:1 denotes:1 particles:2 models:1 state:6 does:2 cambridge:2 above:1 selecting:1 shows:1 satisfy:4 after:1 august:1 nature:1 respectively:2 stefan:1 however:3 quite:1 paper:1 equals:1 conditioning:1 represented:3 consideration:2 standard:2 directions:1 hilbert:2 thank:1 both:2 pairs:2 obj:2 numerator:1 zangh:1 similar:1 taking:2 allows:1 filter:1 etc:3 conditioned:1 karin:1 cos:2 hence:1 uni:2 nonexistence:1 photons:1 first:1 comment:1 mixture:4 via:1 xn:1 projection:1 probability:2 bell:2 h2:2 variables:11 h1:2 obtaining:1 corresponds:1 jβ:2 system:2 instances:1 nevertheless:1 general:2 simply:1 pp:1 teufel:2 operator:4 impossible:1 bizarre:1 considers:1 given:1 institut:1 would:1 similarly:3 positive:4 adjoint:2 there:1 due:1 construct:1 statement:1 eqn:3 shimony:1 ph:1 analyze:1 more:2 separated:1 preparation:1 direction:1 arises:1 corresponding:1 quantities:1 operators:2 holt:1 problem:1 but:3 speakable:1 proven:1 particular:1 x2:2 x3:2 x1:2 true:1 x4:2 must:3 case:2 valued:3 whether:1 der:1 ij:2 second:1 value:4 reproduce:1 matter:1 while:1 cip:1 values:4 three:1 situation:1 distribution:1 proves:1 example:1 gisin:12 mechanics:1 associated:2 defined:2 ip:4 pass:2 thus:7 covers:1 denote:1 states:6 discussions:1 itself:1 performed:1 need:1 take:2 distributions:2 clearly:1 subsystems:2 zero:1 locality:1 rather:1 mathematik:2 self:2 holds:1 when:1 lett:2 oai:4 event:2 application:3 quant:1 generalized:4 widely:1 mixtures:1 about:1 out:1 dimension:1 ensemble:2 conclusion:1 mathematisches:1 product:8 used:1 shelly:1 shall:1 may:1 put:1 measures:3 upon:2 different:3 expectation:4 plane:1 germany:1 nothing:1 explained:1 choice:2 revealed:1 causality:1 implies:1 described:1 considered:1 calculated:1 well:1 correspond:1 obviously:1 amounts:1 points:1 so:1 unspeakable:1 urr:1 observables:5 model:8 quantity:2 chsh:2 original:1 fact:2 usual:1
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quant-ph9608020.txt |@word monte:3 consider:3 illustrates:2 results:2 intracavity:2 avalanche:1 computation:1 gm:1 ptr:1 whose:2 certainly:2 feeding:1 aug:1 theorique:1 tr:1 contained:2 environment:1 critical:1 matlab:1 under:1 tf:4 stochastic:6 case:1 updated:2 photocount:1 advantage:1 g0:4 far:1 frequencies:1 focus:1 wishes:1 every:3 govern:1 resonant:1 experimentally:2 infrared:1 matrices:1 cool:1 2κa:1 hamiltonian:5 mle:7 iǫ:1 t0:5 t1:3 vector:1 small:1 optics:6 application:1 averaged:1 houches:1 trend:1 jump:5 rate:8 design:1 ψc:2 dynamics:3 carlo:3 toolbox:1 what:1 appear:1 near:1 uniform:1 current:2 version:2 above:8 method:3 contrast:1 full:1 chose:1 lange:1 here:3 focused:1 separation:1 making:1 along:1 strong:1 equations:3 change:1 obtained:3 institute:1 spontaneous:1 feasibility:1 studied:1 suggests:2 loop:2 action:1 makes:1 cˆ0:1 cˆ1:1 examining:1 showing:1 formulated:1 family:2 marginal:1 private:1 turchette:4 odinger:2 counts:1 des:1 tn:7 use:2 stream:1 usa:1 distinct:1 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quant-ph9608021.txt |@word slope:2 grobe:1 consider:15 remarkable:4 caused:1 results:9 four:30 generalize:1 higher:1 gn:4 expressions:3 disk:1 devoted:1 whose:3 hold:1 const:8 aug:1 paris:1 iii:2 concerned:2 tn:3 quasi:3 squeezing:20 present:2 excluded:1 under:2 dramatically:1 case:9 belonging:1 amplitudes:1 straightforward:2 shifters:8 wave:30 putting:1 figs:1 laser:1 nieto:2 difference:9 exact:5 condition:6 preserve:4 splitter:4 nd2:1 conjugating:2 tani:1 presented:4 turns:1 t2:2 solution:2 large:9 discrete:5 vector:2 small:8 eigenvalues:2 referred:1 optics:2 employing:3 specially:1 foundation:1 miller:1 sin2:4 direct:1 hillery:6 cosh:15 approximation:2 second:4 ij3:3 j22:1 further:4 port:1 quite:3 canonical:3 even:1 index:4 what:3 nonlinear:1 sum:1 near:3 expressed:6 goes:1 overcomplete:2 expresses:1 increasing:6 boost:1 method:2 satisfy:2 edited:1 simultaneously:3 vi:1 respectively:11 concepts:1 here:9 following:1 groups:4 peˇrina:3 active:12 luis:3 along:1 strong:2 directions:2 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quant-ph9608024.txt |@word represent:1 code:1 global:1 activated:1 results:1 four:3 gd:1 edu:2 consists:1 activates:1 c1:1 aug:1 tr:1 quasi:1 under:6 1p:1 norm:1 finkelstein:4 rise:1 account:2 govern:1 exact:1 school:2 level:5 discrete:3 vector:2 sign:2 zz:1 further:1 dynamics:6 quite:1 linear:4 even:1 index:1 appear:1 cell:6 above:1 here:4 atoms:1 xλ:1 108b:1 groups:3 others:1 strong:1 imperfections:1 change:2 suitably:1 institute:3 shift:1 su3:1 su2:1 action:3 spacetime:12 diffeomorphisms:1 scaled:1 annihilator:1 condensates:1 subfactors:1 unit:1 clifford:1 use:1 superpositions:1 would:1 next:1 kinematics:1 type:1 theoretical:1 slim:1 composite:1 operators:7 must:4 ii:1 springer:1 defines:1 lefthanded:1 quantized:1 permits:1 work:1 eigenkets:1 infinitesimal:3 spontaneous:1 example:1 nearest:1 links:2 give:2 relativistic:1 cited:1 permutations:2 states:1 counting:2 quark:1 lacks:1 ahler:1 rather:1 acts:1 product:3 algebra:6 may:1 earlier:2 hence:1 summarize:1 third:1 higgs:1 element:3 diffeomorphism:1 fundamental:2 sl:3 representation:1 order:1 typical:1 restriction:1 breaking:1 gauges:1 constituents:1 over:7 interpreted:1 still:1 excitations:1 its:6 vacua:8 group:2 relativity:1 coordinates:2 forms:1 meissner:1 lq:1 mail:3 defining:1 shear:1 tentatively:1 non:2 propose:1 isomorphic:1 effects:1 they:2 now:1 day:1 february:1 2p:1 assemblies:2 identified:1 sufficiently:1 mode:1 each:3 beneath:1 mean:1 differential:2 successively:1 energy:2 ιg:1 inhomogeneous:1 isospin:1 poincare:1 quantum:18 special:1 out:1 network:11 space:6 nuovo:1 singular:1 bonus:1 seriously:1 issue:1 correct:1 foundation:1 normed:1 theory:7 interactions:1 diagonal:1 standard:5 usual:1 interaction:1 geometry:1 david:2 turn:5 iso:3 isl:1 consequence:1 generalizations:1 first:2 initial:1 parastatistics:4 symmetry:1 grade:6 number:3 defects:1 quadrupole:1 array:1 angular:2 1q:2 interchange:2 given:1 long:1 extrinsic:1 system:2 construct:2 their:3 too:2 hypothetical:1 1m:1 immediate:1 translation:1 than:1 require:1 cimento:1 namely:1 matter:2 posit:2 exhibit:1 unintended:1 symmetries:6 nonabelian:1 spectrum:1 say:2 need:1 null:1 any:5 self:1 gravity:5 high:2 take:2 forces:3 modulus:1 heisenberg:1 antihermitian:1 hypervolume:2 germany:1 sheets:2 intrinsic:1 ritz:1 hestenes:1 clear:1 accounted:1 left:2 physics:7 fact:1 show:1 chances:1 supported:2 converge:1 gauge:3 analogue:1 dilation:1 q2:1 parameters:2 topological:4 only:2 generators:2 molecules:1 local:3 abelian:1 truly:2 ones:1 resolve:2 qv:4 fields:3 arxiv:1 fixed:1 ql:1 commutation:1 set:3 extensor:1 unexpectedly:1 see:1 δxµ:1 violates:2 subject:1 c2q:2 tensor:1 nuclear:1 bitnet:1 dipole:1 symmetric:3 state:1 identification:1 simplest:1 invariant:5 conditions:1 terms:1 creating:1 points:8 however:1 concentrate:1 hypothesis:1 analyzed:1 ket:3 tensors:3 topology:1 both:1 hypercubic:1 ir4:3 improves:1 kets:8 arbitrarily:1 among:2 point:7 simple:4 ca:1 xν:1 cd:1 dimensional:2 simply:2 diff:2 crystalline:1 ether:1 torsion:3 basis:2 locally:1 due:1 much:1 ph:1 algebras:3 abstract:1 relations:1 corresponding:1 deeper:1 covariance:8 coherent:2 representative:1 atlanta:2 spin:1 present:1 georgia:4 unlike:1 tang:3 empirical:2 unitary:2 metric:3 thus:2 them:1 clearly:1 respected:2 superconducting:1 itself:1 il:1 dual:2 technology:2 conserve:1 grant:1 make:1 same:1 poincar:4 quant:1 descend:1 finite:3 higher:1 used:2 keys:1 phy:1 uses:5 invariance:1 off:1 modes:2 nevertheless:1 locality:1 analysis:1 patterns:1 sets:4 coordinate:2 model:6 dimension:1 subgroup:1 manifold:1 just:1 less:2 being:2 newton:1 identify:2 109b:1 occupants:1 transparent:1 lattice:1 easy:1 save:1 heidelberg:1 momentum:4 munich:1 early:1 vacuum:16 dirac:7 color:1 like:2 δx:3 follows:1 flux:1 continua:2 c1q:2 topologically:1 parity:2 upshift:1 because:1 liml:1 classical:4 creation:1 some:1 respect:1 proper:1 root:1 superselection:1 linkages:1 referential:1 trautman:1 fermidirac:1 assembly:3 obey:3 arbitrary:1 qnd:9 stage:1 working:1 metrical:2 mutually:1 range:1 neighbor:2 automatically:1 into:3 hypercharge:1 nsf:1 three:2 down:2 square:1 references:1 einstein:1 operator:3 statistics:1 vac:5 support:1 there:1 u1:1 specifically:1 start:1 restricts:1 conservation:1 way:1 call:2 xµ:1 was:2 naturally:2 form:2 governs:1 but:8 volume:1 gatech:2 link:3 multilevel:2 subsidiary:1 heinrich:1 partially:1 minkowski:1 cells:1 variations:1 up:1 crystal:1 fermi:4 nµ:1 defined:1 certain:1 universal:2 general:5 guessed:1 right:1 interchanged:2 crystals:1 commuting:2 physical:2 grassmann:1 no:1 zhong:2 when:2 hns:1 handed:2 field:2 other:3 nq:1 elements:4 superposition:2 separate:1 models:1 includes:3 generated:1 structure:3 calls:1 assume:3 factors:5 rule:1 depth:6 n1:2 n2:2 n3:2 n4:2
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quant-ph9608025.txt |@word limited:1 code:18 partial:1 consider:2 rev:15 demand:1 desirable:6 focus:1 noisy:1 existing:3 roy:1 mp2:1 computation:3 follow:1 causes:4 devoted:1 particles:2 amplification:7 terms:1 calculate:1 aug:1 irrelevant:1 environment:1 finally:1 protocols:3 under:1 analogous:1 p2:7 very:4 account:1 general:3 affect:1 paz:1 level:1 transmission:5 eve:7 large:7 solved:1 small:12 optics:1 noted:1 tremendously:1 grateful:1 deutsch:1 rate:9 further:2 even:5 will:3 errors:34 stands:2 3p:1 decoding:4 version:1 3l:1 new:4 increasing:1 error:74 here:3 understanding:1 believed:1 lev:1 others:2 concluding:1 strong:1 obtained:1 involved:1 elaborate:1 changed:1 allows:3 suggests:1 schumacher:1 bob:6 devices:2 makes:1 useful:1 projection:5 bounds:1 explained:1 eiφj:1 decrease:1 apply:1 jection:1 use:6 would:1 ψr:1 jozsa:1 contains:1 throw:1 distributing:1 few:1 therefore:3 memory:5 encode:5 goldenberg:4 type:2 theoretical:1 more:9 israel:1 successful:3 initial:2 eiφ2:2 eiφ3:2 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quant-ph9608026.txt |@word limited:1 code:35 saturating:1 consider:1 interference:1 results:1 gx:3 leads:1 roy:1 computation:1 spaced:1 row:1 aug:1 knill:1 concerned:1 those:3 th:1 applied:1 g2:4 g1:8 orthogonal:2 far:1 gz:3 worst:1 fall:1 matrices:2 condition:2 swapping:1 gf:1 large:3 vector:2 small:5 deleting:1 smaller:1 among:2 sign:2 rate:1 further:3 odd:1 linear:1 even:4 established:1 what:1 errors:2 xor:1 appear:1 giving:1 above:1 values:1 method:9 satisfy:6 respectively:1 here:2 alone:1 ratio:1 change:1 obtained:7 symetric:1 study:2 changed:1 qualify:1 amount:1 resulting:1 published:4 action:1 changes:1 via:1 sloane:3 apply:1 total:1 undergone:1 would:2 codewords:1 distinct:1 tabulated:2 comparing:2 therefore:2 more:2 duals:1 introducing:1 becomes:1 controlling:1 known:1 must:4 grassl:1 word:3 equation:10 obvious:1 concepts:1 following:6 example:1 stimulating:1 proof:3 bennett:1 states:1 minimum:8 dxi:2 string:1 information:10 straightforward:1 discussion:1 indirectly:2 isi:1 how:3 optimal:6 undergoing:1 may:3 after:3 derived:3 applications:1 produce:1 gottesman:5 whenever:2 explicit:1 ones:1 so:3 fundamental:1 subsequently:1 words:2 produces:1 over:2 satisfied:2 paper:3 its:3 before:1 perfect:2 acknowledge:1 better:1 hzt:4 lt:2 constitutes:1 gtx:1 gtz:1 might:1 maximal:1 non:4 good:4 than:5 conversations:1 steane:4 they:2 oxford:2 now:1 2t:11 channels:1 several:1 2r:12 university:1 2d:1 transmitted:1 neccessary:1 found:2 2n:1 macchiavello:1 2k:1 subset:2 england:1 weight:4 stabiliser:10 eg:1 reduce:1 idea:1 related:1 society:1 combining:1 quantum:45 laboratory:1 out:2 divincenzo:1 shown:3 matrix:5 space:1 rev:7 increase:1 daniel:1 formula:1 induction:3 correct:1 foundation:1 theory:5 state:2 possibility:1 clarify:1 completely:2 hand:3 muller:11 pairs:1 interaction:1 geometry:2 length:1 leading:1 first:4 features:1 encoding:1 coding:1 number:4 xz:1 entanglement:1 adopted:1 directly:1 size:4 given:7 unknown:4 construct:1 their:2 too:2 wootters:1 bits:3 final:1 gives:1 part:6 authors:1 shortly:1 completes:1 distance:8 holland:1 showed:1 second:2 submitted:2 computer:1 were:2 enables:1 extracting:1 prospect:2 sees:1 correction:11 defecting:1 locations:1 bitwise:3 miquel:1 close:3 need:1 seen:2 any:4 built:1 zero:7 efficient:4 self:2 able:1 parks:1 note:1 k2:2 k1:2 take:3 finding:1 multiple:1 though:1 who:1 falls:1 extending:1 importantly:1 ht:1 significant:1 pair:1 why:1 especially:1 considered:1 clear:1 hamming:2 physics:1 fact:4 shor:4 particularly:1 show:3 supported:1 recipe:1 discovered:1 spaces:1 relation:3 find:1 based:1 parameters:8 ox1:1 should:2 only:1 explicitly:1 generators:1 notation:2 means:3 zurek:1 cannot:1 dz:5 dx:7 processes:1 arxiv:1 summary:1 contain:2 stabilisers:1 set:6 constructing:1 see:3 individual:1 usefulness:1 recently:1 best:3 subject:1 fails:1 currently:1 written:1 simplest:2 checks:1 notice:1 terms:1 august:1 qubits:4 attention:1 suggested:1 many:2 equal:1 previously:5 enabling:1 qubit:2 whole:1 finds:1 arbitrarily:1 generalisation:1 conclude:1 simple:1 corresponds:1 concluding:1 table:5 described:1 addition:1 detected:1 been:1 much:1 combined:1 interest:1 basic:1 ph:10 lett:3 corresponding:1 quantities:1 subspace:1 systematic:1 c2:4 c1:4 present:2 case:3 will:9 error:25 situation:1 property:2 procedure:1 generate:5 vectors:1 laflamme:2 thus:1 them:1 correctable:1 dual:5 ie:6 binary:3 macwilliams:1 author:1 paz:1 same:2 clearly:1 parts:2 quant:10 hxt:1 physical:1 used:3 counterparts:2 possible:1 infinite:1 recent:1 numbered:1 off:1 makes:1 rains:2 left:2 calderbank:5 less:2 obtain:2 rest:2 stored:1 alternative:1 yet:1 previous:1 adding:1 preprint:10 generator:11 extracted:1 point:1 royal:1 location:1 easy:1 easily:1 3pu:1 increases:1 using:3 bit:6 correcting:13 helpful:1 rotate:1 like:2 particle:1 follows:1 either:3 works:1 specifies:1 parity:2 right:1 classical:17 some:1 examples:3 specified:2 happens:1 comments:1 does:1 l2:1 proc:1 refer:2 noise:1 use:2 clarendon:1 refers:1 simpler:1 most:1 dzi:1 prove:1 discussed:1 seeds:1 dzt:1 krm:7 mixed:1 mean:1 consequently:1 processor:1 road:1 soc:1 h2:1 communication:1 h1:1 bound:1 because:1 references:1 amsterdam:1 next:2 rows:9 r2493:1 few:1 class:1 workshop:1 way:5 was:4 hz:3 decoded:1 hx:7 north:1 form:5 smolin:1 but:2 construction:9 reed:11 encoded:1 illustrative:1 ux:3 places:1 uz:3 whether:1 up:1 us:1 limit:1 problem:2 similar:1 storing:1 proved:1 relevent:1 abstract:1 general:3 single:1 exist:2 our:1 quantph:1 check:1 constructed:3 codes:42 no:1 amounts:1 ekert:1 when:2 field:1 other:7 department:1 markus:1 deriving:1 generated:2 important:1 independently:1 together:2 having:2 n1:1 4d:1 starting:1 strings:1 restored:1
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quant-ph9608027.txt |@word aln:1 represent:1 villeurbanne:2 consider:4 dθθ:1 global:1 results:4 leads:4 λz:1 generalize:1 grateful:1 go:2 follow:1 expressions:2 research:2 8e:2 devoted:1 c0:6 calculate:2 aug:1 technique:1 noncompact:1 passage:1 presents:1 finally:5 tk:8 whatsoever:1 ρdρ:2 γb:1 γa:1 must:2 ın:1 p2:6 provides:1 advantage:1 very:3 mn3:4 springer:1 quesne:1 putting:2 mpp:7 nieto:2 condition:7 jqq:3 immediately:3 level:1 louis:2 july:1 solution:7 deals:1 solved:3 english:1 differential:3 math:9 small:2 eigenvalues:6 noted:1 upp:1 employing:2 zi:2 zj:3 prudnikov:1 sin2:3 sign:10 l2q:1 second:5 uk:4 zz:2 further:1 ter:6 chem:8 odd:8 theory:3 even:7 established:1 θlm:4 zhedanov:2 plays:1 stands:1 morse:7 3s:6 section:6 lαn:2 expressed:1 pleased:1 reminiscent:1 version:1 fifth:3 goes:1 lifshitz:1 new:5 change:3 method:1 satisfy:3 compact:1 honour:1 component:4 discrete:3 here:3 agreement:1 cylindrical:27 cos2:1 separation:12 tnl:3 path:1 along:1 xα:1 equations:10 z2:4 deduced:1 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quant-ph9608028.txt |@word represent:1 code:6 interference:1 results:3 leads:1 gf:1 computation:2 consists:1 denotes:3 repetition:1 aug:1 knill:1 presents:1 th:2 under:1 case:1 orthogonal:1 very:1 sons:1 decide:1 paz:1 four:7 presented:4 knight:4 correct:4 large:2 dealt:4 small:2 noted:3 smaller:1 zi:2 deutsch:1 likely:1 further:2 dynamics:1 even:6 errors:30 current:1 errorcorrecting:1 above:2 international:1 ever:1 contrast:1 edited:1 outgoing:6 here:2 plenio:4 free:2 active:1 consideration:1 z0:1 z1:1 z2:1 z3:1 obtained:1 incoming:6 involved:1 inspired:1 goldwasser:1 allows:1 through:1 resulting:1 procedure:3 action:6 implement:2 via:1 useful:1 outcomes:2 sloane:2 takes:2 would:11 contains:1 next:1 therefore:1 taken:2 goldenberg:1 theoretical:1 more:6 pless:1 corrected:4 emission:2 known:1 foundations:1 consort:1 science:2 der:1 work:3 following:1 spontaneous:2 example:2 control:1 indicated:2 introduces:1 bennett:1 implementations:1 states:2 numbers:2 council:1 yet:1 occur:9 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quant-ph9608029.txt |@word limited:3 externally:6 partial:1 consider:9 switched:1 rev:8 magnetic:2 results:2 afosr:1 four:3 scalar:1 commute:2 computation:10 constants:1 shot:1 expressions:5 research:2 issues:1 u3:1 terms:12 reported:1 factoring:1 preprint:4 environment:1 answered:1 does:1 present:2 details:1 include:1 division:1 straightforward:2 without:1 far:1 choice:2 affect:1 matrices:6 condition:1 hamiltonian:17 anisotropy:1 solution:1 large:2 destroying:1 science:3 eigenvalues:3 degeneracy:1 force:2 privman:7 deutsch:1 direct:1 literature:3 likely:1 design:7 value:1 further:1 dynamics:1 implemented:1 even:1 what:1 errors:7 xor:4 sub:1 apparatus:1 giving:1 section:11 expressed:1 reminiscent:1 u34:1 u33:1 establishes:1 designing:1 international:1 unrestricted:1 consisting:1 multitude:1 body:1 condensed:3 proliferation:1 chose:1 degree:1 abrupt:1 error:4 modify:1 here:6 desired:2 operating:1 possibility:1 relaxation:1 alone:1 appropriate:1 quite:2 obtained:4 turchette:1 covers:1 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quant-ph9608030.txt |@word secondly:2 concept:1 partial:2 consider:7 represent:5 interference:1 indicating:1 results:4 unchanged:1 four:3 known:1 code:14 entropy:25 computation:6 invariably:1 research:1 reasoning:1 increase:23 preserves:2 inverse:1 superpositions:1 aug:1 transferred:1 pˆi:2 knill:2 pˆj:1 tr:3 acting:1 nonlocal:4 presents:1 summarised:1 program:1 those:3 th:1 under:1 phil:1 worth:2 sent:4 restricting:1 case:11 supported:1 rαβ:1 advantage:1 susceptible:1 far:2 focus:1 print:5 sons:1 every:1 resonant:3 nelson:1 difference:1 matrices:7 condition:1 arrange:2 generalised:1 leads:1 basics:1 giessen:1 moya:1 presented:3 tra:5 knight:6 trc:1 trb:2 tre:1 fewer:1 t1:32 leave:1 convenience:1 session:1 phase:2 subscript:1 indices:4 possibilities:1 optics:2 setup:1 vincenzo:1 upper:2 employing:1 throught:1 foundation:1 cessa:1 ψi:2 direct:8 sign:1 jump:1 second:6 dissipation:1 rigorous:2 further:2 implemented:1 splitting:1 aˆi:12 even:1 aim:4 subadditivity:5 errors:20 proportional:1 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quant-ph9608031.txt |@word sci:1 consider:3 ali:1 magnetic:3 results:8 leads:6 killam:1 scalar:2 disc:1 computation:3 parameterization:1 expressions:6 row:1 compact:2 whose:4 simon:4 depend:1 patches:2 aug:1 concerned:1 similarity:1 removal:1 finally:1 those:1 excluded:1 under:2 alberta:2 analogous:1 fermionic:2 case:41 attribution:1 straightforward:2 far:1 geometrical:26 hannay:1 manageable:1 exact:1 deformations:2 condition:7 four:5 exponential:2 solves:1 hamiltonian:53 irreducible:1 list:1 applicable:2 occurs:1 large:1 solved:1 convenience:1 vector:4 o1:7 eigenvalues:12 degeneracy:18 occurrence:3 foundation:1 det:1 direct:4 sign:3 approximation:1 fold:3 zero:3 concludes:1 chem:1 odd:1 canonical:2 even:1 what:1 section:10 contributed:1 expressed:3 subspaces:2 new:3 method:3 evolving:2 full:3 simultaneously:1 multipole:4 respectively:4 here:3 understanding:1 explore:1 q11:6 groups:1 q12:1 path:2 standard:1 equations:7 z1:4 change:1 z3:2 obtained:6 institute:1 study:1 studied:4 dri:1 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quant-ph9608036.txt |@word sector:2 show:5 brisbane:1 indeed:1 over:4 obtains:2 press:1 attempts:1 disc:1 grateful:1 integer:1 consists:1 substituting:2 expressions:3 d2:2 find:1 tables:2 knight:1 derive:1 group:2 knowledge:1 aug:1 bringing:1 regarded:1 complex:1 lemma:1 only:2 permanent:1 factor:1 jacobi:5 defining:1 stegun:1 iφ:2 non:1 australia:1 legendre:2 de:1 term:1 dx:4 vacuum:1 dv:1 using:5 now:1 dr:1 school:1 2p:13 2q:2 follows:4 university:4 arxiv:1 2x:4 berlin:1 racah:5 integrals:3 each:1 2m:4 2n:14 optics:1 view:1 mathematical:1 performing:1 gegenbauer:2 classical:1 achieved:1 pnα:1 series:1 some:1 direct:3 related:1 elegant:1 literature:1 result:2 quantum:1 carry:1 expression:3 odd:5 best:1 out:4 even:1 shown:1 matrix:1 space:2 ways:1 sum:1 ensures:1 rev:3 integration:2 denotes:1 state:1 does:1 above:1 steps:1 evaluation:1 attention:1 terms:6 ibid:1 found:1 abramowitz:1 p2n:1 use:5 here:2 standard:1 squeezed:6 address:1 based:2 properties:1 proceed:1 bu:1 c2n:2 am:1 equal:3 times:1 a2:2 products:1 hence:2 hospitality:1 2k:2 makes:1 other:2 origin:1 hyderabad:2 schur:1 letter:1 point:1 into:1 yuen:1 integral:6 number:4 travel:1 infinite:1 written:6 references:1 relations:1 another:1 changing:1 operator:5 constant:2 xp:1 our:1 unit:3 given:2 rewritten:1 prove:1 question:1 been:1 their:2 encounters:1 handbook:1 listed:1 statement:1 ph:1 compactly:1 pn:8 entails:1 pm:1 survives:1 cnα:1 complete:1 commutes:1 centered:1 thus:1 a13:1 plane:1 coherent:2 carrying:1 intermediate:1 x2:2 denote:1 must:2 explicitly:1 springer:1 made:1 pacs:1 wish:1 submitted:1 fock:6 values:1 a41:1 following:2 making:1 similar:1 proof:7 associated:3 calculation:1 ip:9 abstract:1 india:1 generalization:1 general:1 states:10 reads:1 manner:1 turns:1 need:1 my:1 vanish:1 identities:3 any:2 elements:1 agarwal:1 different:1 completeness:2 πl:5 no:1 theoretic:1 make:1 ryzhik:1 when:1 oliveira:1 tanh:1 quant:1 generalized:2 department:2 kim:1 gets:1 sin:4 investigated:1 calculating:1 may:5 functions:2 polynomials:8 applications:1 involving:2 fd:1 award:1 demonstrating:1 queensland:3 ξa:2 acknowledgements:1 zek:1 identity:6 iodd:3 physics:3 grant:1 explicit:1 yielding:1 su:1 thought:1 academic:1 so:1 fact:2 exp:2 thoroughly:1 thank:1 dover:1 resolution:5 order:1 furnish:1 chaturvedi:2
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quant-ph9608039.txt |@word holman:2 concept:2 consider:3 pointing:2 priori:1 caused:1 forbidden:1 results:4 leads:1 houches:1 follow:1 expressions:1 eiξ:7 causes:1 whose:2 catastrophe:3 description:1 tr:1 presents:1 γj:2 finally:3 does:5 γn:17 th:1 under:3 breach:1 analogous:1 presentation:1 subtleties:1 returning:1 very:20 activation:1 rise:2 ψk:2 wave:19 electron:1 sons:1 stays:1 resonant:4 affect:1 trouble:1 exact:1 condition:11 entire:1 unlike:1 hamiltonian:1 turns:1 solution:7 try:2 admissible:1 differential:1 math:1 small:11 eigenvalues:1 accumulation:1 smaller:1 slower:1 sin2:3 sign:1 approximation:3 rate:13 iκn:2 substituting:1 rigorous:1 dynamics:1 substitute:1 linear:1 even:4 trick:1 what:1 opaque:1 giving:1 trivial:2 section:13 brief:2 poles:3 issues:1 above:2 lifshitz:1 values:6 net:1 method:5 contrast:1 satisfy:3 ufrj:2 κn:31 respectively:3 equals:1 here:5 understanding:1 highly:1 beck:1 fairly:1 olica:1 them:1 free:6 address:1 causality:1 strong:1 equations:2 appears:1 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quant-ph9608040.txt |@word represent:1 kt2:2 consider:4 interference:5 magnetic:1 results:2 perelman:1 four:1 known:1 consists:1 expressions:2 ψcl:27 depend:1 calculate:1 aug:1 compensate:1 present:1 under:2 nodes:3 case:5 orthogonal:1 stroud:2 wave:58 p1:7 every:5 experimentally:3 nieto:1 φnk:8 irreducible:1 t2:2 t1:2 small:2 upper:1 unexpected:1 oscillation:2 pulse:3 jump:1 zero:1 displays:1 ψeven:8 dynamics:2 odd:38 even:35 appear:3 sum:6 selected:1 while:2 agrees:1 experiment:1 causes:2 above:1 fractional:15 new:1 commensurate:2 consisting:2 evolving:1 full:9 simultaneously:1 ibid:6 respectively:2 l1:17 component:1 equals:1 here:6 atoms:2 ionization:3 shape:2 q12:3 bogdan:1 obtained:3 studied:1 simultaneous:1 resulting:1 cesium:2 proof:1 studies:1 examining:1 spatially:1 ratios:1 scales:8 noordam:4 addressed:1 psec:9 decrease:1 total:1 unit:2 plot:2 use:1 superpositions:2 would:5 prove:1 distinct:2 predictions:2 definiteness:1 disregarding:1 call:2 therefore:3 taken:1 indiana:1 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quant-ph9608042.txt |@word homomorphism:1 chevalley:5 four:2 fortiori:1 consists:11 sch:1 relationships:1 whose:1 const:5 aug:1 akµ:1 γt:2 γj:2 γi:6 γo:1 γn:5 γm:3 under:2 γc:2 γb:3 γa:6 γg:9 rise:2 replaces:1 summarized:1 encounter:1 vector:20 ifab:4 consistent:1 direct:3 second:4 rigorous:1 even:21 ˆa:1 sunder:1 above:15 new:17 ˆk:2 consisting:2 coefficient:1 dahl:5 here:15 represented:6 quite:3 interpret:1 obtained:7 gln:5 study:9 characterizing:1 fourier:3 divide:1 explained:2 glni:1 highly:1 unitary:1 γu:1 unit:7 tn0:1 would:41 bundles:3 negative:1 noting:4 call:4 therefore:1 m2:1 type:1 fractions:1 curvature:1 aware:1 berlin:3 hold:2 must:17 me:5 springer:4 word:1 quartic:1 mm:5 rξ:3 work:5 mk:1 theories:5 cocycle:3 mq:2 mp:2 nonlinear:1 concepts:1 tnm:5 root:12 example:12 nαβ:2 impose:1 unilateral:2 indicated:1 give:11 preserving:3 involve:1 caution:1 cartan:19 want:7 absolute:2 φx:1 end:2 thing:2 provide:1 how:16 imbedded:1 symposium:2 ordinary:10 βa:1 classifying:1 untill:1 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