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quant-ph9805041.txt |@word caused:3 magnetic:4 global:1 results:2 indicates:1 follow:2 expressions:1 contributions:2 causes:1 whose:1 inverse:1 calculate:2 paris:1 γp:2 tr:1 tp:1 former:1 finally:2 program:1 th:1 analogous:1 tr2:2 tr4:2 amplitudes:1 springer:1 semi:1 wave:4 electron:2 particules:1 matrices:4 condition:6 quantized:1 hamiltonian:3 turns:1 solution:2 integrated:1 leave:1 discrete:2 vector:4 small:1 eigenvalues:5 originally:1 configurations:1 upper:1 lagrangian:1 occurrence:1 approximation:6 second:6 value:1 pass:1 rigorous:1 further:1 dynamics:5 accompanying:1 situated:1 canonical:1 even:1 index:3 what:1 morse:1 exactly:1 xφ:2 find:2 reminiscent:1 above:4 new:1 method:4 satisfy:1 eigenbundle:1 degree:2 respectively:1 here:2 objects:1 ansatz:4 address:2 represented:1 based:1 along:4 equations:7 appears:1 interpret:1 obtained:4 remark:4 villars:1 weinstein:2 study:1 vectors:1 allows:3 commonly:1 controversy:1 periodic:7 bol:1 poisson:1 action:1 abteilung:1 fourier:2 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quant-ph9805042.txt |@word customary:1 consider:3 similarity:2 rev:4 leads:2 spiridonov:1 computation:1 edu:4 gh:1 referring:1 equivalence:2 th:1 under:2 analogous:1 characterised:1 presentation:1 seemingly:1 choice:1 fall:3 inequivalent:1 condition:4 entire:2 hamiltonian:6 discrete:1 unrelated:1 eigenvalues:12 sukhatme:3 alhassid:2 zero:1 street:1 linear:4 spectral:2 what:1 plays:1 appear:1 chicago:4 section:4 brief:1 expressed:1 above:6 obvious:1 ever:1 method:2 satisfy:2 edited:1 respectively:1 component:1 here:1 diagonal:1 following:1 explore:1 along:2 equations:2 change:1 obtained:2 suitably:1 changed:1 completely:2 accomplished:1 superpotential:4 action:3 hospitality:1 changes:1 oschl:3 a21:2 planar:1 establish:3 unit:1 plot:1 additive:3 would:4 positive:1 next:1 few:1 ψn:7 m0:13 m2:3 type:2 theoretical:2 more:2 formally:1 started:2 operators:21 odinger:2 warm:1 basically:1 tangerman:1 particular:1 known:8 iii:1 must:1 equation:2 constraint:5 oscillator:2 anywhere:2 values:5 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quant-ph9805044.txt |@word represent:3 consider:3 chain:1 maximum:4 interference:3 davies:1 global:1 amplifier:1 splitting:2 intracavity:5 leads:5 scalar:1 generalize:1 follow:3 expressions:4 contributions:4 reynaud:3 devoted:1 inverse:3 depend:1 calculate:4 paris:3 concerned:1 αeff:16 compensate:1 squeezing:1 those:1 th:4 under:1 analogous:3 ωt2:2 case:26 breathing:1 amplitudes:3 far:3 frequencies:17 discrepancy:1 rise:3 brossel:1 results:7 introduction:1 every:1 remarks:1 resonant:2 experimentally:4 difference:4 matrices:5 condition:5 progression:1 presented:3 transmission:5 positions:2 permits:1 t2:7 eve:1 occurs:2 large:12 discrete:1 phase:2 math:1 affect:1 succession:1 small:17 optics:1 round:11 configurations:1 heidmann:1 upper:3 smaller:8 force:4 monotonous:3 oscillation:15 dealing:1 sin2:2 prediction:1 pulse:5 sign:1 equation:5 imply:2 compensates:1 enhancement:5 equal:7 further:2 odd:4 amplified:1 theory:2 even:4 aim:3 sud:1 plays:2 appear:1 giving:1 sum:6 while:4 lhomond:1 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quant-ph9805045.txt |@word represent:1 since:4 partial:1 equiprobable:1 alternatives:1 four:2 grateful:1 whose:2 const:2 integral:1 tr:3 program:1 grabowski:1 sent:2 ωt1:1 p2:3 belonging:2 orthogonal:6 frequencies:2 springer:1 wave:9 mattle:1 mixing:1 experimentally:1 emphasized:1 difference:5 splitter:1 level:2 notes:1 t2:9 t0:1 t1:10 convenience:1 small:1 enhance:1 employing:1 dealing:2 second:6 further:2 employ:1 apparatus:1 sum:2 ˆa:1 twins:1 above:1 new:1 public:1 coefficient:1 simultaneously:1 teleportation:15 here:2 following:2 them:2 address:1 represented:1 depend:1 appears:1 obtained:2 institute:1 shift:4 leaves:1 resulting:2 schumacher:2 opinion:1 fourier:2 changes:1 spatially:1 extra:1 outcomes:4 boolean:1 resolutions:2 operational:1 unit:1 eiωt:1 use:1 lecture:1 commun:1 remains:1 positive:4 a51:1 nanoelectronics:1 a53:1 therefore:2 dω3:1 separated:1 nauka:2 anticorrelation:1 operators:4 corrected:1 known:4 account:1 eiω2:1 work:1 fock:3 values:3 canonically:1 making:1 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quant-ph9805046.txt |@word consider:1 similarity:1 results:1 quadrature:1 generalize:2 consists:1 replacements:2 presents:1 quasi:2 th:2 breach:1 anharmonic:1 brown:1 straightforward:1 wave:2 every:1 exact:2 smithey:1 solves:1 presented:1 issue:1 discrete:6 science:1 optics:1 noted:1 2k0:2 direct:1 zero:2 further:2 ter:1 chem:1 odd:2 even:1 nonlinear:1 appear:1 giving:1 contributed:1 expressed:4 current:7 merical:1 reconstruction:9 new:1 increasing:4 method:12 raymer:3 full:1 lee:1 hydrodynamical:9 here:2 beck:2 free:1 equations:5 change:1 obtained:4 survey:1 fourier:2 involves:1 plotted:1 uniquely:1 regardless:1 divide:1 leonhardt:2 weigert:1 herzog:1 use:1 would:1 contains:2 negative:4 hilbert:3 therefore:3 today:1 more:5 company:1 odinger:2 basically:1 particular:1 known:3 analogous:1 must:2 states:6 integrating:1 recall:1 equation:7 oscillator:1 ρn:2 values:16 us0:1 f0:3 f1:2 f2:2 f3:1 give:1 reconstructed:2 taking:1 rescaling:1 information:1 end:1 recursive:1 discussion:1 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quant-ph9805047.txt |@word rev:3 results:1 existing:1 leads:1 counterfactual:2 follow:2 reasoning:2 whose:1 certainly:4 depend:2 ac03:1 description:2 deterministic:1 answered:1 does:12 present:1 under:15 include:1 division:1 very:1 choice:15 liability:1 every:1 summarized:1 conception:1 difference:1 condition:13 disturb:2 progression:1 level:1 did:1 forth:1 couched:1 evades:1 ups:1 disclaimer:1 says:5 occurrence:2 dealing:1 prediction:3 imply:1 rigorous:1 even:1 what:14 appear:2 apparatus:1 incompatible:1 remain:1 expressed:1 experiment:7 goes:1 blur:1 expresses:1 connected:1 respectively:1 commercial:1 here:4 following:1 them:1 berkeley:3 consideration:3 appears:10 change:6 depended:1 obtained:5 great:1 employees:1 changed:3 allows:1 contradiction:1 suggests:1 simultaneous:1 products:1 advertising:1 makes:2 inference:3 merely:1 explained:2 logical:6 outcomes:2 hardy:2 privately:1 should:1 causal:1 use:3 proceed:1 would:20 remains:1 predictions:2 adequacy:1 choosen:1 therefore:2 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quant-ph9805059.txt |@word secondly:1 consider:1 chain:1 limited:1 magnetic:3 computation:8 spin:18 finally:2 swap:4 marks:1 advantage:1 sitting:1 far:2 frequencies:3 amorphous:1 induce:1 electron:1 replaces:1 every:1 cellular:5 resonant:4 affect:1 difference:1 bringing:1 swapping:2 level:1 anisotropy:1 solution:5 cascading:2 large:3 solved:1 science:4 small:2 periodicity:1 pulse:1 fold:1 design:1 quebec:1 concludes:1 initialized:3 port:2 machines:1 even:5 abc:6 appear:1 near:1 consequent:1 method:1 body:2 respectively:1 hours:1 desired:3 explore:1 them:2 possibility:1 relaxation:2 directions:1 along:4 strong:2 technical:1 larger:1 qualify:1 periodic:4 resonance:2 implement:1 automaton:4 studies:1 montreal:1 via:5 brought:1 addressed:1 unit:2 would:1 contains:1 next:1 automata:6 call:1 therefore:2 memory:1 type:3 more:2 posting:1 relax:1 berlin:1 excellent:1 hold:1 room:3 thousands:1 originally:1 work:2 protons:1 example:2 nearest:6 figure:1 preserving:1 share:1 numbers:1 simple:2 information:11 needs:1 end:1 thing:1 rather:2 algorithms:1 chemical:3 how:3 adjacent:1 gate:1 ensemble:3 simplicity:2 intended:1 huge:1 may:12 after:1 containing:1 efficiently:1 maybe:2 register:1 wald:1 purification:1 so:6 mcgill:2 keeps:1 dream:1 order:1 operations:2 gershenfeld:1 indeed:1 over:1 move:1 course:1 through:1 its:3 symmetry:1 decay:2 actually:2 fig:3 mail:1 overcome:2 non:2 good:2 material:2 break:1 units:2 slichter:1 they:1 compound:1 rotation:1 possess:1 easily:2 university:1 sufficiently:1 each:3 inherent:1 higher:2 individually:1 doing:1 principles:1 constitute:1 frequency:2 quantum:41 laboratory:1 operation:8 transitions:1 special:2 out:1 canada:1 divincenzo:2 shown:2 impurity:7 rev:6 shows:1 interactions:2 pumping:1 free:2 standard:2 vazirani:1 completely:1 initialize:1 beginning:1 could:1 computers:5 days:1 xue:1 exponentially:1 onto:1 first:2 major:1 daunting:1 probability:1 powerful:1 number:1 2a7:1 spinning:3 done:4 loaded:1 size:1 necessarily:1 temperature:8 xin:1 their:3 cooling:1 perfectly:5 final:1 store:2 serve:2 optical:1 manipulation:3 than:2 havel:1 preparation:1 enables:1 distinguished:4 defect:2 unlikely:1 further:1 need:1 weinfurter:1 any:7 efficient:1 mechanism:2 polarization:1 donor:2 subject:1 unless:2 solidified:1 price:1 reach:1 most:2 letter:2 measured:1 why:1 achievement:1 especially:1 request:1 drive:6 physica:1 points:1 doped:4 degrades:1 bring:2 chuang:2 lloyd:2 find:1 completion:1 ratio:3 just:1 implementation:1 written:1 should:3 only:1 local:3 do:1 get:1 scalable:1 preferred:1 ones:1 fields:1 arxiv:1 summary:1 gammon:1 pulses:3 set:2 art:1 achieved:2 up:4 computer:4 spinpolarization:1 powder:2 techniques:1 project:1 fails:1 nuclear:10 sites:3 state:11 won:1 between:3 tens:2 barenco:1 ability:1 qubits:5 however:2 aspin:1 selectively:1 sleator:1 both:1 many:1 region:1 present:1 logic:4 qubit:5 whole:1 experimental:1 nearby:2 load:1 among:3 reasons:1 ca:1 environments:1 dimensional:3 simply:1 doping:2 broadening:2 ensures:1 due:3 springerverlag:1 ph:4 systems:1 controlled:1 coherence:1 bulk:2 external:1 careful:1 irrelevant:1 those:1 case:1 novel:1 exponential:2 pacs:1 solid:6 orthorhombic:1 single:6 will:1 while:1 lx:1 polymer:2 h3a:1 overlooked:1 thus:2 site:17 ready:1 rid:1 technology:1 different:1 resetting:1 perform:1 make:2 same:2 shifts:1 quant:4 dhw:1 difficult:2 used:2 upon:1 effect:2 driven:1 moving:5 recent:3 prescribed:2 lower:1 suitable:1 off:2 well:2 sets:1 firstly:1 position:2 model:1 dimension:1 gates:2 proposed:2 less:1 proximity:2 scattering:1 candidate:1 wei:1 except:1 lattice:8 setting:2 lett:5 input:3 tolerable:1 identical:1 around:2 possible:1 department:1 using:2 bit:4 unique:1 scaled:1 necessary:1 exploiting:1 signal:3 serves:1 specific:1 output:2 cooled:1 right:1 conditional:3 some:10 back:4 selectivity:1 growth:1 specified:2 proper:1 scale:3 swaps:2 provides:1 chains:2 measuring:1 noise:3 nmr:13 detuned:1 molecule:2 shifting:6 post:2 cory:1 schulman:1 about:1 discussed:1 spins:13 subset:1 into:4 within:1 three:7 down:3 promise:1 assumed:1 support:1 there:1 question:1 start:2 low:3 enough:1 but:2 proposal:2 coupling:1 reset:1 breakthrough:1 applying:2 embedded:2 flip:1 crystal:11 problem:4 piece:2 associated:1 computing:1 universal:3 moved:2 engineering:1 interchanged:1 our:1 crystals:3 intentionally:1 physical:1 again:2 ingredients:1 sublattice:3 reality:1 field:1 other:4 electrical:1 test:1 transferring:2 superposition:1 stay:1 restoration:1 nucleus:3 structure:4 dimensions:3 building:1 longer:1 assume:1 required:1 together:2 having:1 time:1 nuclei:3 starting:1 original:2
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quant-ph9805060.txt |@word unavoidable:1 transitions:1 preparation:1 induces:2 magnetic:2 roc:1 desirable:1 results:2 existing:1 facilities:1 quadrature:3 commute:1 restated:1 compliance:1 consists:2 denotes:1 reynaud:1 whose:2 depend:1 referring:1 zone:1 fellowship:1 similar:2 eα:1 subjected:1 deterministic:1 tr:1 braginsky:1 containing:1 environment:6 finally:2 mediated:1 those:1 th:1 under:2 stochastic:1 differing:1 worth:1 detect:1 case:12 supported:2 straightforward:1 far:1 alternatives:1 continues:1 springer:2 induce:1 choice:2 grundlagen:1 every:1 figs:1 entries:1 resonant:1 difference:1 matrices:1 condition:1 nonselective:5 vigneron:1 josephson:1 vibrational:1 level:15 die:1 ramond:3 ρf:17 proposals:1 large:1 solved:3 detected:1 science:1 small:4 hospitality:1 optics:2 der:1 configurations:1 application:1 sapienza:1 computation:1 cessa:1 consistent:1 edu:1 measurable:1 pulse:1 approximation:1 second:4 traveling:2 tm:3 further:1 dynamics:10 implemented:2 cfr:1 quite:1 linear:1 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quant-ph9805066.txt |@word concept:1 homomorphism:6 consider:5 caused:1 results:1 four:8 eds:3 scalar:2 proposition:8 during:1 mcmullin:2 displaying:1 reasoning:1 causes:21 preserves:2 referring:1 deterministic:3 acting:2 γk:2 finally:1 does:9 certain:1 those:1 excluded:2 quarterly:2 analogous:3 must:3 midwest:1 norm:1 belonging:1 supported:1 g2:4 straightforward:3 orthogonal:3 very:1 springer:1 stipulate:2 every:16 interpreting:1 decide:2 lecture:1 condition:6 leads:1 induction:2 notes:1 admissible:10 commute:1 recall:2 indices:2 establishing:1 α2k:10 direct:7 maintain:1 zero:3 akp:1 further:2 defines:1 linear:3 even:3 will:3 what:7 stands:1 richard:2 giving:1 section:11 selected:1 while:3 goes:3 values:1 equivalent:1 satisfy:6 q1:2 notions:3 never:1 here:7 cos2:5 standard:7 equations:5 interpret:1 obtained:1 orthomodular:8 technical:2 separatedness:1 larger:2 allows:1 completely:2 contradiction:3 resulting:1 published:2 charybdis:1 proof:6 makes:3 genuinely:3 emerge:1 formulated:6 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quant-ph9805067.txt |@word represent:1 partial:2 consider:3 remarkable:1 helstrom:1 results:1 four:1 entropy:2 depend:2 tv:1 subjected:1 tr:2 case:4 very:1 frequencies:1 hughes:1 choice:1 worst:1 matrices:2 transmission:5 trb:2 small:1 trs:2 maximization:1 direct:1 b21:1 b20:1 second:3 further:3 machines:1 even:1 uniform:1 subspaces:1 new:1 here:3 represented:3 obtained:3 institute:1 changed:1 resulting:2 real:2 makes:1 mutual:3 addresses:1 marginal:3 apply:2 linearly:1 use:1 working:1 probabilities:8 positive:1 hilbert:3 therefore:3 memory:1 marginally:1 more:5 introducing:1 formally:1 correspondingly:1 known:2 cases:1 must:2 mc:1 ρi:2 recall:1 work:1 following:7 example:2 calculation:1 introduces:1 bennett:1 allahverdyan:1 states:20 sense:1 distinguishable:1 occur:1 cloning:10 information:17 redundancy:1 fortunately:1 acts:1 nuts:1 orthogonality:3 write:1 pure:4 answer:1 instead:1 parameter:1 sin:8 barnum:1 may:1 clone:1 after:6 minimized:1 applications:1 gammal:1 realized:1 st:1 broadcasting:1 so:3 holds:1 trade:1 symbols:2 course:1 paper:2 through:1 y1:2 ieee:1 machine:7 supplemented:1 ln:6 exact:2 distinguishing:2 choose:3 maximal:5 non:3 propose:2 nonorthogonal:2 yz:1 they:1 optimal:5 brothers:1 now:6 discuss:2 eigenvalue:2 ensemble:6 transmitted:3 each:2 done:1 traces:1 constraints:1 el:1 related:1 measurement:4 quantum:24 our:5 operation:1 eq:1 really:1 divincenzo:1 shown:1 matrix:2 space:3 rev:2 increase:1 alikhanian:1 maximized:2 print:1 formula:3 get:1 nonorthogonality:1 theory:5 perfectly:1 free:2 forbids:1 r1:6 r2:6 messages:4 hence:1 think:1 first:2 origin:1 there:5 probability:2 variables:1 coding:5 channels:4 simplified:1 blank:5 xs:1 message:1 checked:1 unknown:2 system:2 their:4 calculations:1 realization:1 scheme:3 bits:1 final:2 moscow:1 broadcast:7 part:1 copy:1 coefficients:1 detection:1 wootters:3 zero:1 determined:1 distinguished:1 usefulness:1 seen:1 any:3 subsystems:1 min:2 convenient:1 generalized:1 channel:21 trace:1 shall:1 trσ:1 measures:2 most:1 connected:1 considered:2 average:2 later:1 cover:1 physics:2 fact:1 quantity:1 show:2 contemporary:1 degraded:3 decoding:5 d0:3 d1:5 x1:2 ensembles:3 state:6 should:10 only:6 cryptography:1 means:1 dependent:1 zurek:2 cannot:4 arxiv:1 2b1:1 fixed:1 set:1 computed:1 observed:1 see:3 result:3 capacity:1 written:3 between:9 conditions:1 recently:1 reproduced:1 nature:1 armenia:1 problem:5 cos:9 last:1 many:1 equal:3 against:1 connection:3 contribution:3 estimation:1 adapted:2 2b21:1 simple:1 dimensional:3 described:2 transformations:1 pz:2 px:4 py:2 copies:1 been:2 povm:1 reduction:1 ensured:1 pe:12 expected:1 ph:2 wants:1 life:1 corresponding:4 sufficient:2 subspace:1 σi:3 coherent:1 determination:1 external:1 c1:3 c0:3 p2:4 p0:2 p1:4 reliable:1 value:3 will:1 noised:1 suppose:1 error:10 a20:2 a21:2 unitary:4 thus:5 different:1 make:1 same:7 quant:2 copying:3 capacities:3 independent:2 used:2 functions:1 hand:1 action:3 user:7 entanglement:9 uˆ:6 totally:1 off:1 scenario:1 minimize:2 whole:1 well:3 academic:1 without:1 sets:1 dimension:1 usual:1 less:1 obtain:1 sources:3 stratonovich:1 generator:1 density:3 source:3 other:6 lett:1 theorem:1 transformation:8 opt:4 breaks:1 possible:6 increases:1 press:1 broadcasted:1 like:1 qualitative:1 arbitrary:1 yerevan:2 because:7 classical:10 sequence:2 conditional:4 some:1 understood:1 b0:5 b1:4 indistinguishability:1 users:7 electromagnetic:1 opposite:2 does:1 proc:1 minimal:4 noise:8 equivalent:1 communicate:1 step:1 optimize:1 simpler:1 discussed:2 meaning:2 plus:1 mixed:1 introduced:3 obtaining:1 three:1 references:1 span:1 additional:4 initial:3 question:1 long:1 start:1 function:1 complete:1 form:1 smolin:1 but:2 cloned:3 construction:1 clones:3 wish:1 distinguishability:1 us:2 d21:1 distribution:2 called:1 nauka:1 defined:1 recognize:1 abstract:1 measure:2 direction:1 general:3 exist:1 distributions:3 ina:1 physical:2 coder:2 no:2 when:3 field:1 priori:6 role:1 out:1 denote:1 generates:2 separate:1 symbol:1 a1:4 a0:5 generated:1 important:3 correlated:1 practically:1 assume:3 d20:1 time:1 n1:3 n2:3
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quant-ph9805068.txt |@word secondly:2 entropy:8 sch:1 paris:1 unanswered:2 presents:1 under:2 accardi:1 conjecture:6 every:2 manin:2 school:3 34a:1 solution:11 convenience:1 vector:2 direct:1 approximation:3 second:7 rigorous:2 implemented:1 haake:2 even:5 established:2 above:7 new:4 consisting:1 evolving:1 kicked:5 κa:1 here:12 met:1 q10:2 κt:4 obtained:4 derivable:1 study:18 approaches:1 procedure:4 adopting:1 suitable:1 appropriately:1 replace:5 total:1 univ:1 linearly:1 derivatives:2 would:7 motivate:1 negative:1 therefore:12 type:20 solitons:1 odinger:22 berlin:1 springer:11 room:6 work:2 concepts:2 koopman:11 example:22 give:6 relativistic:1 indicates:4 want:15 times:3 end:2 provide:1 feature:1 how:3 answer:4 field:7 oscillatory:1 description:10 replacing:1 effects:2 constants:5 attempt:2 differ:1 order:5 interpretation:1 over:5 satisfied:1 belavkin:1 majewski:11 exhibits:5 better:1 connes:2 versus:1 them:1 they:1 shadows:2 represents:1 lorenz:1 each:2 side:1 mean:5 lifted:2 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quant-ph9805071.txt |@word limited:1 partial:1 consider:2 switched:1 caused:3 both:3 results:5 existing:1 pulsing:1 higher:1 revealed:1 causes:1 amplification:4 alamos:3 send:3 finally:1 compensate:1 those:1 th:1 under:5 analogous:1 include:1 dramatically:1 indoor:1 orthogonal:3 hughes:4 wave:9 every:4 atmospheric:4 final:1 collocated:1 splitter:2 perceived:1 induced:1 pbs:7 level:2 transmission:10 notes:2 eve:18 large:1 bers:2 optics:5 upper:3 smaller:1 demonstrations:2 feasibility:2 rate:22 noise:4 imental:1 traveling:4 pass:1 further:3 implemented:2 port:1 even:2 errors:7 sub:1 opaque:2 sun:1 eavesdropping:1 contributed:1 shares:1 find:3 cell:5 experiment:4 shared:1 appeal:1 public:2 contrast:1 revealing:1 full:5 led:1 elect:1 never:2 here:2 them:2 groups:1 same:3 path:17 along:2 commercially:1 imperfections:1 change:1 extreme:1 luther:1 drops:1 arc:3 sender:1 precursor:1 losses:1 allows:1 amount:3 resulting:2 launched:1 poisson:2 advantages:1 bob:34 birefringent:1 makes:1 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quant-ph9805072.txt |@word ibid:1 represent:2 logarithms:1 concept:4 allowed:4 consider:11 lack:1 results:8 existing:1 leads:3 proposition:4 entropy:22 computation:1 partial:1 remarkably:1 revealed:1 causes:1 excludes:1 certainly:6 maximally:2 referring:1 integral:1 producing:1 subjected:1 tr:2 acting:1 send:3 environment:3 finally:1 according:1 present:3 under:3 analogous:4 te:8 worth:1 sent:1 hill:1 applied:1 conjecture:2 supported:1 orthogonal:17 far:2 reader:1 choice:4 putting:1 fth:1 little:1 matrices:2 condition:12 dim:3 quantitatively:1 immediately:3 hamiltonian:1 knight:2 who:1 large:1 mnk:1 deliberately:1 recall:4 gc:1 vincenzo:1 prevent:1 mn:3 hans:1 grateful:1 deutsch:1 haar:1 consistent:1 charles:1 second:3 rigorous:1 further:1 canonical:1 even:3 nothing:2 what:3 adds:1 unavailable:1 cycle:1 section:5 selected:1 pawel:2 grover:1 above:17 new:5 increasing:1 method:2 satisfy:2 supporting:1 full:2 notions:4 degree:1 exchange:1 component:1 teleportation:4 here:9 understanding:1 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quant-ph9805073.txt |@word four:19 consists:2 relationships:1 whose:11 violate:1 γq:7 γj:5 under:6 worth:3 rise:1 every:3 negations:1 summarized:1 solution:1 convenience:2 vector:22 succession:1 indices:5 cmu:2 estimates:1 horn:1 second:10 machines:5 even:10 established:3 errors:3 above:4 new:2 ˆj:1 here:6 represented:3 path:2 κv:2 interpret:1 obtained:21 luther:1 study:4 changed:1 procedure:3 symmetrical:1 adopting:1 suitable:4 changes:1 buˇzek:6 explained:1 replace:1 achievable:1 unit:6 would:5 e1:3 negative:35 noting:5 call:1 therefore:7 m3:1 m2:1 e2:3 type:7 tell:3 reversible:2 hold:3 must:9 ml:1 work:4 theories:1 mq:5 concepts:1 erl:4 erm:1 root:4 example:4 indicated:2 bennett:2 india:1 absolute:11 end:2 machine:27 how:2 nontrivial:1 significance:1 answer:2 gate:3 brassard:2 replacing:1 after:3 parallel:1 attempt:1 effective:1 summing:3 enter:1 βk:5 order:18 operations:4 restriction:2 interpretation:1 diagonalizes:1 over:12 satisfied:11 eavesdropping:5 fidelity:5 diagonalized:3 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quant-ph9805074.txt |@word measurements:4 consider:2 issued:1 results:3 existing:1 chameleons:5 reasoning:1 issues:1 whose:3 certainly:1 subjected:1 laid:1 environment:1 company:1 finally:2 behave:2 those:1 under:2 summarizes:1 sound:1 orthogonal:1 very:2 rise:2 wave:2 telling:2 experimentally:1 presented:1 did:1 shock:1 solved:1 vector:1 eigenvalues:1 shows:1 dip:1 configurations:1 concluded:1 core:1 direct:1 sign:1 imply:2 machines:1 even:1 what:8 apparatus:4 incompatible:2 giving:1 deeply:1 section:5 celebrated:1 expressed:1 find:1 experiment:11 new:1 contrast:1 paradoxical:1 simultaneously:3 component:1 understanding:2 behaviour:2 met:1 objects:13 others:1 directions:4 along:3 appears:2 receive:1 involved:1 leaves:1 vectors:1 experience:1 existent:1 york:1 beautiful:1 inference:2 logical:1 objectively:1 total:1 univ:1 duca:1 standing:2 use:3 metaphor:3 would:6 contains:1 next:1 live:1 call:1 mysterious:1 type:3 tell:1 more:1 sort:2 inclined:1 apparent:1 tested:3 carrying:2 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quant-ph9805075.txt |@word represent:1 consider:2 chain:1 lack:1 splitting:3 yurtsever:1 four:1 scalar:1 commute:1 entropy:7 ga:2 consists:1 expressions:1 primer:1 contributions:7 subjects:1 particles:5 certainly:1 tr:1 behave:1 those:2 under:1 exit:2 analogous:1 divergent:1 g3:2 presently:1 straightforward:1 far:3 3aa:1 rise:1 putting:2 specific:2 trouble:1 difference:2 bringing:1 generalised:3 annihilated:1 4n1:1 riemann:1 hamiltonian:14 αg:2 manifestly:1 consistent:1 discover:1 sign:1 past:5 second:2 cost:1 invariant:1 copenhagen:1 3a1:2 machines:13 canonical:1 even:4 index:1 what:4 appear:2 sum:1 supplied:1 above:4 values:3 3a:6 bird:1 filled:1 satisfy:2 supporting:1 respectively:1 here:3 diagonal:2 asymmetry:2 objects:1 them:2 free:2 directions:2 diagonalised:1 strong:1 equations:3 change:1 wesley:1 technical:1 shift:3 study:1 studied:1 exiting:1 action:1 makes:3 extra:2 9a:3 2δn:2 highly:1 summation:1 traversing:1 counts:2 spawned:1 interest:1 use:1 eye:1 indicated:1 would:10 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quant-ph9805087.txt |@word consider:1 ceases:1 rev:4 particular:1 results:1 leads:1 overlap:2 localized:1 inverse:1 calculate:2 finally:1 does:1 lecomte:1 stable:1 mpg:1 jensen:1 evolves:1 very:4 continues:1 wave:4 every:1 mixing:1 experimentally:4 continued:1 condition:4 squares:1 level:1 positions:3 occurs:1 large:5 small:8 eigenvalues:2 anal:1 uncovers:1 smaller:1 measurable:1 bracco:1 further:2 dynamics:2 chem:2 even:1 established:1 errors:1 trapping:5 while:5 rotter:5 poles:13 above:1 increasing:2 waveguide:18 method:4 coefficient:1 here:1 atoms:1 simon:1 eikx:1 strong:1 equations:1 change:1 incoming:1 parameters:1 institute:2 study:5 studied:5 contradiction:1 published:1 decouple:1 studies:2 via:1 scales:1 marked:1 decrease:2 planck:1 plot:2 use:2 additive:1 asymptotic:2 remains:1 nucl:1 therefore:1 analysing:1 resonator:6 theoretical:1 separated:1 flat:2 brems:1 autoionizing:1 becomes:3 under:1 interaction:1 controlling:1 excellent:1 states:30 account:1 equation:3 work:1 krasnoyarsk:1 following:1 rssi:1 example:1 figure:2 sokolov:1 high:4 attract:1 axis:4 information:1 varied:1 provide:1 holds:1 write:1 located:1 pure:2 ockel:1 parameter:4 sin:1 staying:1 may:1 max:1 after:1 derived:1 different:4 applications:1 plane:3 physik:2 data:1 parallel:2 short:7 third:2 lines:1 correspond:1 so:3 allow:1 wigner:2 help:1 over:1 statistical:1 differs:1 still:1 its:4 delay:11 systeme:1 decay:1 energies:2 solving:1 decreases:1 li:1 attraction:1 choose:3 τw:6 them:2 numerically:1 reflected:2 scaling:4 billiard:13 they:1 half:1 now:1 day:1 gamow:1 fully:2 presented:1 identified:1 2g:1 mode:2 each:2 aligns:1 found:1 universit:1 interfering:1 reactions:1 domain:1 directly:2 energy:10 idea:1 related:3 used:1 changed:1 quantum:1 eq:1 out:1 ru:1 shown:1 resonators:1 nuovo:1 since:4 interference:3 increase:4 denoted:1 size:1 plotting:1 math:2 shows:1 foundation:1 dittes:1 theory:1 barrier:3 possibility:1 standard:1 approaches:2 formation:1 dirichlet:2 widths:4 times:1 motion:2 technische:1 first:1 probability:1 number:1 theoretische:1 another:1 open:2 illustrate:1 given:1 start:2 system:2 zelevinsky:1 mpipks:1 their:3 realization:1 dfg:1 e52:1 trapped:5 academy:2 continuous:4 persson:3 part:1 authors:1 x0:6 representing:1 distance:1 accordance:1 cimento:1 amplitude:1 russia:1 acknowledged:1 ann:1 spectrum:4 need:1 border:1 strength:2 angle:1 billiards:1 isolated:3 oriented:1 sciences:2 potential:3 coincide:1 strengths:1 channel:4 spectral:1 play:1 investigations:2 systems:1 connected:4 letter:2 analytically:1 considered:1 neighboring:1 calculated:1 proceedings:1 exp:1 physics:5 lying:1 quantity:1 phenomenon:3 show:2 nπ:2 text:1 supported:1 threshold:1 longer:1 find:1 ground:1 spite:1 only:2 means:1 de:2 ones:3 words:1 collisional:1 justified:1 transversal:2 continuum:4 komplexer:1 fields:2 arxiv:1 investigate:2 exists:1 achieved:1 lifetimes:3 prague:1 see:5 individual:2 result:3 arg:1 discussions:1 contour:1 instance:1 bifurcate:1 eigenfunctions:1 ways:1 nuclear:3 b364:1 case:3 state:7 various:1 between:8 boundary:4 numerous:1 recently:1 ikx:1 weak:1 however:1 gratefully:1 both:2 taking:1 equal:1 chosen:1 disappears:1 experimental:4 among:1 point:1 corresponds:1 height:1 dimensional:2 cz:1 respect:1 panel:2 described:1 union:1 three:7 been:3 damping:1 ph:1 fig:2 dots:1 lived:8 corresponding:3 θf:1 coherent:1 decreased:1 present:2 applied:1 sommers:1 pacs:1 value:1 rectangular:5 will:1 near:2 behavior:2 identical:1 unitary:2 coupled:2 almost:1 thus:1 surface:1 reads:1 exterior:2 containing:1 grant:1 same:2 complex:8 quant:2 gets:1 independent:1 investigated:1 numerical:1 evin:1 hand:1 resonance:32 changing:1 tune:1 lower:1 reflection:1 acknowledgement:1 well:2 analysis:1 solve:1 coordinate:1 position:2 model:1 arising:1 distances:1 agency:1 λv:2 being:1 rotated:2 valuable:1 shape:2 uller:2 density:1 smith:2 rˆole:1 extends:2 lett:3 5g:1 transformation:6 real:3 iθ:1 possible:2 increases:2 rescales:1 using:3 unique:1 imposed:1 follows:1 soff:1 become:4 smoothly:1 czech:4 moreover:2 lead:2 electromagnetic:1 microwave:1 critical:1 prog:1 dresden:4 location:1 equivalent:1 wavefunctions:5 properties:2 eψ:1 tracing:1 dependence:1 mixed:3 germany:2 into:4 obtaining:1 bound:1 lies:1 theoretically:2 institut:2 log:1 seba:2 twodimensional:1 a53:1 long:4 width:5 accordingly:1 appl:1 low:1 gorin:1 function:12 form:1 but:1 partially:1 inside:6 attached:2 up:1 differentiable:1 ur:2 fyodorov:1 darker:1 int:1 certain:2 proven:1 general:1 single:2 arises:1 dθ:1 lifetime:1 spends:1 interferences:3 again:1 functions:1 nk:1 no:3 whereas:1 wavefunction:5 when:4 detail:2 other:8 republic:2 details:1 er:1 excitation:2 time:13 important:2 coupling:11 practically:1 starting:1 resonances:6 4g:1 resolution:2 rep:1
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quant-ph9805088.txt |@word consider:3 results:8 grateful:1 compact:1 whose:5 aug:1 tr:6 finally:2 worth:1 subtleties:1 applied:1 orthogonal:1 very:2 transmission:1 erratum:1 solution:1 fewer:1 large:3 extrema:1 generalises:1 deutsch:1 sign:1 zero:13 street:1 implemented:1 above:1 fractional:1 shared:3 ever:1 method:2 teleportation:1 here:1 plenio:1 represented:1 strong:1 respect:1 great:1 leaves:1 allows:1 approaches:2 products:1 schumacher:1 action:2 bob:5 involves:1 specified:1 addressed:1 apply:1 use:1 asymptotic:1 would:1 massar:4 distinct:2 positive:3 negative:1 ψi:12 taken:1 theoretical:3 more:5 linden:4 successful:1 operators:4 carrying:1 particular:2 known:1 given:4 must:8 states:33 ρf:4 nonmaximally:1 example:1 f0:6 give:4 bennett:5 share:3 stressing:1 high:1 want:1 arise:1 simple:2 information:1 rays:1 rather:1 holds:1 write:1 maps:2 pure:15 answer:1 explains:1 may:3 after:1 applications:1 produce:8 unentangled:1 constants:2 natural:2 succeeded:1 whenever:1 purify:1 purification:23 generic:6 so:7 increase:1 serge:1 operations:8 produces:3 over:2 produced:1 including:1 statistical:1 fidelity:11 its:1 before:1 perfect:1 how:1 actually:1 systems:6 workable:1 derivative:1 might:2 maximal:3 non:8 greater:4 combination:2 practice:1 finitedimensional:2 they:5 now:3 silver:1 nor:1 several:1 university:1 concave:1 orthonormal:1 sufficiently:1 each:4 constraints:2 subset:1 schemes:3 financial:1 revised:1 society:1 sandu:1 expect:1 measurement:1 quantum:4 special:1 out:3 noiseless:1 matrix:3 since:6 rev:7 particles:10 acting:1 kent:1 conjectured:1 shows:1 linear:2 lmp:7 diagonal:2 possibility:1 difficulty:1 completely:3 formation:1 ask:2 9ew:1 pairs:1 tolerant:1 adrian:1 hence:4 onto:1 first:2 intuition:1 already:1 probability:4 number:4 rank:8 channels:1 entanglement:4 construct:1 carry:2 impossible:1 clarity:1 open:1 differ:1 necessarily:1 similarly:1 least:4 their:2 scheme:21 gives:1 relationship:1 explanation:1 continuous:1 copy:1 than:6 perfectly:1 third:1 require:2 second:1 preparation:2 ana:1 generality:1 measure:1 argument:4 need:1 seem:1 any:21 ray:1 lie:1 efficient:1 note:1 extracted:1 take:1 algorithms:1 maxa:1 channel:2 though:1 singlet:7 most:2 involving:1 letter:1 pair:2 acknowledgements:1 why:2 takes:1 surprising:1 clear:1 stronger:1 countable:1 generalising:1 principle:1 physics:1 show:8 discovered:1 spaces:1 inconsistent:2 d2:1 proposed:1 entangling:1 proportion:2 state:34 should:1 failed:1 only:6 attained:1 bernstein:1 local:22 hope:1 do:1 mixture:5 quantph:1 means:2 df:1 simplest:1 countered:1 generalise:1 cannot:10 new:1 arxiv:1 yield:1 summary:1 rotationally:2 fixed:1 set:1 bounds:1 individual:5 result:4 discussions:1 close:1 symmetric:1 written:1 between:2 invariant:1 discovery:1 recently:2 august:1 hypothesis:2 essentially:1 taking:1 according:1 exceeds:1 qubit:1 comment:1 strongly:1 bell:9 pov:1 effective:1 dimensional:3 werner:7 sequences:1 moreover:1 throughout:1 singlets:8 described:1 locally:1 been:2 defined:1 interest:2 ph:2 pi:5 corresponding:1 michal:1 else:1 maximally:7 spin:8 those:1 case:2 value:1 will:1 optimization:1 suppose:4 purifying:3 unitary:3 thus:1 them:1 technology:1 perhaps:1 suggest:1 make:1 belong:2 same:2 quant:2 mixtures:2 party:1 finite:3 higher:1 independent:3 used:1 infinity:1 infinite:2 relies:1 lower:2 no:13 well:1 without:1 ekert:1 popescu:5 less:1 being:1 generally:5 obtain:3 purified:7 contradicting:1 density:3 noah:1 conclude:1 royal:1 source:1 imposes:1 lett:5 easy:1 theorem:1 bnb:1 spin1:1 remaining:1 increased:5 showing:1 possible:2 entangled:24 using:1 loss:1 helpful:1 contradict:1 collective:2 alice:5 communications:5 continue:1 steps:1 either:4 arbitrary:1 become:1 classical:5 sequence:4 some:8 examples:2 sight:1 convex:2 possibilities:1 dimensions:2 measurements:9 does:3 decomposition:1 tends:1 minimal:1 noise:3 martin:1 analyses:1 properties:1 simpler:1 practical:2 range:6 mixed:26 cambridge:2 follows:1 rotations:2 raises:1 parties:4 operator:2 normalised:1 support:1 there:7 question:1 class:2 doubt:1 way:1 form:2 but:4 hb:1 encoded:1 ha:1 true:4 applying:1 horodecki:4 whether:4 welldefined:1 maximum:2 below:1 limit:1 problem:2 similar:1 b1:1 detailed:1 separated:2 constant:1 ai:5 describe:1 am:1 remove:1 general:1 single:2 locality:2 na:4 nb:4 when:1 other:2 details:1 department:1 mathematics:1 conventionally:1 prepared:1 a1:1 cb3:1 implies:1 together:1 original:1
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quant-ph9806001.txt |@word logarithms:1 partial:1 gr:2 results:1 roy:1 computation:12 query:7 eη:1 issues:1 whose:2 simon:2 const:1 alamos:1 rf:3 passage:1 tj:3 sped:1 norm:1 applied:1 amplitudes:2 choice:2 print:3 every:5 difference:1 turns:1 solution:8 t0:1 large:2 solved:2 indices:1 upper:1 mn:2 says:2 grateful:1 deutsch:2 zero:2 further:1 victor:1 even:1 established:1 what:2 section:2 sequential:1 above:1 new:5 3a:1 method:1 notions:2 respectively:1 aij:3 discrete:1 here:5 amplification:1 others:1 strong:3 equations:1 change:3 extreme:8 obtained:1 search:14 technical:1 vectors:1 contradiction:1 professor:1 published:1 action:1 bounds:5 boolean:6 apply:2 establish:2 estimate:1 use:3 asymptotic:1 would:2 prove:2 jozsa:2 toffoli:1 next:1 perr:16 msk:1 therefore:2 type:1 more:1 bennett:2 solitons:1 academician:1 correspondingly:1 particular:2 foundations:2 cases:2 cardinality:2 analogous:1 must:4 me:2 high:1 account:1 word:5 science:2 equation:2 work:15 oleg:1 grover:4 values:3 following:8 dec:1 my:1 example:1 proof:8 give:5 predict:1 preserving:1 states:5 contradicts:1 minimum:1 walsh:1 numbers:2 sense:2 s1:1 machine:1 how:1 opposite:1 significance:1 answer:6 optimal:2 brassard:4 may:3 after:3 applications:1 fe:1 evaluations:1 constants:1 natural:1 third:1 computations:6 light:1 complexity:6 sh:2 algorithms:4 allow:1 sb:5 counted:1 developed:1 over:1 vary:1 soon:1 differs:1 ieee:2 its:3 thank:1 chosen:10 theorem:12 fix:3 lj:8 choose:3 mail:1 maximal:1 them:2 fourth:2 speeding:1 they:2 symposium:2 perror:1 rotation:1 now:7 verifying:1 university:1 orthonormal:1 2e:3 inequality:5 each:10 found:2 2n:6 referred:1 financial:1 ej:13 ed:1 idea:3 society:2 measure:1 substantially:2 our:6 out:1 ru:1 shown:2 matrix:1 space:2 induces:1 chaos:1 acting:1 reader:1 denoted:3 induction:1 correct:4 weaknesses:1 vazirani:2 small:2 yuri:2 put:8 fixe:1 inductive:1 card:6 e2:1 definition:1 r0:3 launch:1 computers:2 times:1 turn:1 length:3 hence:1 first:3 xi:1 probability:29 variables:1 cj:7 number:6 oracles:4 lond:1 done:1 summarize:1 xt:9 given:3 similarly:1 introduction:2 unknown:1 system:1 least:1 their:1 observations:1 siam:1 final:6 gives:7 hoyer:6 moscow:2 exactly:3 part:1 authors:1 x0:3 x1:2 than:5 diffusion:1 wide:1 target:1 require:1 second:3 russia:1 generality:1 beforehand:1 bitwise:1 randomly:7 discussions:1 say:2 need:2 any:1 issue:1 depending:3 si:2 note:1 take:2 finding:1 so:1 strengths:1 cl:3 philadelphia:1 shall:7 who:1 systems:1 most:1 letter:1 device:1 acknowledgements:1 χt:13 observation:2 considered:1 average:1 proceedings:3 points:2 mechanical:1 physics:1 sum:1 χi:11 shor:2 show:1 random:7 solutions:3 find:3 principal:1 tapp:2 ratio:1 distributed:2 peculiar:1 lemma:9 only:4 bernstein:2 extremum:3 do:1 his:2 dj:2 dh:4 means:3 beat:1 expectation:3 da:4 aim:1 words:1 stoc:1 prime:1 evolution:1 querying:2 places:1 arxiv:1 factorization:1 qc:2 fixed:3 view:4 formly:1 redefine:1 set:15 modulo:1 exists:2 ebj:1 up:4 depends:2 computer:10 result:10 fail:1 best:1 ways:1 state:15 between:2 αi:3 approach:1 qubits:1 attention:1 hypothesis:1 dates:1 last:1 taking:1 annual:2 item:3 finds:3 boyer:2 arbitrarily:2 among:2 point:18 simple:1 ca:1 asymptotically:1 dimensional:1 iterations:2 polynomial:1 constant:1 pp:2 basis:2 addition:1 informed:1 workshop:1 basic:5 ph:4 define:5 corresponding:1 oφ:2 concerning:1 propositions:1 bulk:1 observe:1 c1:3 case:3 look:2 value:3 will:5 institute:1 suppose:3 error:5 35th:2 mistake:1 unitary:5 vi:2 metric:1 thus:2 ij:3 vt:7 ready:1 sequentially:1 different:3 make:1 same:2 shorter:1 stimulated:1 complex:2 quant:4 fairly:1 used:1 effect:2 hand:3 ˆlj:2 lower:10 database:1 well:1 without:1 sets:2 eζ:2 maslov:1 less:4 obtain:8 transforms:2 questions:1 integer:5 facts:1 λj:18 speed:1 nov:1 elj:2 rapid:1 regarded:1 conclude:2 add:1 belongs:2 technological:1 extensive:1 transformation:1 real:1 possible:1 np:1 background:1 press:2 using:2 unique:1 fractals:1 loss:1 modifications:1 like:1 follows:3 admitted:1 separately:1 steps:1 arbitrary:2 ˆbj:1 δa:4 because:4 applicability:2 classical:5 sequence:1 some:11 searching:4 proofs:1 provided:1 sufficiently:2 measurements:1 per:1 does:2 δj:1 proc:1 power:1 performed:1 uniformly:1 journal:1 bj:6 step:3 santa:1 hadamard:1 hilbert:2 takes:3 integers:3 about:1 rare:1 usa:1 theorems:1 o:14 oz:7 converging:1 soc:1 previously:1 into:1 bound:7 phase:1 references:1 determine:1 england:1 assumed:1 support:2 there:3 question:1 transform:4 fast:2 los:1 pa:1 lov:1 was:1 function:18 form:7 but:2 back:1 especially:1 count:2 made:1 applying:2 evident:1 maximum:9 preimage:1 ui:3 problem:6 called:1 distance:1 proved:6 computing:5 defined:2 abstract:1 am:1 denote:6 quantum:38 single:5 durr:4 constructed:1 incorrect:1 functions:19 nm:1 no:1 when:2 tight:1 other:3 2da:2 department:1 mathematics:1 really:1 sufficient:1 superposition:1 problems:2 n0:2 generated:1 important:1 variable:5 faster:2 algorithm:19 assume:6 dχ:1 lanl:3 eξ:2 fact:1 time:13 oracle:14 n1:2
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