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quant-ph0703249.txt |@word ibid:1 represent:1 concept:3 partial:2 consider:5 ali:1 global:2 desirable:2 focus:1 vr:1 leads:1 scalar:1 ρjk:2 generalize:2 lewenstein:2 expressions:1 research:3 increase:2 lkl:1 dimensionality:2 depend:1 calculate:1 iii:3 tr:6 nonlocal:1 intensive:1 th:4 under:8 decomposition:2 indicating:1 lack:1 advantage:2 orthogonal:1 very:2 huang:1 springer:1 otteler:1 results:1 every:1 qutrits:3 experimentally:7 difference:1 matrices:8 fan:1 four:1 school:1 presented:1 knight:1 guo:1 ρi:2 convenience:1 math:4 small:2 eigenvalues:1 subindex:2 mahler:7 lk0:1 inserting:1 ρj:6 estimates:1 measurable:1 hillery:1 sign:1 outcomes:2 zero:3 chen:3 further:1 implemented:1 odd:3 click:1 even:4 index:1 what:2 plays:1 power:2 multiqubit:1 diag:1 section:1 lawrence:1 expressed:1 witnesses:1 ˆa:6 ˆb:5 above:1 overcomplete:1 international:1 ˆk:1 method:3 contrast:1 simultaneously:1 lee:1 degree:2 respectively:2 l1:1 component:1 equals:1 here:1 guise:1 asymmetry:1 plenio:2 groups:1 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quant-ph0703252.txt |@word secondly:1 chinese:1 qian:1 results:12 existing:5 leads:1 edp:1 calculate:2 ts:1 finally:1 program:2 sent:2 kraus:1 very:4 rise:1 worst:1 lecture:1 condition:1 level:1 transmission:12 notes:1 guo:1 eve:2 large:2 convenience:1 rk:4 upper:6 smaller:1 deutsch:2 pulse:3 acin:1 rate:29 cost:2 chen:1 even:1 y1l:1 what:2 errors:1 expressed:1 experiment:7 above:3 utkenhaus:3 new:21 method:12 component:1 here:2 adachi:11 china:1 groups:2 along:1 equations:1 change:2 obtained:1 institute:1 items:1 changed:2 allows:2 through:1 harrington:1 bob:9 makes:1 transmittance:3 useful:2 secure:3 counts:9 total:1 detecting:1 kobayashi:1 scarani:2 use:11 would:1 next:1 comparing:2 approach:1 therefore:1 heralded:1 theoretical:1 more:9 silberhorn:1 mismatch:1 berlin:1 known:4 detects:1 must:1 impair:1 springer:1 ma:3 science:1 setup:1 work:3 zhao:2 values:10 following:4 europhysics:5 example:1 unconditional:1 numbers:1 beijing:1 weaker:1 wang:13 give:1 bennett:2 india:1 states:4 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quant-ph0703265.txt |@word gulde:1 concept:1 similarity:1 induces:1 concern:1 fabricated:5 four:1 ge:1 edu:1 consists:1 atat:3 assembled:3 layers:2 whose:1 etching:2 technique:14 young:1 ilya:1 program:1 indicate:1 ti:1 4nm:1 nodes:1 alternating:1 brown:1 supported:1 cantilever:1 schoenfeld:1 kroner:2 results:1 electron:1 resonant:2 affect:1 al0:1 entire:2 presented:1 proposals:1 gayral:1 demonstrated:1 small:2 govorov:1 barbara:1 warburton:3 10k:3 sacrificial:1 past:1 rate:3 design:3 enhancement:1 further:3 spectral:5 employ:1 detuned:2 richard:1 experiment:2 above:1 new:1 increasing:4 consisting:1 coefficient:1 full:1 pinhole:1 lee:1 microdisk:1 respectively:1 modify:1 reported:1 deposition:1 focused:3 address:1 active:1 november:1 strong:1 respect:1 change:1 shift:15 allows:2 completely:2 experience:1 chemical:2 microcavities:2 resonance:7 narrow:2 changes:2 plotted:2 gwinn:1 deterministic:1 useful:1 nanocavity:3 manipulate:1 wang:1 gaas:13 feb:1 faraon:3 would:1 distinct:3 next:2 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quant-ph0703266.txt |@word ptk:2 consider:5 pti:1 induces:2 global:4 dynamic:1 results:2 leads:2 roy:1 scalar:1 commute:2 ga:1 consists:5 expressions:2 gk:3 assembled:2 gi:5 rom:1 compact:7 whose:5 preserves:1 const:4 bivector:2 γr:1 tt:1 equivalence:1 γt:1 γk:8 γi:11 γh:7 under:2 atlas:1 stochastic:1 case:7 rise:1 induce:1 splitting:3 every:1 rm:1 exact:2 condition:8 quantized:4 hamiltonian:37 prolonged:2 admissible:3 convenience:1 vector:21 gauge:1 inertial:2 says:1 direct:1 further:1 dynamics:1 canonical:3 plays:3 section:5 gj:2 current:3 above:5 contrast:1 satisfy:1 respectively:4 equals:2 fiberwise:2 desired:1 tangent:3 represented:3 consideration:2 along:8 enveloping:4 equations:6 z2:1 stalks:1 leaves:1 vectors:1 products:1 poisson:34 action:1 tu:2 ipk:2 glance:5 readily:4 ıa:1 use:2 takes:5 covariant:11 contains:3 bundles:2 linear:2 derivation:2 call:1 therefore:6 vi:2 type:2 theoretical:1 more:1 flat:1 clearly:1 operators:23 germs:3 odinger:13 curvature:2 berlin:2 appendix:2 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quant-ph0703267.txt |@word consider:3 12s2:1 oss:2 results:1 ladders:1 follow:1 displaying:1 calculate:2 29b:1 finally:1 divergent:1 mohammad:1 ibrahim:1 wave:5 exact:1 condition:2 four:1 level:2 solution:1 solved:1 dieperink:2 eigenvalues:6 karimi:2 degeneracy:1 force:2 setare:1 second:3 chem:8 richard:1 morse:1 3s:1 sun:1 section:1 en:3 above:4 new:5 satisfy:3 iran:1 component:1 atoms:1 groups:1 address:1 directions:1 change:1 obtained:1 study:2 usually:1 varshni:1 hulthen:13 ipm:1 establish:1 use:2 would:1 levine:3 approach:2 ψn:23 associated:4 more:1 lowering:1 ugge:1 operators:11 odinger:2 particular:2 springer:2 rotational:2 ma:2 science:1 equation:6 values:1 following:11 example:2 f1:26 states:3 degenerate:1 provide:2 s2:22 write:1 4s3:4 mar:1 mat:2 algebra:2 ladder:3 wiley:1 dx2:1 applications:2 law:1 fl:1 short:1 branches:1 dynamical:5 whenever:1 correspond:1 su:4 order:1 over:1 years:1 paper:3 iachello:7 its:1 group:2 forms:1 systems:2 mail:2 therefor:1 ze2:1 equidistant:2 they:2 oxford:1 now:5 teller:1 eigenvalue:1 february:1 several:1 2s:52 university:2 identified:1 establishing:1 l0:1 each:1 2l:1 2m:2 2n:12 em:1 differential:1 dong:13 energy:6 hypergeometric:1 investigated:1 expect:1 quantum:3 our:1 whit:1 beyond:1 eq:11 special:2 description:1 shown:3 since:1 rev:3 math:2 benjamin:1 theory:1 frank:1 possibility:1 standard:1 york:4 wanted:1 degeneracies:4 could:1 consequence:1 first:3 origin:1 symmetry:6 number:2 clear:1 relations:2 another:2 angular:1 given:3 publication:1 similarly:1 introduction:1 eqs:2 system:6 construct:1 their:2 too:1 molecular:1 polyatomic:1 quan:2 ebrahim:1 than:1 coefficients:1 variational:1 namely:1 annihilation:3 f12:1 treated:1 symmetries:2 rewrite:3 ann:1 spectrum:1 say:1 tables:1 lie:2 zero:1 lim:2 εm:1 εn:3 take:1 finding:1 techniques:1 unless:1 algebraic:7 2s2:1 commutation:2 calculated:2 physics:3 dover:1 lebedev:1 show:1 12s:1 relation:7 substituting:1 d2:3 find:1 based:1 parameters:2 should:1 molecules:2 factor:2 dx:1 dy:13 dr:1 gen:1 areas:1 fields:1 arxiv:1 expansions:1 see:3 computer:1 result:1 ark:2 subject:1 satisfying:1 eigenfunctions:4 review:1 state:2 boundary:3 conditions:1 nature:1 last:1 many:1 region:1 expand:1 expression:1 harmonic:1 2nd:1 table:3 pp:1 due:1 been:3 interest:1 expected:1 ph:1 define:1 field:1 direction:1 corresponding:4 coherent:1 astron:2 present:1 case:4 tang:1 value:1 will:1 near:1 property:1 ir:2 thus:2 different:5 quant:1 widely:1 finite:1 φn:3 used:2 effect:1 v0:5 action:1 potentials:2 infinite:1 normalization:2 recent:1 schr:2 well:1 directly:1 coordinate:3 arising:1 possesses:1 obtain:7 silverman:1 atomic:1 scattering:1 oriented:1 infinitely:1 eckart:2 potential:14 lett:3 momentum:1 generalized:1 term:6 oschel:1 fys:2 know:1 press:1 using:6 mod:3 like:1 28a:1 either:1 translated:1 therein:1 methods:6 classical:2 czech:1 creation:3 some:3 respect:2 cooper:1 refer:1 substituted:1 11s:2 properties:1 chapter:1 o:3 practical:1 range:1 perelomov:1 considerations:1 into:1 bound:3 square:1 references:2 determine:1 operator:6 van:3 there:1 start:1 appl:1 physicists:1 way:2 function:4 form:3 arima:1 raising:1 limit:3 spectroscopy:1 problem:1 called:1 mechanics:1 ac:1 ab:2 constant:2 introducing:1 int:5 abstract:1 wybourne:1 am:1 single:1 ar:1 inc:1 functions:4 nn:14 variety:1 when:1 application:1 other:2 department:1 mathematics:1 conclusion:1 47s:1 intend:1 commutator:1 important:2 bounded:1 variable:1 geometrical:1 pseudo:1 4s:1 n2:2
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quant-ph0703268.txt |@word secondly:1 concept:1 partial:1 consider:3 equalities:1 results:2 llu:1 gx:3 four:4 follow:1 poorly:1 ıs:1 maximally:1 depend:1 violate:12 concerned:1 tr:10 acting:5 nπ:12 those:1 under:1 stochastic:8 include:1 resources:2 applied:1 supported:1 straightforward:1 g0:1 rise:2 choice:3 unitaries:1 every:1 little:1 exact:1 convexity:1 school:2 obvious:1 tra:2 turns:1 solution:2 large:4 convenience:1 vector:2 c00:2 c01:2 anal:1 specified:1 smaller:1 illustrating:1 farkas:2 second:2 replicated:1 linear:1 even:5 aim:1 stands:1 brackets:1 giving:1 analogously:2 witnesses:2 experiment:4 above:4 shared:2 acknowledgments:1 contrast:1 satisfy:3 respectively:3 never:1 component:3 teleportation:1 jointly:2 desired:1 them:2 represented:1 strong:1 respect:1 box:1 generalizing:1 involved:1 leaves:1 larger:1 allows:1 contradiction:4 mx:2 suggests:1 amount:2 resulting:2 permutation:1 bob:2 involves:2 useful:3 family:1 explained:1 outcomes:5 first:3 unit:1 use:4 asymptotic:1 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quant-ph0703269.txt |@word represent:1 consider:4 caused:6 results:7 leads:3 grateful:1 contributions:3 calculate:9 charge:1 case:7 string:2 very:1 frequencies:1 hinrichsen:1 witten:1 experimentally:1 difference:10 hamiltonian:5 cnj:4 maggiore:1 mangano:1 noted:4 upper:2 smaller:1 specially:1 prediction:2 approximation:3 second:1 qualitatively:1 estimated:1 substitute:1 canonical:2 tkachuk:3 3s:1 section:4 above:3 new:1 increasing:1 method:1 contrast:1 respectively:4 here:4 following:3 represented:3 consideration:1 obtained:16 shift:12 ignoring:1 suggestion:1 chang:1 useful:2 highly:1 derivatives:5 use:4 proceed:1 would:1 h0:3 contains:2 finally:2 few:1 linear:4 taken:1 theoretical:8 today:1 more:5 introducing:1 operators:5 1s1:1 particular:1 known:1 states:2 account:2 deformed:10 ml:7 work:8 modified:2 theories:1 values:5 growing:1 compare:2 figure:1 give:2 calculation:1 organized:1 high:1 want:1 xmin:2 conversely:1 lamb:12 e2s:2 rather:1 hydrogen:18 discussion:2 utilize:1 write:3 ens:1 fourth:1 instead:1 ordinary:1 parameter:6 mar:1 algebra:5 may:1 corrections:22 data:5 constants:1 stress:2 natural:1 third:1 lines:1 so:16 verify:1 representation:3 order:7 developed:3 over:5 years:1 paper:3 including:1 mentioned:2 existence:4 satisfies:1 y2:2 its:1 thank:1 ln:5 interesting:1 systems:2 mail:1 hidden:1 might:1 deformation:8 eur:1 good:1 investigated:4 jentschura:2 effects:1 2s1:1 eigenvalue:1 term:1 2s:16 university:1 level:2 magnitude:1 2b:1 2m:4 2n:25 side:1 constraints:4 el:2 domain:2 series:1 energy:11 ea:1 frequency:1 quantum:5 our:10 transitions:4 special:5 shown:5 space:2 rep:2 since:1 rev:7 investigation:1 evaluation:2 math:3 shows:3 theory:9 abramowitz:1 given:1 possibility:5 approaches:2 perturbation:8 york:1 put:1 8s:1 estimate:1 e2:16 βp:3 transition:1 nonnegative:1 length:43 place:1 δij:1 consequence:1 neglect:1 first:4 xj:2 xi:14 manuscript:1 franko:2 precisely:1 angular:1 1s:17 1r:3 rewritten:1 similarly:2 introduction:1 leading:4 relations:10 assumption:1 calculations:3 gives:3 somewhat:3 authors:2 than:1 effective:1 karshenboim:1 supposed:1 str:1 were:4 ktf:1 rewrite:3 correction:1 spectrum:5 generalization:1 dash:2 already:1 say:2 min:1 latter:1 gravity:2 note:1 take:4 accuracy:1 heisenberg:4 investigations:3 most:1 mende:1 measured:2 eigenfunctions:1 considered:2 ckl:1 calculated:5 takeuchi:1 giving:1 inaccuracies:2 mechanical:3 physics:1 sum:1 dot:1 dover:1 precise:1 12d:1 show:1 shelyuto:1 relation:6 eides:1 parameters:7 written:1 should:1 only:5 stegun:1 get:1 between:3 lviv:3 ones:1 dr:1 c2n:1 e1s:2 arxiv:1 acknowledgments:1 uncalculated:1 investigate:1 contain:1 analytical:1 national:1 see:4 radius:1 result:1 y0:7 discussions:1 commutation:11 state:1 simplest:1 reading:1 approach:1 terms:4 tensorial:1 p2k:1 problem:7 received:5 last:3 brau:2 ua:2 uncertainty:1 equal:1 contribution:1 estimation:16 expression:11 experimental:8 cn:12 appeared:1 proton:1 dimensional:2 three:1 been:1 much:1 interest:1 expected:1 ph:1 pi:9 fig:1 ukraine:1 observable:1 precision:1 czarnecki:1 ψns:14 6s:1 determination:2 decreased:1 careful:1 present:1 p2:9 holzwarth:1 exception:1 p4:3 solid:1 estimations:5 value:1 will:2 suppose:2 behavior:5 many:1 procedure:1 pachucki:2 discrepancy:1 different:7 develop:1 author:1 minic:1 make:1 same:5 strange:1 quant:1 units:1 dimensionless:2 independent:1 used:4 disadvantages:1 numerical:1 hand:1 levels:23 arose:1 recent:3 well:1 bohr:1 de:1 mann:1 dashed:1 position:5 kempf:5 stringent:1 proposed:1 accurate:3 obtain:5 yet:1 previous:10 simple:5 lett:4 easy:3 excited:1 momentum:5 gave:2 represents:1 february:1 increases:1 using:12 ns:4 necessary:4 like:1 follows:1 interestingly:1 continue:1 arbitrary:10 ivan:1 works:4 introduce:1 reduced:1 mathematical:1 exceed:1 right:1 some:2 b2:10 nonzero:1 gross:1 avoid:1 comments:1 does:2 eliminate:1 prof:1 struve:3 bessel:5 minimal:43 cni:4 obey:4 agreement:1 takes:1 comparison:3 y2l:2 y2n:2 grotch:1 dependence:1 important:3 introduced:3 cutoff:1 undeformed:1 h2:3 into:4 numerically:1 bound:2 appropriate:1 references:1 ξa:1 there:1 nucl:1 noticed:1 handbook:1 way:2 forward:1 was:16 function:1 hy:1 form:4 but:5 pj:5 atom:18 line:3 up:1 us:2 spectroscopy:1 distribution:1 similar:1 khz:4 abstract:1 general:3 examine:1 constructed:1 functions:8 compared:1 eψ:1 dotted:3 na:2 when:7 department:1 theor:3 enlarge:1 calculating:2 hδij:1 preceding:4 problems:2 variation:2 a3:3 a2:2 allowing:1 generalized:3 implied:1 time:1 inaccuracy:1 n2:6 n3:3 having:5
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quant-ph0703277.txt |@word consider:3 global:1 results:4 four:1 tripartite:2 generalize:1 per:1 broader:1 consists:1 implement:1 contributions:4 row:1 dimensionality:1 depend:2 graph:1 concerned:1 equivalence:1 rightmost:1 monotonically:5 squeezing:9 present:1 under:5 resources:5 alternating:2 applied:1 preserved:1 far:3 implicitly:1 focus:1 every:1 formula:1 experimentally:3 difference:2 roscilde:1 groups:1 severely:1 immediately:1 presented:1 turns:1 quadrature:1 discrete:1 operationally:2 smaller:2 grateful:1 quantifiers:1 direct:2 cosh:1 second:1 perspective:2 further:2 implemented:1 canonical:2 established:2 what:2 rate:1 incompatible:1 sum:3 cai:1 shares:1 above:2 shared:7 order:2 consisting:1 themselves:1 body:1 pictorially:1 condensed:1 full:3 simultaneously:1 nonmaximal:1 respectively:1 applies:1 teleportation:7 here:1 understanding:1 decay:1 sinh:4 making:1 concluding:1 strong:13 obtained:4 sending:1 fisciano:1 generalizing:1 involved:1 larger:2 completely:3 exploitation:1 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quant-ph0703278.txt |@word neighbors:33 represent:4 looped:1 consider:5 illustrates:1 excepting:1 equalities:2 global:1 results:4 extends:1 illustrated:2 commute:3 computation:2 edu:1 winds:1 gn:1 expressions:3 research:2 gj:4 row:5 compact:1 whose:9 preserves:1 transferred:1 graph:137 tt:16 equivalence:50 lence:1 acting:1 removal:1 uniqueness:1 according:2 indicate:2 swap:3 th:1 under:14 connecting:1 nodes:104 undirected:1 caltech:1 indicating:1 case:10 updated:1 supported:1 worse:1 orthogonal:1 very:1 terminate:2 rise:1 keeping:1 choice:1 unitaries:2 every:2 figs:1 entries:4 1s:3 matrices:12 four:3 disturb:1 swapping:4 presented:1 t6:4 ref:1 t4:2 developing:2 t2:2 t3:3 t1:6 deals:1 assignments:1 convenience:1 vector:2 dealt:1 small:2 chuang:1 originally:9 zl:7 upper:1 neighborhood:2 zj:1 zk:1 variables:1 sss:4 sign:38 translating:2 fold:1 zero:1 follow:7 oneto:1 quite:1 canonical:10 subscripts:1 employ:1 what:1 plays:1 appear:2 iterating:1 incompatible:1 giving:2 equiva:1 section:6 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quant-ph9412006.txt |@word consider:2 remarkable:1 illustrates:1 four:12 commute:1 remarkably:1 whose:2 johansen:1 containing:1 norm:1 supported:1 orthogonal:14 far:1 matrices:1 did:1 michael:1 fewer:1 vector:15 eigenvalues:2 inspection:1 smaller:4 direct:2 sign:1 zero:1 specker:11 odd:1 even:4 appear:3 incompatible:1 sum:11 version:2 above:5 new:1 degree:1 respectively:2 component:1 answers:2 reported:1 σ3x:2 σ3z:3 represented:1 based:1 equations:5 appears:7 obtained:1 remark:1 institute:1 involved:1 vectors:36 contradiction:8 makes:1 involves:2 projection:12 demands:1 outcomes:1 unit:3 readily:2 use:1 would:5 distinct:4 properties:1 eleven:1 explicitly:1 therefore:3 selects:1 until:1 more:2 fractions:1 introducing:1 israel:2 becomes:1 operators:14 ascribe:1 tested:1 everywhere:1 known:6 none:1 equation:1 work:1 remain:1 values:10 concepts:1 dec:1 example:3 proof:10 abcd:1 claim:1 weaker:1 stated:1 predict:1 high:1 indicates:1 performed:1 bechmann:1 compatible:2 ones:4 goal:1 rather:1 discussion:1 means:2 how:1 pure:4 answer:1 product:2 may:1 philosophy:1 variant:1 mapping:1 produce:1 horizontal:1 natural:1 lines:1 correspond:1 provide:1 cannot:2 so:3 asserts:2 gerard:1 holds:2 numbers:2 indeed:2 over:2 produced:2 course:2 london:1 its:3 before:2 group:1 chosen:1 actually:2 systems:1 redhead:1 hidden:3 tentatively:1 them:4 incompleteness:1 adjacent:1 thereby:1 they:3 oxford:1 now:3 eigenvalue:2 finite:1 always:3 university:1 asher:1 each:25 2n:3 side:1 realism:1 mean:1 subset:1 spinor:1 formulate:1 σ2z:3 σ2x:2 combining:1 quantum:10 our:2 out:1 canada:1 3k7:1 matrix:3 space:5 furthermore:1 rev:3 research:1 particles:2 occurs:1 math:3 shows:3 theory:3 diagonal:1 generate:1 definition:1 pairs:1 could:1 times:4 plane:2 first:2 symmetry:1 variables:2 number:10 rank:4 restrict:1 done:3 reached:1 array:1 given:4 their:1 eqs:1 system:6 construct:1 needed:5 listed:4 1l:2 exactly:1 proving:1 lists:1 western:1 representing:1 than:3 determines:1 unfortunately:1 see:2 determined:1 minus:1 generality:1 argument:1 randomly:1 seen:4 any:4 angle:1 noncontextual:1 mermin:3 latter:1 able:1 note:1 instance:1 generalized:1 shall:1 who:2 reach:2 most:1 eight:1 nothing:2 probabilistic:1 inconsistency:1 technion:1 dordrecht:1 later:1 mechanical:1 physics:2 selection:1 random:1 find:2 fifth:1 ratio:1 state:13 should:1 only:7 bases:2 columns:3 do:1 notation:1 get:1 σ1z:3 σ1x:2 gen:2 contextual:1 arxiv:1 twice:3 kochen:12 set:3 contextuality:1 exists:1 achieved:1 unpublished:1 achieves:1 namely:3 computer:1 result:1 nonlocality:2 best:1 ways:1 definite:1 written:1 unable:1 simplest:1 incompatibility:1 recently:1 complementary:1 however:1 here:2 ir8:5 both:1 ir3:1 ir4:1 according:1 attributed:1 σz:2 σx:1 adapted:1 asked:1 experimental:4 bell:3 simple:1 others:2 corresponds:1 dimensional:3 moreover:2 basis:6 three:2 been:4 much:1 combined:3 collected:1 ph:1 empty:1 choose:1 digits:1 corresponding:2 sufficient:1 propositions:3 subspace:2 fund:2 demand:1 spin:2 those:2 case:1 value:14 swope:1 will:1 replaced:2 irrespective:1 unpaired:1 seven:1 larger:1 thus:3 non:1 encouragement:1 100th:1 experts:1 technology:1 binary:3 different:4 belong:1 same:7 complex:1 quant:1 arguments:1 avoids:1 several:1 independent:1 used:3 l175:1 hand:4 invariance:1 eigenvectors:1 mech:1 well:1 components:6 usual:1 being:1 obtain:1 questions:4 yes:7 kluwer:1 valid:1 lett:1 easy:1 theorem:8 remaining:4 real:4 tests:1 easily:2 rules:3 sums:1 possible:6 spanned:2 department:2 five:2 press:1 using:3 mod:2 appearing:1 particle:1 specific:3 either:3 because:5 methods:1 some:1 n6a:1 table:15 dimensions:3 lead:3 counterfactual:1 contributing:1 does:1 provides:1 preassigned:1 selecting:1 clarendon:1 hilbert:4 about:2 simplify:1 column:4 certainty:1 theorems:1 meaning:2 nonvanishing:1 mutually:5 discard:1 conway:1 into:5 clifton:1 down:1 pair:2 right:1 determine:2 operator:2 proportional:1 physical:2 ontario:1 span:1 assumed:1 there:8 question:2 strict:1 low:1 way:4 labelling:2 was:4 lowest:1 complete:3 construction:3 haifa:1 line:3 whether:1 up:5 us:2 planes:5 eigenvector:1 mechanics:4 associated:6 choosing:2 abstract:1 am:2 peres:4 ap:1 single:1 associating:1 commuting:4 defines:1 entirely:1 no:7 amounts:1 when:1 other:6 test:3 conclusion:1 symbol:1 prepared:2 generated:1 variable:1 requires:1 original:2 once:1
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quant-ph9412007.txt |@word represent:1 consider:2 lack:1 results:6 leads:2 consists:2 contributions:2 row:2 whose:1 violate:1 does:6 those:4 under:1 breach:1 divergent:2 very:3 matrices:14 encounter:2 entire:1 school:1 issue:1 large:2 small:1 eigenvalues:10 inspection:1 smaller:3 pmr:2 pms:2 consistent:1 qmr:2 direct:1 riesz:1 approximation:1 second:1 qmn:3 notwithstanding:1 pmn:7 odd:9 theory:1 even:7 appear:3 sum:14 above:3 obvious:1 here:3 represented:1 consideration:1 appears:2 extreme:1 box:2 institute:2 larger:1 commonly:1 example:5 resulting:1 domains:1 classification:1 explained:1 integrations:1 summation:1 total:1 use:1 would:1 positive:3 contains:1 negative:2 properties:1 definiteness:1 therefore:4 m2:10 taken:1 type:1 more:1 israel:5 becomes:1 operators:6 rigid:1 virtue:1 particular:3 mn:9 cancellations:1 values:2 ms:1 concepts:1 following:1 mx:1 give:1 caution:1 degenerate:1 arise:2 counting:1 occur:2 rather:1 s2:5 s4:1 write:2 how:2 occasionally:1 instead:1 sin:1 oscillatory:1 product:1 blocks:3 may:6 after:1 dx2:2 wrong:1 law:4 sz:1 attempt:1 dynamical:1 sp:1 element:1 so:5 sn:1 gerard:1 representation:1 order:9 δmn:3 indeed:1 over:2 its:5 sciences:1 chosen:1 interesting:1 squaring:1 quant:1 main:1 defining:1 non:1 combination:1 recipes:1 practice:1 introduce:1 reflected:1 they:1 yu:1 eigenvalue:5 term:2 2p:1 asher:1 qrs:2 radial:1 found:4 2n:3 side:5 associative:4 2k:8 domain:3 differential:1 another:1 series:1 related:1 quantum:4 eq:11 out:1 try:3 shown:1 matrix:18 space:2 since:1 research:3 smn:3 surprise:1 ref:1 occurs:1 foundation:1 linear:2 diagonal:1 quite:1 difficulty:4 completely:1 york:2 additional:1 definition:2 pairs:1 r2:1 deleting:1 could:1 computers:1 turn:1 gordon:1 removing:2 neglect:1 first:1 variables:1 number:2 directly:1 brychkov:1 indices:2 size:1 given:1 eqs:1 prudnikov:1 approximately:1 their:2 listed:1 calculations:3 gives:1 academy:1 lists:1 part:2 pnm:1 representing:2 than:4 double:1 depends:1 doubly:1 were:1 toward:2 powers:1 result:2 lowest:1 spectrum:1 randomly:1 prs:2 seen:1 null:2 any:2 lim:1 self:3 isolated:1 converges:2 note:1 instance:1 empirically:3 coincide:1 opposite:3 sequence:1 ofir:1 algebraic:2 why:2 technion:3 considered:2 average:1 sometimes:1 points:1 mechanical:1 usual:1 physics:1 fact:1 laws:1 ambiguities:1 supported:3 nagy:1 notations:1 d2:2 q2:9 q4:1 ungar:1 explain:1 should:5 only:7 factor:1 integrable:1 columns:3 do:1 cube:1 overall:1 dx:17 new:2 runs:2 qt:1 arxiv:1 summary:1 twice:1 common:2 fixed:2 set:1 sep:1 namely:2 truncating:1 qtn:2 close:4 rmn:2 fails:1 nondegenerate:2 currently:1 tend:1 symmetric:1 written:2 difficulties:2 various:1 between:1 drawn:1 boundary:2 conditions:1 terms:10 adjoint:2 however:8 both:1 contrasted:1 last:2 many:1 ill:2 alon:1 according:1 fulfilled:1 marichev:1 improves:1 contribution:3 whole:1 comes:1 otherwise:1 point:2 simple:1 dimensional:1 table:6 pp:1 basis:2 three:1 much:3 basic:1 expected:1 ph:1 define:3 fund:3 qst:2 convergent:2 present:2 case:6 exception:1 value:1 while:1 replaced:1 ought:1 investigating:1 endpoints:2 vol:1 thus:1 encouragement:2 vanish:4 technology:2 id:5 different:2 verified:1 perform:1 belong:1 same:9 parts:2 adjointness:1 largest:2 finite:6 higher:1 used:3 see:2 numerical:3 hand:8 delicate:1 infinite:7 kept:2 expression:2 humanities:1 well:3 analysis:2 obviously:1 chemistry:1 latter:1 left:1 moiseyev:1 obtain:3 positions:1 kluwer:1 infinitely:1 except:3 mathematically:1 source:1 valid:2 swope:1 momentum:3 identical:1 psn:4 sums:5 possible:1 unique:1 nimrod:1 apart:1 counterintuitive:1 particle:2 contradict:1 integrals:1 become:2 parity:4 because:8 methods:4 truncated:9 some:3 moreover:1 curious:4 happens:1 orthonormal:1 illustrated:1 avoid:1 separate:1 integration:1 conditionally:2 behave:2 tends:4 run:1 obey:1 each:3 oea:1 hilbert:1 rearranging:1 integers:3 column:2 discussed:1 o:1 nonvanishing:1 conceals:1 block:4 unbounded:2 into:1 functional:1 hermitian:7 square:2 operator:5 vanishingly:1 rows:3 log:1 few:1 assumed:1 there:1 question:2 inner:1 way:1 was:5 function:1 mundane:1 complete:3 form:1 but:5 convergence:3 haifa:2 highest:1 true:1 truncation:2 compute:1 whether:2 up:1 us:1 um:8 dordrecht:1 below:1 un:10 limit:1 mechanics:2 diverges:3 defined:11 likewise:3 abstract:1 general:2 peres:2 ap:1 examine:1 right:4 work:3 physical:1 functions:4 nm:1 no:1 when:7 vanishes:1 graduate:1 other:6 department:2 vanished:1 conclusion:1 elements:5 truncate:1 emerges:1 irmn:1 preceding:1 includes:1 meaning:1 lead:1 restores:1 interval:2 4k:1 n2:12
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quant-ph9412008.txt |@word monte:1 concept:1 consider:4 rev:2 magnetic:1 lack:2 results:3 leads:1 commute:2 generalize:1 rebbi:1 go:1 whose:1 depend:2 friedberg:1 tr:1 finally:1 th:1 fax:1 string:2 very:5 rise:3 p0:3 choice:1 witten:1 ultraviolet:1 affect:1 difference:2 exact:3 condition:5 presented:2 wegner:1 solution:14 discrete:12 convenience:1 vector:1 gauge:5 force:1 specially:2 dealing:2 consistent:1 coefficient:1 direct:1 approximation:1 second:3 concludes:1 dynamics:3 carlo:1 theory:5 ˆs:2 const:2 ˆu:2 giving:1 section:8 anywhere:1 above:4 ˆh:1 new:1 ever:1 method:1 ˆn:4 y2:2 iran:3 lee:1 here:1 address:1 path:3 xα:1 equations:1 change:1 deduced:1 box:2 publisher:1 larger:1 completely:1 action:29 fourier:1 studies:2 involves:2 useful:1 addresses:1 ipm:1 orderings:2 total:2 unit:1 readily:2 use:6 would:1 distinct:1 nucl:1 kinematics:2 therefore:4 renormalisation:1 criteria:3 themselves:1 until:1 more:3 operators:11 odinger:5 hold:1 iii:33 must:2 quartic:1 equation:30 det:3 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quant-ph9501008.txt |@word since:8 partial:3 consider:17 chain:1 lagrangian:1 lack:2 results:4 leads:4 scalar:1 γaαβ:3 entropy:40 comments:1 ga:1 sαl:6 consists:2 follow:2 expressions:2 research:1 reasoning:1 cb:1 excludes:2 λii:2 inverse:4 depend:6 calculate:1 simple:1 tr:33 contained:1 gab:3 finally:1 those:3 excluded:1 under:3 analogous:1 circumstances:2 symmetries:1 wiley:1 me:1 global:2 mγ:2 straightforward:1 very:1 implicitly:2 assuming:1 quadruples:1 springer:2 choice:5 electron:3 putting:2 get:2 decide:1 experimentally:1 matrices:7 electronics:1 differentiable:3 sαk:13 minkowskian:1 hamiltonian:16 turns:1 specifies:1 solution:1 correct:2 leave:2 admissible:2 vector:2 phase:1 math:2 iba:3 indices:7 eigenvalues:4 warszawa:1 ρk:17 concluded:2 upper:1 abbreviated:1 cybernetics:1 iα1:3 hψ:1 ρl:1 approximation:1 hyperboloid:2 second:3 perception:1 ρa1:3 perspective:1 equal:4 further:3 dynamics:9 ρn:4 santilli:2 theory:12 even:7 index:5 what:4 nonlinear:27 appear:1 brackets:3 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quant-ph9501009.txt |@word ito:1 forget:1 correlation:1 being:1 pointed:1 supported:1 osi:5 bring:1 wiener:2 via:1 solutions:1 statistical:1 unrestricted:1 hungary:1 belavkin:3 still:1 its:2 whose:2 rmki:1 pearle:1 solving:1 than:1 jan:1 simple:2 only:1 explicitly:2 board:1 under:1 mail:1 5a:2 prosperi:1 norm:1 5b:1 correspondence:1 do:1 non:1 his:2 di:5 very:1 disentangled:1 between:1 processes:1 wave:3 ones:1 should:1 dt:3 5ab:3 discuss:1 nor:1 formal:1 notations:1 budapest:1 like:2 particle:1 presented:1 turns:1 interestingly:1 hamiltonian:3 expectation:1 specific:1 vector:3 either:1 integrals:3 alternatively:1 output:3 works:1 reduces:1 mathematical:1 available:1 arxiv:1 filtering:1 version:1 devised:1 reduce:1 idea:1 cim:1 understood:1 depends:2 used:1 us:1 measurement:8 quantum:7 led:1 halliwell:1 eq:1 special:1 techniques:3 hartle:1 appear:2 restricted:3 review:2 measurements:6 rev:9 brief:1 expressed:1 research:1 particles:1 transforming:1 state:4 utα:2 percival:1 emerged:1 kfki:2 denoted:1 neither:1 caves:1 ref:4 method:3 body:1 noise:1 recently:2 theory:4 found:1 grassi:1 respectively:1 equivalent:1 separate:1 quite:1 following:1 white:1 selective:4 complicated:1 diosi:1 lajos:1 become:1 stochasticity:1 path:7 standard:3 equations:5 problem:2 milburn:1 originates:1 both:2 great:1 barchielli:2 institute:1 components:1 discussed:1 dependence:1 furthermore:1 noted:1 addition:1 important:1 context:1 gisin:2 first:1 conserving:1 deterministic:1 co:1 elaborating:1 probability:2 within:1 radical:1 into:2 explained:2 integral:4 functional:2 concluding:1 references:1 ψt:8 another:1 rpi:12 fruitful:1 improvement:1 pob:1 denotes:1 given:3 pq:2 leads:1 may:1 introduction:1 eqs:1 there:1 system:1 been:7 inevitable:1 underlying:1 start:1 linear:1 master:1 mathematically:1 statement:1 basic:1 resulted:1 free:1 ph:2 was:4 refs:2 cited:1 lett:6 function:1 rather:1 complete:1 observable:2 naive:2 continuous:9 about:1 hu:1 technique:1 basically:1 stochastic:3 provide:1 cases:1 former:1 present:2 me:1 evolves:1 ut:1 equation:5 work:1 submitted:1 propagator:2 record:1 obvious:1 time:1 promoted:1 investigating:1 distribution:2 more:1 auto:1 called:1 proof:1 mensky:5 derivative:1 coupled:1 process:1 certain:1 abstract:1 conjecture:1 case:1 itself:1 anticipating:1 formalism:3 any:2 recapitulating:1 functions:1 compared:1 monitoring:1 otka:1 grant:1 efficient:2 make:1 ghirardi:1 ideas:1 note:1 complex:2 quant:2 papers:1 unnormalized:1 out:3 elements:1 intend:1 unconventional:1 though:1 replacing:1 earlier:1 ξt:1 odinger:2 regular:2 value:1 letter:2 position:1 remarks:1 comparison:1 structure:1 independently:1 short:1 schr:3 outline:1 effective:2 nevertheless:1 no:1 explicit:1 lanz:1 feynman:1 nuovo:1 without:1 so:1 sect:4 exp:2 nuclear:1 fresh:1 model:3 heuristically:1 physics:1 bulletin:1 fact:2 labelled:1
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