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quant-ph9908045.txt |@word similarity:5 results:1 fluids:1 ge:1 expressions:1 whose:1 inverse:2 aug:1 subjected:1 technique:1 removal:2 th:4 analogous:1 mehta:1 applied:1 g2:1 straightforward:1 wave:2 exact:1 cmm:1 hamiltonian:6 positions:1 applicable:2 t0:31 large:2 convenience:1 differential:1 degeneracy:1 zn:1 integrability:1 zt:1 dynamics:1 canonical:2 established:1 gibbons:1 above:8 method:3 satisfy:1 lee:2 degree:2 here:5 making:2 equations:1 obtained:2 azuma:1 great:1 hbn:3 shift:2 studied:1 products:1 permutation:2 makes:1 altshuler:1 apply:1 use:3 would:1 sake:1 contains:2 intense:1 few:3 nucl:1 generators:3 type:3 initial:1 berlin:1 known:3 hole:1 springer:1 hamiltonians:1 equation:2 oscillator:3 theories:1 values:1 following:3 akin:2 arrive:1 decoupled:3 give:1 india:2 states:14 mohanty:1 csm:7 needs:1 g1:1 srinivasan:1 maps:1 instead:1 g12:1 parameter:1 mat:1 algebra:6 oscillators:5 earlier:2 mapping:1 demanding:1 fluid:1 applications:1 representations:1 realized:1 sectors:1 spectra:1 explicit:4 yielding:1 su:6 representation:2 order:1 xk:1 developed:1 including:1 existence:1 still:1 its:4 singular:3 chosen:2 solving:1 coordinates:1 systems:4 them:1 matches:1 uhl:1 school:1 bound:3 they:1 inception:1 hall:1 eigenvalue:2 term:2 university:1 identified:1 irreducible:2 found:1 2n:2 homogeneous:3 square:1 financial:1 series:1 energy:5 gaussian:3 measure:3 quantum:2 our:2 eq:3 out:1 shown:1 space:1 sutherland:5 furthermore:1 since:3 rev:7 particles:4 investigation:1 print:1 math:2 hcm:8 after:4 linear:1 panigrahi:6 interactions:2 diagonal:2 free:1 khare:1 e0:12 iso:1 hence:1 xj:10 hyderabad:2 xi:19 features:1 number:2 xz:2 done:1 construct:1 open:1 given:4 rewritten:2 similarly:1 system:2 relations:2 their:1 quadratic:3 realization:3 scheme:1 ranging:1 townsend:1 gives:1 relationship:1 ryzhik:1 asymmetric:1 minahan:1 x2:2 sˆ:3 je0:2 see:3 final:1 were:1 enables:1 pre:1 rao:1 spectrum:2 chen:1 manner:1 conjugate:2 seen:1 polychronakos:2 calogero:14 note:1 recognizing:1 k0:1 generalized:3 finding:1 coincide:1 murthy:1 olshanetsky:1 chart:1 algebraic:4 gradshteyn:1 phase:1 class:1 eigenfunctions:1 constructed:3 typeset:1 kr:2 exp:4 physics:3 show:1 purely:1 gauge:1 solutions:3 raju:1 find:1 ground:4 only:5 explicitly:4 black:2 factor:4 moser:6 establishes:1 straightforwardly:3 ones:1 areas:1 arxiv:1 through:2 fixed:1 qm:2 body:4 set:1 modulo:1 computed:1 achieved:1 connections:1 depends:1 result:3 operated:1 recently:2 subject:1 satisfying:1 interacting:4 symmetric:3 state:12 various:2 between:4 approach:1 αn:1 knowing:1 terms:1 ability:1 unnormalized:2 configuration:1 both:1 extendable:2 x2i:6 x2j:1 many:5 connection:2 context:1 casimir:3 point:1 inc:1 harmonic:6 dimensional:1 constant:1 cp:1 basis:1 due:1 laplacian:1 much:1 interest:1 deliberately:1 ph:2 abstract:1 define:1 corresponding:1 commutes:1 coherent:13 present:1 case:3 novel:5 pacs:1 value:1 will:2 lαn:1 bhaduri:1 procedure:2 2t0:1 unitary:2 simons:1 ii:1 cond:1 ernet:2 agarwal:3 capture:1 containing:1 verified:1 lett:9 same:2 shifts:1 quant:2 gets:1 higher:3 independent:1 extended:1 i2:2 effect:1 purpose:1 sivakumar:1 identity:1 center:1 well:1 academic:1 kawakami:1 without:2 coordinate:1 model:8 dimension:1 usual:1 unified:1 solvability:1 rest:1 homogeneity:1 thanks:1 using:2 momenta:1 scattering:14 eigenstates:5 adv:1 tables:1 other:2 transformed:1 treatment:1 easy:1 mod:1 transformation:5 euler:1 identical:1 aspects:1 easily:1 press:1 immediately:1 apart:1 like:1 particle:7 interestingly:1 performing:1 yields:1 integrals:1 arbitrary:3 pereira:1 therein:1 deal:1 phenomena:1 algebraically:1 choosing:1 sen:1 provided:1 dimensions:2 extensively:1 provides:1 bessel:1 inserting:1 rep:1 bn:4 revtex:1 although:1 hilbert:1 freedom:1 o:1 remains:1 nothing:1 perelomov:2 jα:1 pair:1 references:2 been:7 operator:4 statistics:2 hep:3 additional:1 comparing:1 removing:1 support:1 there:1 haschke:1 describes:3 naturally:1 function:1 form:1 removes:1 but:3 displacement:1 construction:1 removed:1 made:2 wise:1 uu:1 multiplicity:1 up:1 below:1 problem:2 pm:23 proved:1 universal:1 ez:1 tˆ:3 diverse:1 kl:1 physical:1 ni:2 functions:2 compared:1 no:2 when:1 cˆ:6 valid:1 becomes:1 conclusion:1 explaining:1 models:3 problems:2 polynomials:4 jastrow:4 independently:1 coupling:1 ghosh:1 factors:1 holes:1 mass:1 4g:1 chaturvedi:4 starting:2 having:2 once:1
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quant-ph9908046.txt |@word represent:1 concept:2 consider:3 pth:1 rev:1 leads:1 roy:1 scalar:1 generalize:1 whose:4 aug:1 helps:1 under:3 include:1 norm:2 orthogonal:3 misunderstanding:1 induce:1 unchen:1 difference:1 matrices:2 condition:6 hamiltonian:3 vector:1 abbreviated:1 dealing:1 zero:2 further:1 linear:2 even:1 what:1 diag:1 specification:1 above:2 new:2 satisfy:1 full:1 here:1 desired:1 groups:1 equations:1 obtained:1 antisymmetric:2 institute:1 vectors:15 usually:1 hospitality:1 studies:2 involves:1 via:1 inducing:1 brought:1 unitary:1 summation:1 planck:1 use:1 would:7 covariant:1 call:1 theoretical:1 preserved:1 introducing:1 thus:7 operators:9 valued:1 equation:1 work:1 following:2 arrive:1 example:2 numbers:1 states:5 sphere:1 cartan:9 sense:2 information:2 notation:1 rather:2 holds:1 write:1 how:4 pure:1 instead:1 ordinary:1 product:2 undergoing:1 may:4 max:1 physik:1 representations:1 choice:1 parallel:20 sz:1 sy:1 sx:1 dynamical:1 su:3 element:1 so:1 nonsensical:1 indeed:1 interpreted:1 including:1 looks:1 its:2 before:1 group:4 thank:1 chosen:2 d35:1 forms:1 choose:2 derivative:2 main:1 might:2 non:1 they:2 rotation:1 now:4 easily:1 university:1 orthonormal:2 each:1 found:1 mean:1 differential:3 formulate:1 ea:8 idea:1 eb:7 begun:1 quantum:6 our:5 eq:21 stodolsky:2 space:3 furthermore:1 induces:1 eja:2 get:1 sliding:1 theory:1 diagonal:16 quite:1 york:1 generate:1 definition:2 pairs:1 language:1 geometry:2 could:3 motion:1 flanders:1 hence:1 uses:1 undergo:1 neglect:1 south:2 first:1 initial:1 striking:1 reintroduced:1 reflected:1 preservation:2 ring:1 precisely:1 given:2 their:3 unitarity:2 indicate:1 statement:1 convention:1 gives:2 relationship:2 anandan:2 clarifying:1 kind:2 second:1 determined:1 argument:3 say:2 manner:1 need:1 any:2 lie:3 latter:1 note:1 potential:1 take:1 δnm:1 heisenberg:1 trace:2 germany:1 pair:1 dreibein:2 intrinsic:1 why:2 mechanical:4 physics:1 sum:1 dot:2 quantity:1 saying:1 show:1 rotating:1 relation:1 tempted:1 commutators:4 explain:2 state:2 should:1 only:2 explicitly:2 generators:6 factor:2 local:1 carolina:2 meant:1 do:1 viewpoint:1 means:2 dependent:2 cannot:1 evolution:1 arxiv:1 yield:2 london:1 fixed:2 discussing:2 view:1 requirement:2 set:7 ser:1 frame:4 namely:2 result:2 definite:1 written:1 between:3 geometric:1 terms:1 august:1 however:4 δab:1 last:1 ohringer:1 connection:1 berry:3 context:1 expression:1 among:4 point:2 dimensional:1 werner:1 simply:3 respect:1 submanifold:3 basis:10 been:2 ph:1 algebras:1 define:1 corresponding:2 quantities:3 subspace:3 present:1 case:3 will:3 euclidean:1 while:3 larger:1 iu:1 obeying:2 ambient:1 different:1 verified:1 same:2 complex:3 quant:1 arguments:1 subalgebra:2 higher:2 used:1 columbia:1 viewing:1 moving:6 necessity:1 normalization:2 task:1 academic:1 without:2 reexpressed:1 usual:4 just:1 being:1 λz:1 λy:1 λx:1 λb:7 λa:18 identify:1 λj:4 generator:1 conclude:1 seems:1 a392:1 treatment:1 transformation:3 real:7 iλ:1 represents:1 press:1 advanced:1 necessary:1 like:4 follows:4 yields:1 classical:7 spring:1 some:2 transport:18 lead:2 comments:1 does:1 proc:1 refer:2 elucidate:1 mpi:1 conventional:1 conveyed:1 imaginary:1 includes:1 rearranging:1 automatically:1 considerations:1 soc:1 rotations:1 phase:4 hermitian:1 frames:1 jerusalem:1 institut:2 there:5 transform:1 restricts:1 was:4 complete:4 form:3 but:4 removed:1 true:1 absent:1 applying:1 ur:1 un:1 those:5 problem:3 more:1 associated:2 certain:2 geometrical:2 general:3 formulation:2 mutual:1 no:3 wavefunction:1 when:3 application:1 other:1 department:1 conclusion:1 briefly:2 elements:3 kinds:1 symbol:3 transported:2 commutator:4 generated:1 astronomy:1 matrix:2 implies:1 implied:1 fact:1 time:3 reserve:1 original:1
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quant-ph9908047.txt |@word aided:3 partial:9 consider:1 chain:1 results:2 entropy:16 computation:1 research:1 minω:13 dimensionality:3 tr:1 γk:1 quasi:1 under:5 very:4 corollary:1 arrange:1 trk:1 transmission:1 knight:1 t2:2 large:1 small:1 enhance:2 noted:1 upper:7 smaller:2 direct:3 zero:3 even:4 what:2 witnessed:1 assisted:5 above:13 betas:1 increasing:2 method:1 explosion:1 teleportation:1 understanding:1 plenio:7 address:1 strong:1 logarithmic:1 obtained:1 convert:1 popescu:2 larger:1 suggests:3 amount:7 schumacher:1 hospitality:1 bob:3 involves:1 useful:2 family:3 limn:1 achievable:2 apply:3 should:2 indecomposable:1 additive:1 asymptotic:3 would:7 prove:3 remains:1 positive:3 negative:4 hilbert:1 classically:1 partite:13 therefore:2 jonathan:2 more:3 introducing:1 distillation:25 particular:2 known:5 ibm:1 work:3 values:1 minimisation:2 following:2 my:1 example:1 proof:6 locc:11 process:1 bennett:3 share:1 states:31 minimum:3 performed:1 information:2 provide:1 rippin:1 far:1 pure:5 answer:1 product:4 communicating:1 produce:4 fe:1 concentrating:1 types:1 third:1 counter:1 greek:1 so:6 allow:1 words:1 order:1 operations:4 help:2 over:6 years:1 symbols:1 course:3 paper:2 existence:2 fidelity:2 still:3 its:2 before:3 group:1 thank:2 maps:1 lo:1 offers:1 systems:12 mail:1 main:4 might:5 maximal:1 non:4 greater:1 disentangled:1 processes:1 they:3 half:1 oxford:1 nov:1 now:2 february:1 finite:2 equality:4 always:3 university:2 concave:1 inequality:3 each:1 found:1 2n:4 mean:1 subsystem:2 domain:1 related:1 measure:3 quantum:16 laboratory:1 happen:1 beyond:1 special:1 er:2 leave:1 space:2 furthermore:1 since:7 rev:8 denotes:1 increase:2 acting:2 print:3 gov:4 math:2 shows:2 linear:1 diagonal:2 free:5 reason:1 formation:4 term:1 eigenvalues:1 org:1 hand:2 definition:3 pairs:1 created:1 could:4 omit:1 keep:2 terhal:2 place:1 βn:1 support:1 first:4 separable:6 omitted:1 number:8 directly:1 open:1 given:1 necessarily:1 system:1 their:4 assumption:2 wootters:1 speaking:1 fraction:1 completed:1 exactly:1 manipulation:1 than:7 relative:15 kind:1 require:1 namely:1 distill:2 future:1 providing:2 result:10 questionable:1 need:1 any:9 min:7 lim:1 able:1 parks:1 note:2 useless:1 finding:1 channel:1 centre:1 who:2 singlet:1 considered:1 clear:1 sometimes:1 quantifying:1 assistance:1 fact:8 quantity:1 shor:1 particularly:1 show:5 dbe:1 keywords:1 find:1 based:1 just:2 explain:1 ox1:1 completes:2 lemma:4 only:5 bernstein:1 local:5 achieve:1 do:1 notation:2 means:3 unassisted:1 quantified:1 cannot:8 closely:1 during:1 evolution:1 transposition:8 arxiv:1 yield:2 acknowledgments:1 investigate:1 contain:1 thessaloniki:1 set:3 exists:1 achieved:1 achieves:1 see:2 usefulness:2 discussions:1 subject:1 inequalities:1 review:1 ωk:5 state:28 between:1 limit:1 subscript:1 recently:3 nature:1 qubits:3 confusion:1 transpose:1 however:6 inseparable:1 efficiency:2 comm:2 improve:1 improved:4 limits:1 many:1 taking:1 according:1 display:1 qubit:2 safely:1 otherwise:1 arbitrarily:1 supply:1 reasons:1 asymptotically:3 considering:1 question:1 singlets:4 second:4 basis:1 addition:3 create:1 locally:1 copies:4 been:1 interest:1 enlarging:1 choose:1 lives:2 last:1 maximally:7 present:3 case:5 multi:2 schmidt:1 pacs:1 will:10 contemp:1 suppose:4 applies:2 aid:1 property:1 procedure:1 von:1 thus:3 them:1 equal:2 ready:1 different:3 perform:1 make:1 same:4 tells:1 quant:4 distilled:5 several:1 higher:1 used:1 trivially:1 unlimited:4 possible:3 investigates:1 entanglement:47 tighter:1 recent:2 relies:1 task:2 off:1 well:5 without:2 dimension:3 know:3 protocol:1 proposed:2 actions:2 identify:1 previous:1 adding:2 catalytic:1 surprises:2 bell:1 simple:1 valid:1 lett:3 theorem:1 mor:1 posed:1 3pu:1 entangled:15 distillable:2 immediately:1 like:3 follows:7 reduces:1 alice:3 server:3 panos:1 either:1 arbitrary:1 become:1 reduced:1 because:2 neumann:1 classical:1 some:3 understood:2 happens:1 does:3 provides:1 processing:1 bi:11 clarendon:1 although:1 properties:2 bz:1 distilling:1 tracing:1 discussed:3 stand:1 mixed:2 consequently:1 road:1 own:1 presence:3 previously:1 communication:1 into:1 obtaining:1 bound:37 three:1 lies:1 distillability:1 references:1 parties:1 log:7 removing:1 strictly:3 there:4 vedral:8 start:1 way:2 was:6 function:2 smolin:2 but:8 lindblad:2 true:3 ph:4 partially:1 inverse:1 intuitive:1 horodecki:9 whether:2 wish:2 bounds:1 us:3 below:2 ωm:5 ωn:8 problem:3 similar:1 called:2 distance:1 strongly:2 defined:1 certain:2 abstract:1 proven:1 general:9 single:1 exist:3 aristotle:1 our:6 no:5 rains:4 when:4 other:6 elements:1 denote:2 divincenzo:3 symbol:1 visits:1 chance:1 important:2 bounded:4 tailored:1 implies:1 assume:2 invest:1 lanl:4 together:2 starting:1 once:1
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quant-ph9908048.txt |@word ψcs:1 consider:1 rev:13 results:1 four:1 expressions:1 whose:1 const:2 calculate:1 aug:1 alamos:2 tn:7 finally:3 certain:1 those:2 alberta:1 eprint:2 include:1 sent:1 hill:1 division:1 orthogonal:2 differently:2 wave:8 normalizability:2 maali:1 putting:2 figs:2 mixing:1 emphasized:1 preuss:1 vibrational:1 level:1 bn:18 positions:1 t4:6 t5:5 michael:1 solution:1 hillery:2 occurs:1 large:1 solved:1 eigenvalues:1 optics:2 pollaczek:1 upper:1 smaller:1 za:1 α2n:2 cosh:5 approximation:1 second:2 further:2 cat:3 odd:23 even:24 what:2 appear:3 t2n:1 sum:6 symbolically:1 debate:1 3j:1 above:3 scientists:1 new:3 3a:2 d1:2 method:7 satisfy:3 simultaneously:1 ibid:4 realizations:2 component:1 here:2 ansatz:1 sinh:5 others:1 z4:15 t2:7 equations:1 z1:18 z2:17 z3:20 obtained:1 ref:3 technical:1 shift:1 leaves:1 studied:2 drt:1 commonly:1 p2:1 orm:1 products:2 complicated:2 changes:1 y12:1 composed:3 matos:1 although:1 ix:1 hermite:3 private:1 malkin:1 apply:1 use:3 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quant-ph9908049.txt |@word secondly:1 consider:1 limited:1 caused:1 results:4 existing:3 four:1 received:1 quadrature:12 calculate:1 aug:1 knill:1 technique:4 sinatra:1 braginsky:2 send:1 squeezing:5 under:1 must:3 γg:1 sent:4 supported:1 amplitudes:1 g2:1 very:3 springer:1 mixing:2 difference:1 condition:3 splitter:6 modulator:1 presented:1 gǫ1:1 large:1 small:1 optics:1 noted:1 sin2:2 second:1 further:2 implemented:1 port:1 victor:3 even:1 nonlinear:2 sum:1 experiment:2 reconstruction:2 new:2 net:1 increasing:1 contrast:1 satisfy:2 outgoing:1 degree:3 respectively:4 teleportation:38 atoms:2 reported:1 cos2:2 strong:1 obtained:3 incoming:8 sender:2 institute:1 shift:2 losses:1 commonly:1 minsk:1 resulting:3 characterizing:1 usually:1 bob:15 transmittance:4 via:4 va:2 kilin:2 use:4 takes:1 poizat:1 comparing:2 depicted:1 usp:4 2y2:1 today:1 more:1 teleports:1 successful:1 becomes:1 berlin:1 furusawa:1 eβ:5 account:1 science:2 work:1 oscillator:1 measures:3 reviews:1 values:7 growing:1 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quant-ph9908050.txt |@word secondly:1 consider:2 rev:3 results:3 four:2 lewenstein:1 compact:9 particles:8 aug:1 paris:1 γp:1 send:1 thapliyal:3 γi:2 critical:6 manifolds:2 under:2 applied:1 orthogonal:3 very:1 every:7 entries:1 mixing:2 matrices:17 condition:1 dim:4 presented:2 fewer:7 large:1 vector:6 h11:3 small:1 h12:1 upper:1 hk2:1 hk1:3 direct:1 second:4 picked:1 linear:2 spectral:2 what:1 ak2:2 section:1 3p:1 expressed:1 values:2 ever:1 consisting:2 told:1 herm:21 respectively:2 hkp:3 never:3 component:1 equals:1 here:2 following:5 tangent:5 groups:1 others:1 narasimhan:1 along:1 appears:1 differential:4 great:1 naval:2 study:1 studied:1 funded:1 controversy:1 pick:1 barely:1 proof:2 schack:1 bounds:2 apply:2 establish:1 use:7 would:2 prove:2 h1p:1 positive:7 contains:7 finally:1 next:1 few:1 call:1 therefore:2 criteria:1 a58:1 more:9 linden:1 department:1 particular:7 projective:2 hold:1 must:3 md:1 none:1 balls:2 mm:2 recall:2 equation:1 caratheodory:2 nine:1 exceptions:2 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quant-ph9908051.txt |@word logarithms:1 sch:1 rx:3 magnetic:6 results:1 four:2 scalar:1 generalize:2 computation:12 involved:1 simon:1 depend:1 aug:1 alamos:1 description:1 technique:3 contained:1 supported:1 matrix:1 glaser:1 compensate:1 preserved:1 th:3 under:2 case:2 methyl:13 presently:1 very:2 frequencies:1 maas:1 readout:1 experimentally:2 matrices:2 leftmost:2 believed:1 school:1 level:1 evaluation:1 proposals:3 vagner:1 large:2 solved:1 minimizing:1 small:5 chuang:5 configurations:1 application:1 smaller:1 verifiable:1 ten:1 deutsch:1 rθ:2 cond:1 direct:1 pulse:15 sign:1 translating:2 second:3 design:1 uk:1 nmr:16 spect:1 acid:7 repeaters:1 blue:1 transfer:5 what:1 errors:7 sum:2 selected:2 contributed:1 expressed:1 decoding:9 current:1 experiment:10 above:3 resilient:1 new:3 contributes:1 consisting:1 schumacher:1 margolus:1 chose:1 degree:1 respectively:1 unobserved:1 component:4 teleportation:1 here:3 diagonal:1 reported:1 selective:5 groups:2 relaxation:2 represented:1 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quant-ph9908053.txt |@word spiess:2 partial:1 consider:4 remarkable:2 caused:2 magnetic:13 varying:1 dynamic:1 splitting:2 gx:3 leads:1 eds:1 ga:2 reson:1 sci:1 remarkably:1 amplification:1 depend:2 aug:1 producing:1 subjected:1 finally:1 does:3 present:1 γb:1 applied:1 supported:2 very:3 frequencies:1 2γg:1 results:2 sons:1 putting:1 experimentally:1 vibrational:3 level:7 large:3 solved:3 science:3 small:1 eigenvalues:1 solutions:3 specm:1 force:1 computation:1 second:3 value:5 chem:1 situated:1 stands:1 ˆz:3 selected:1 uniform:1 pawel:2 above:2 ˆi:1 ibid:3 fields:1 here:3 ryszard:1 following:5 address:4 directions:1 ratio:2 along:1 strong:4 obtained:5 michal:1 leung:1 suitably:1 institute:2 allows:1 reports:1 amount:1 stressed:1 resonance:2 via:3 projection:1 a121:1 hermite:1 first:3 stern:4 total:1 univ:3 select:1 derivatives:1 conventional:1 would:2 fea:1 ψn:2 centre:1 scope:1 theoretical:2 becomes:2 generically:1 particular:2 cases:1 mounted:1 iii:1 must:1 sample:4 recall:1 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quant-ph9908055.txt |@word consider:7 interference:14 magnetic:1 roc:1 results:5 gy:1 existing:1 leads:4 iim:1 generalize:1 garching:1 amplification:1 depend:1 aug:1 re:3 iii:3 presents:1 quasi:9 σcc:6 under:10 include:2 di3:1 applied:1 g4:2 g3:2 g2:14 orthogonal:2 very:9 rise:4 harmonics:1 splitting:1 sons:1 refractive:4 resonant:2 affect:1 difference:4 condition:7 rotating:2 incoherent:3 level:15 knight:5 solution:4 large:12 solved:1 small:10 eigenvalues:2 dip:1 noted:2 fleischhauer:1 11e:1 zh:1 consistent:1 literature:1 sign:1 approximation:3 rate:2 haan:1 enhancement:1 further:6 quite:1 canonical:2 even:5 index:5 what:2 trapping:13 imamo:3 giving:1 while:4 current:1 poles:1 above:6 new:10 contributes:1 90o:2 contrast:1 coefficient:1 aγ2:2 lee:2 ibid:1 respectively:2 modify:1 here:7 diagonal:6 reported:1 plenio:1 inversion:2 separation:4 relaxation:2 alone:1 along:1 strong:4 equations:16 appears:1 change:1 obtained:2 study:3 studied:4 reason:1 experience:1 periodic:1 resonance:1 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quant-ph9908056.txt |@word represent:1 partial:1 consider:4 desirable:1 results:3 four:2 quadrature:1 computation:2 compliance:1 λij:1 simon:1 calculate:1 tr:2 finally:1 squeezing:7 present:3 under:2 g2:9 g1:9 orthogonal:3 very:1 experimentally:1 matrices:4 condition:7 gg:1 transmission:3 turns:1 guo:1 solution:1 fourier:2 λi1:3 loock:1 work:2 naumann:1 mi:1 cosh:1 approximation:1 zero:4 linear:2 plays:1 expressed:7 experiment:1 above:1 increasing:1 acknowledgments:1 satisfy:4 degree:1 respectively:2 teleportation:2 believed:1 china:2 sinh:1 strong:3 equations:2 great:3 study:1 larger:1 funded:1 resulting:1 suitable:1 makes:1 ipj:1 austria:1 apply:2 total:10 unit:2 prove:3 remains:2 positive:4 m1:5 milburn:1 msi:1 m2:7 taken:1 type:6 today:1 more:4 composite:1 becomes:2 operators:17 emission:1 aware:1 normalized:1 particular:1 must:4 springer:1 ρg:6 science:4 mn:1 det:11 remain:1 ms:2 following:13 example:1 unconditional:1 proof:6 indicated:1 calculation:1 bennett:1 states:28 numbers:1 inseparability:17 verlag:1 information:2 means:2 write:1 how:2 criterion:16 furusawa:1 parameter:1 displacements:1 product:1 mar:1 singular:1 after:4 αd2:1 physik:1 natural:1 lemmas:1 so:8 correlation:9 representation:1 acknowledges:1 operations:3 separable:14 wigner:4 indeed:2 over:1 satisfied:4 course:2 thermal:4 paper:2 through:5 left:2 differs:1 austrian:1 satisfies:2 its:2 diagonalized:2 rapidly:1 ln:1 forms:3 lu:1 systems:3 main:2 good:1 propose:1 mention:1 they:2 bogoliubov:1 now:3 realize:1 easily:1 2r:4 always:2 university:1 inequality:10 mode:4 2b:1 universit:1 difficult:1 side:2 mean:1 another:1 ed:1 ρi1:3 gaussian:29 related:1 ρi2:3 frequency:1 exceeded:1 quantum:15 laboratory:1 operation:2 eq:17 χii:3 out:1 divincenzo:1 shown:2 matrix:13 iλj:1 furthermore:1 since:4 rev:5 denotes:1 denoted:3 shows:3 foundation:1 theory:1 gardiner:1 standard:16 completely:1 ρii:5 tudes:1 definition:1 βp:1 r1:25 r2:16 stiftung:1 hence:4 first:5 xj:12 initial:1 u1:2 number:2 theoretische:1 parkins:1 least:1 directly:2 given:4 necessarily:1 eqs:2 system:1 construct:1 obtainable:1 gives:2 continuous:18 17b:1 17a:1 optical:3 x2:6 branches:1 x1:7 than:1 annihilation:1 determined:1 generality:3 fluctuation:1 unchanged:1 ming:1 say:1 need:2 vaidman:1 any:16 convenient:2 mr2:3 note:4 combining:1 heisenberg:1 added:1 normal:1 preparations:1 pair:6 class:1 exponent:1 reduces:2 average:1 later:1 stronger:1 braunstein:6 part:2 exp:5 mi2:1 fact:1 show:1 violation:1 notations:1 relation:3 lloyd:1 substituting:2 d2:1 find:3 subtracting:1 based:4 parameters:3 commutators:3 state:37 should:1 lemma:4 only:6 local:6 continuity:1 get:3 v1t:1 beam:1 dv:1 during:1 processes:1 podolsky:3 arxiv:1 invariants:1 european:1 influenced:1 investigate:1 experiments:1 coefficient:1 set:2 exists:2 p21:1 result:1 subject:1 satisfying:2 inequalities:1 definite:1 tend:1 symmetric:2 enough:1 x21:1 email:1 x22:1 terms:1 nature:1 importance:3 transpose:1 inseparable:1 hefei:1 however:1 problem:3 last:2 many:1 uncertainty:3 equal:1 became:1 variance:11 expression:3 otherwise:1 splitters:1 ci:1 co:1 v2t:1 simple:2 2nd:1 dimensional:2 moreover:1 nr1:3 ensures:1 friedrich:1 three:1 been:2 2a20:1 cauchy:1 combined:1 pj:11 ph:6 pi:14 choose:1 corresponding:1 sufficient:11 photon:3 remark:1 c2:8 c1:7 maximally:3 protocols:2 p2:7 p1:5 pacs:1 value:2 transformation:4 will:3 suppose:1 squeezed:3 property:4 a20:3 opt:1 unitary:2 thus:3 ii:8 duan:2 ni2:1 technology:1 submission:1 same:4 quant:6 diagonalize:1 party:1 dimensionless:1 ampli:1 higher:1 independent:1 used:2 i2:1 hand:2 v0:3 v1:5 v2:6 entanglement:4 recent:4 lower:2 task:1 modes:3 nx2:1 epr:8 obviously:1 without:3 know:2 λr:5 proposed:2 rosen:3 obtain:1 transforms:2 λj:1 preprint:1 zoller:1 density:4 absorption:1 conclude:1 seems:1 cc:1 transformed:3 lett:5 easy:1 theorem:9 guarantees:1 eigenstate:1 real:6 innsbruck:2 entangled:10 vacuum:2 using:2 u0:3 loss:3 necessary:8 like:4 semi:1 follows:3 interestingly:2 steps:1 schwarz:1 arbitrary:5 essential:1 right:2 some:8 ourselves:1 nonzero:1 tmr:1 calculating:1 lead:1 when:2 does:2 decomposition:2 provides:4 yields:1 2a:1 noise:5 11a:1 11b:1 equivalent:1 step:1 2n:2 15a:1 uibk:1 practical:2 15b:1 ensure:1 mixed:1 communication:4 into:5 rotations:1 bound:8 included:1 einstein:3 operator:4 proportional:1 institut:1 additional:1 vac:1 support:1 there:5 question:1 transform:2 u2:3 much:1 low:1 way:1 was:2 damping:1 function:9 form:18 but:2 hj:3 2ηt:3 line:1 removed:1 true:1 applying:2 horodecki:6 characteristic:5 ur:1 ul:4 below:3 limit:2 distribution:1 semiclass:1 ac:1 separability:4 defined:1 certain:2 aj:1 influence:2 general:2 peres:3 kimble:3 proves:1 exist:1 our:2 check:1 physical:3 ni:1 nm:2 no:1 whereas:1 generally:1 role:1 concerning:2 picture:1 completes:2 a12:2 symbol:1 a1:3 a0:5 generated:1 a2:14 bounded:3 variable:17 network:1 assume:4 required:1 changed:1 together:1 time:3 n1:6 n2:7 original:1
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quant-ph9908057.txt |@word sci:1 consider:15 maximum:6 rev:3 results:4 existing:3 leads:3 maxima:3 consists:1 expressions:2 peshkin:1 depend:1 aug:1 presents:1 finally:1 tm:1 those:5 under:3 cm2:1 amplitudes:1 keeping:1 wave:9 electron:60 refractive:2 varshalovich:1 difference:1 condition:2 beating:22 unlike:1 presented:4 transmission:1 turns:1 solution:1 t0:3 t1:3 large:1 kondo:1 vector:3 small:1 optics:1 noted:1 hora:30 upper:2 smaller:1 zh:2 estimates:1 literature:3 approximation:1 bergmann:1 second:5 traveling:1 picked:1 pass:1 further:2 targets:1 linear:4 even:1 index:2 appear:1 thickness:5 current:5 experiment:7 above:1 new:5 body:2 edited:1 outgoing:2 eksp:2 kept:2 here:6 agreement:5 reported:7 focused:3 cos2:5 groups:1 represented:4 const:2 along:2 sine:4 appears:1 change:3 obtained:5 lipkin:1 thirty:2 institute:1 study:1 allows:5 reports:1 periodic:2 published:1 usually:1 figure:3 explained:3 plenum:1 modulated:1 gordon:1 contradictions:5 plots:2 total:6 use:1 asymptotic:1 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quant-ph9908058.txt |@word limited:1 φn1:4 four:2 consists:3 whose:9 const:3 calculate:7 aug:1 auf:1 presents:1 whatsoever:2 under:2 worth:1 divergent:8 distorts:1 unrenormalized:1 every:2 figs:1 logarithmically:4 vast:2 called:3 convenience:1 vector:1 enclosing:2 indices:1 force:45 deutsch:1 consistent:2 direct:2 second:15 qualitatively:2 even:6 established:2 complexities:1 specification:1 ˆa:1 above:9 new:4 net:1 ˆk:1 κm:2 discontinuity:1 simultaneously:1 equals:2 here:38 reported:1 asymmetry:3 represented:6 logarithmic:3 stresses:1 endpoints:3 study:8 changed:1 approaches:3 reports:1 circumferences:2 unsymmetric:3 suitable:1 spacetime:1 cancellation:1 appropriately:1 2δn:3 2δi:2 highly:1 brought:1 total:3 unit:4 plot:5 would:17 chooses:1 occupying:1 m4:1 call:3 therefore:10 m2:72 type:3 until:1 odinger:6 interaction:7 hold:2 nonuniformity:2 must:12 ma:2 pursue:1 ml:52 work:17 theories:1 determining:1 akin:1 example:5 renormalization:14 indicated:1 give:3 involve:1 indicates:1 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quant-ph9908061.txt |@word gu:2 amplifier:1 results:8 scalar:1 proposition:3 whose:1 inverse:1 aug:1 alberti:3 company:1 finally:1 squeezing:5 those:2 under:1 connecting:1 applied:3 advantage:1 orthogonal:12 transitively:1 account:2 entries:1 matrices:7 iut:1 condition:2 notations:1 applicable:1 vector:2 math:8 optics:3 upper:3 mi:1 direct:4 second:1 peredachi:1 canonical:5 bilinear:1 appear:1 giving:1 section:11 ch2:1 1t:1 above:4 new:1 d1:1 nakamura:1 satisfy:2 γz:4 respectively:2 exceptions:1 situation:3 entire:1 strong:1 equations:1 balian:3 obtained:34 remark:3 property:7 antisymmetric:1 institute:1 sjs:1 vectors:3 allows:1 action:5 scutaru:4 fourier:1 composed:1 schur:2 useful:1 projection:1 pxp:1 elude:1 analogously:1 apply:3 total:1 use:3 projector:4 prove:4 probabilities:7 positive:9 contains:1 quasi:19 linear:3 vi:8 means:2 e2:4 theoretical:1 preserved:2 operators:11 normalized:1 particular:3 known:1 iii:10 must:5 dominicis:3 mg:1 valued:2 equation:1 det:17 labeled:1 fock:7 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quant-ph9908062.txt |@word consider:4 pointing:1 results:1 roy:15 grateful:1 whose:4 depend:1 aug:1 deterministic:9 superficially:1 th:1 analogous:4 worth:1 p2:5 belonging:1 kumar:1 unfamiliar:1 wave:1 al3:1 solves:1 hamiltonian:2 vector:3 eigenvalues:5 setup:1 encloses:1 consistent:1 imply:1 further:2 specker:5 canonical:1 even:2 xop:8 section:1 new:4 method:1 body:1 simultaneously:7 ibid:2 kowalski:1 respectively:2 equals:2 here:5 canonically:1 consideration:1 along:1 observing:2 great:1 ǫx:2 institute:1 vectors:1 allows:2 contradiction:3 simultaneous:5 products:2 usually:1 marginal:2 replace:1 viz:2 apply:1 causal:5 use:2 refers:1 indicated:1 would:1 prove:3 remains:2 positive:11 contains:1 predictions:2 linear:3 therefore:3 more:3 separated:1 bhabha:1 operators:14 foundations:2 cases:2 must:6 me:1 obeying:1 equation:4 oscillator:1 reproduce:4 values:7 following:2 example:1 proof:8 cosmological:1 give:1 calculation:1 sense:1 india:1 involve:1 assumptions:2 allowed:2 january:1 holds:1 ghirardi:1 how:1 instead:1 ordinary:2 sin:7 may:2 earlier:2 derived:1 microstate:1 constants:1 realized:4 dynamical:1 joint:1 counter:1 ordinarily:1 hypotheses:1 σ1x:11 allow:1 pleasure:1 wigner:3 eigen:1 essence:2 over:2 held:1 london:1 before:1 acknowledge:1 microscopic:1 systems:1 mail:1 hidden:1 might:1 easier:1 non:4 combination:1 mention:1 they:4 identically:2 discuss:2 continuum:1 eigenvalue:1 2v:1 always:1 university:2 ensemble:1 realistic:4 each:4 found:2 side:2 reproducing:1 subset:2 arxiv:1 accelerator:1 σ2z:5 series:1 energy:1 σ2y:10 manifests:1 quantum:36 eq:4 special:1 out:1 shown:1 matrix:1 space:23 res:1 since:4 rev:3 research:1 particles:3 conjectured:1 correct:1 math:2 shows:1 theory:10 mω:10 possibility:1 pramana:2 inevitable:1 could:1 motion:1 hence:5 exhibited:1 first:1 already:1 features:2 probability:17 variables:4 number:1 done:1 impossible:2 given:7 adjoint:1 tata:1 system:3 their:2 assumption:2 brevity:1 too:1 realization:2 postulate:1 challenge:1 observations:1 interests:1 eqn:1 somewhat:1 x2:9 x1:5 than:3 wide:1 holland:1 exhibit:1 cohen:3 spectrum:1 conjugate:1 elsevier:1 seek:1 any:7 routledge:1 noncontextual:3 mermin:2 self:1 ideas:1 mix:1 potential:1 objective:1 coincide:1 gleason:2 broglie:3 fundamental:1 shall:4 collaboration:1 most:1 involving:1 pair:2 acknowledgements:1 measured:3 class:2 considered:1 calculated:1 proceedings:1 exp:3 parenthesis:1 left:1 physics:6 fact:2 show:1 violation:1 dbb:4 relation:2 interpretation:2 cowsik:1 trivial:2 find:3 nehru:1 inspiring:1 quoted:1 spite:1 mumbai:1 written:1 only:4 developed:1 integrate:1 constant:1 hamiltonians:1 probabilities:5 undivided:1 dependent:4 de:3 expectation:1 σ1z:5 σ1y:11 cannot:7 dx:6 international:1 combinations:1 dt:1 dp:4 contextual:2 densities:15 differential:1 grav:1 contain:1 fixed:2 kochen:5 set:7 observed:1 namely:1 individual:2 recently:1 commutation:1 definite:13 symmetric:1 state:6 correctly:1 between:1 approach:1 αn:1 notice:1 terms:2 reproduced:7 however:2 reproduces:3 configuration:6 both:2 cos:7 cot:1 reported:1 many:2 taking:1 equal:1 context:11 expression:1 experimental:4 mechanics:15 bell:4 simple:6 pop:8 dimensional:3 moreover:1 conference:2 transformations:1 trajectory:1 three:1 been:4 ai:4 much:2 marginals:13 ph:1 meeting:1 arises:1 general:1 θx:1 representative:1 maximally:3 spin:4 present:2 applied:1 noncommuting:3 p1:9 subsets:1 pacs:1 contexts:5 value:2 choices:1 replaced:1 situation:1 property:3 procedure:1 spacelike:1 thus:2 ii:2 itself:1 inviting:1 vanish:2 different:8 author:1 realizing:2 same:2 quant:2 pauli:2 defines:1 independent:4 used:1 assigns:1 assignment:1 trajectories:3 hand:2 mech:1 nevertheless:1 no:1 well:1 ccs:11 bohm:3 components:3 sets:1 position:15 dimension:5 usual:1 just:3 captures:1 half:2 obtain:3 assigned:2 glikman:1 contextuality:9 world:1 previous:1 density:12 point:2 except:1 lett:5 easy:2 theorem:14 excited:1 momentum:11 real:1 spinless:1 march:1 delhi:1 deepak:1 hiley:1 know:1 press:1 immediately:1 singh:12 mod:1 like:1 particle:4 follows:1 specific:1 martin:5 specifies:2 because:2 jawaharlal:1 classical:1 some:2 homi:1 dimensions:1 lead:1 theorem1:1 investigations:1 does:1 prog:1 refer:3 obey:2 equivalent:1 bangalore:1 exciting:1 extension:1 universe:1 b350:1 eqns:2 dependence:2 mutually:1 a2:4 ensure:1 road:1 organizers:1 equally:2 cambridge:1 integral:1 phase:16 right:1 references:1 einstein:1 operator:3 tifr:2 additional:2 assumed:1 there:2 question:1 ed:1 scientific:1 was:1 σ2x:10 function:3 complete:2 but:3 repeatedly:2 line:1 applying:1 embedded:1 maximum:1 liouville:1 distribution:2 similar:2 detailed:1 gone:1 ab:1 proved:1 defined:1 abstract:1 am:1 evidence:1 peres:2 single:3 exist:2 corresponding:1 commuting:8 check:1 constructed:5 reexpress:1 2dp:1 locality:2 reality:2 other:3 theor:1 denote:1 a10:1 inherently:1 a1:5 important:2 allowing:1 realised:1 variable:1 honour:1 rajaraman:1 function2:1 implies:1 factors:1 impossibility:1 time:1 observables:6 2mω:1
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quant-ph9908064.txt |@word represent:1 schensted:1 code:5 partial:1 consider:13 priori:1 skip:1 ald:4 desirable:2 results:5 θzz:1 four:9 ρjj:1 commute:3 computation:16 gn:27 involved:1 xxi:5 certainly:1 inverse:1 depend:1 superpositions:2 xxii:1 paris:1 irrelevant:1 tr:7 young:1 unanswered:1 environment:3 ρsb:3 finally:4 does:8 tj:4 those:1 under:13 include:1 friendly:1 indicating:1 ingredient:1 interacting:1 belonging:4 presently:1 ration:1 returning:1 far:1 could:1 bilinear:1 codeword:1 harmonics:1 renormalize:1 suggesting:1 corollary:1 ρb:4 every:1 chuang:3 summarized:2 inequivalent:1 experimentally:1 matrices:18 condition:28 splits:2 entire:4 encodes:1 presented:3 gkα:3 positions:1 anisotropy:2 trb:3 proposals:1 applicable:1 d2:5 t1:2 leave:1 admissible:1 vector:5 dealt:2 small:1 relation:1 optics:2 viola:2 population:1 work:3 zi:9 bacon:7 direct:2 pulse:1 split:1 second:3 qeccs:5 further:3 dynamics:4 choices:1 subduced:1 canonical:1 spectral:1 index:4 what:2 errors:29 appear:7 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quant-ph9908065.txt |@word partial:3 consider:2 remarkable:1 skip:1 global:1 results:5 entropy:7 comments:1 grateful:1 research:1 displaying:1 reasoning:1 synthetic:1 content:1 pointing:1 esf:1 mutatis:1 involve:1 tr:1 acting:1 uniqueness:8 does:1 protocols:3 under:7 mutandis:1 analogous:1 applied:1 straightforward:1 very:11 activation:1 putting:1 convexity:2 dim:3 presented:3 ref:9 list:3 large:4 small:1 vincenzo:1 upper:4 work:1 says:3 direct:2 second:4 pass:2 even:2 will:11 what:3 plays:1 d2:1 pawel:1 version:1 above:8 sup:1 new:1 contrast:1 pioneering:1 full:2 chose:1 respectively:1 teleportation:1 here:1 understanding:2 ryszard:1 desired:1 plenio:5 them:2 groups:2 others:1 ratio:1 strong:2 appears:1 change:1 extreme:1 michal:1 unproven:1 remarks:1 institute:1 involved:1 vectors:1 allows:1 approaches:1 commonly:1 suggests:1 bennett:5 schumacher:2 complicated:2 suitable:1 makes:1 involves:1 tasks:1 replace:1 first:6 put:1 limn:1 linearly:1 use:5 additive:4 asymptotic:7 would:7 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quant-ph9908074.txt |@word consider:2 remarkable:1 interference:1 leads:2 computation:18 consists:1 follow:2 issues:1 soc:3 whose:2 depend:1 concerned:3 deterministic:3 intensive:1 finally:1 program:48 present:1 under:2 analogous:1 orthogonal:1 continues:2 choice:1 every:1 switches:1 cavendish:1 make:2 solved:1 vector:1 commented:1 deutsch:18 second:4 further:3 dynamics:2 machines:1 even:2 what:2 section:2 transforms:1 expressed:1 experiment:1 above:4 suppose:2 order:1 ever:1 consisting:2 simultaneously:1 cam:1 q0:3 respectively:6 here:2 desired:14 others:1 alone:1 appears:4 change:1 remark:1 study:1 changed:1 unitarily:1 example:2 accomplished:1 action:1 hospitality:1 myers:15 makes:1 criticism:1 tasks:1 followed:1 problematic:1 explained:1 total:4 unit:1 use:3 would:5 remains:1 next:4 few:1 mation:1 m1:1 therefore:3 taken:2 type:1 until:1 more:9 linden:2 spoils:2 validity:4 concatenation:10 payne:1 flag:1 particular:2 known:1 cases:1 evolves:1 word:1 quantized:1 heard:1 avoiding:1 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quant-ph9908075.txt |@word homomorphism:2 rˆ:5 controversial:1 consists:1 whose:3 aug:1 under:29 conjecture:1 every:10 summarized:1 lefthand:3 disturb:1 solution:8 unrelated:3 red:5 commented:1 consistent:2 second:1 estimated:1 even:10 established:1 specification:1 establishes:1 new:15 increasing:3 ever:1 consisting:1 pioneering:1 simultaneously:1 abstractly:1 here:28 atoms:3 met:1 represented:5 quite:1 obtained:1 suitably:1 study:3 changed:2 approaches:3 stressed:1 california:2 changes:1 projection:9 replace:3 total:2 unit:2 derivatives:1 quasi:1 would:3 motivate:1 negative:1 axioms:9 call:1 therefore:2 type:5 until:1 composite:1 odinger:3 berlin:2 correspondingly:1 hold:9 must:12 springer:4 word:1 room:1 work:2 theories:2 concepts:6 example:12 renormalization:1 indicated:1 give:6 relativistic:6 want:1 organizer:1 times:1 dalibard:1 turn:1 verify:2 very:13 methodology:3 answer:1 symposium:2 ordinary:19 description:1 replacing:1 after:5 lay:1 summarize:2 law:1 attempt:2 upside:1 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quant-ph9908086.txt |@word logarithms:1 partial:2 maximum:1 rev:10 desirable:1 results:4 interpret:1 entropy:13 edu:1 go:1 primes:1 prop:1 reasoning:1 dimensionality:1 ohya:1 tr:4 finally:1 monotonically:1 those:3 under:7 resources:2 ingredient:3 case:2 provides:1 very:2 emphasized:2 difference:2 matrices:13 presented:1 tra:1 trb:2 large:6 convenience:1 small:1 generalize:1 trr:2 noted:1 work:3 grover:1 maximization:1 elegant:1 second:1 further:1 ruskai:3 plays:1 abm:7 expressed:1 d3:1 abr:1 paragraph:1 above:1 shared:2 increasing:6 acknowledgments:1 satisfy:2 ρab:14 respectively:1 teleportation:1 here:1 understanding:2 behaviour:4 desired:3 plenio:1 ρar:2 σab:14 strong:3 equations:1 change:1 ensembles:1 obtained:5 great:1 institute:3 popescu:5 studied:2 allows:3 reports:1 suggests:1 amount:1 schumacher:2 formation:25 bob:3 involves:1 uniquely:1 useful:6 family:1 problematic:1 replace:1 logarithmic:2 apply:2 operational:2 tools:1 research:1 use:3 additive:6 proceed:1 would:2 prove:2 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quant-ph9908087.txt |@word consider:2 illustrates:1 results:3 eds:1 ge:1 dimensionality:1 infinitesimally:1 include:1 worth:1 norm:1 jensen:1 very:1 springer:1 choice:1 condition:2 scalar:1 large:1 vector:7 relation:1 louie:1 smaller:1 consistent:1 sign:1 zero:2 tangential:3 dynamics:1 even:3 what:1 above:1 new:2 method:1 satisfy:1 full:1 component:1 here:3 ansatz:1 path:1 equations:1 z3:1 obtained:1 vectors:1 pathological:1 via:1 useful:1 brought:1 unit:2 would:3 prove:1 covariant:1 give:1 next:1 m2:1 flat:1 becomes:1 curvature:6 everywhere:2 surface:20 none:1 equation:5 following:1 mott:1 ρz:1 example:2 tsuru:1 gudmundsson:1 stated:1 monge:1 indicates:1 numbers:1 unphysical:1 occur:1 verlag:1 discussion:1 write:1 how:1 nontrivial:2 product:1 may:3 derived:2 mapping:1 applications:1 produce:1 realized:1 natural:1 explicit:1 complexity:1 so:3 enter:1 order:1 tallahassee:1 over:1 through:1 japan:2 regions:2 derive:1 acknowledge:1 ln:1 interesting:1 lateral:1 solving:1 coordinates:1 writing:1 forms:8 absence:1 degrees:1 systems:2 persist:1 derivative:2 main:1 eventually:1 than:2 primary:1 modification:1 effects:1 insisting:1 sρ:8 term:6 university:1 higher:1 constraints:2 arxiv:1 gaussian:1 solution:1 elementary:1 extended:1 static:2 obtains:1 quantum:5 our:1 eq:12 shown:1 space:3 since:1 rev:3 particles:1 theory:1 given:3 standard:2 quasifree:1 approaches:1 york:2 e1:3 e3:6 e2:5 geometry:4 florida:2 flanders:1 consequence:1 first:1 separable:1 number:1 zρ:2 restrict:1 relations:1 cosφ:4 little:1 system:3 approximately:2 their:1 burgess:1 gives:2 part:3 manifestation:1 imposing:1 peculiar:2 anticipate:1 device:1 limiting:1 were:1 sinφ:4 negatively:1 curved:3 constrained:6 ray:2 depending:1 studying:1 note:1 sciences:1 potential:9 subscripts:1 normal:6 object:1 mario:1 but:2 letter:2 pair:1 inserted:1 χt:24 curvatures:1 physica:1 points:2 electrons:2 exp:1 mechanical:1 nanostructure:1 χn:16 charged:3 physics:2 dover:1 show:1 gauge:2 solutions:1 find:1 q1:5 q2:5 should:1 only:3 iea:1 local:3 oct:1 notation:1 familiar:1 da:2 q32:1 nearly:1 dx:2 maksym:1 dr:1 ds:1 dq:2 fields:2 differential:2 acknowledgments:1 imposed:1 gerhardts:1 set:3 physically:1 result:2 discussions:1 close:1 subject:1 surfaces:1 axially:1 review:1 symmetric:2 written:2 closed:1 between:1 publishers:1 terms:7 nature:1 however:1 configuration:1 originates:1 both:1 σi:1 realizable:1 region:1 equal:1 expression:1 whatever:1 dimensional:9 pp:1 decoupling:1 basis:1 three:3 been:2 reduction:1 much:1 interest:2 expected:1 ph:1 direction:1 arises:1 denote:1 present:2 applied:1 novel:1 pacs:1 neal:2 choices:1 will:1 near:2 suppose:1 behavior:1 situation:3 procedure:1 layer:1 vol:1 vn:4 couples:1 confining:1 exterior:1 ie:1 different:1 author:1 wherein:1 quant:1 units:1 finite:1 difficult:1 used:1 costa:2 lower:1 off:1 nevertheless:1 well:1 thought:1 academic:1 cleary:1 materials:1 coordinate:3 model:1 usual:1 being:1 obtain:2 differentiation:1 kluwer:1 priori:1 real:1 read:1 possible:1 confines:1 confined:1 using:1 like:1 appearing:1 particle:12 differentiations:1 follows:1 ashoori:1 serves:1 either:2 admittedly:1 become:1 grouping:1 because:1 often:1 some:1 dimensions:1 heterojunction:1 avoid:1 hodge:1 does:1 provides:1 minimal:1 2q3:1 arbitrary:1 qe3:2 substitution:1 gained:1 constraint:1 freedom:1 discussed:2 o:2 a2:3 plus:1 mean:3 matsutani:2 considerations:1 soc:2 presence:4 into:2 integral:1 cylindrically:1 appropriate:1 references:1 operator:2 proportional:1 methods:1 schrodinger:4 there:4 function:2 elsewhere:2 form:4 ht:1 applying:1 books:1 limit:2 interplay:1 constant:1 abstract:1 general:2 physical:2 effected:1 functions:2 wavefunction:1 when:4 detail:1 field:1 interested:1 brings:1 department:1 star:1 models:1 variation:1 a1:3 a3:9 important:2 massachusetts:1 coupling:2 dψ:1 rule:1 dρ:1 pfannkuche:1
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quant-ph9908088.txt |@word sector:1 show:3 caused:1 λx:5 fapesp:1 ge:1 paper:1 including:1 alternative:1 agrees:1 ground:1 whose:1 based:1 exclusion:1 aug:1 solving:1 seems:1 written:1 cavalcanti:1 should:1 explicitly:1 mail:1 defining:1 into:1 do:1 his:1 de:2 subject:1 every:1 they:2 using:2 postal:1 exact:2 calculate:1 processes:1 dirac:1 particle:1 excluding:1 presented:2 turns:1 disregarding:3 solution:2 correct:1 bag:2 theory:5 either:1 2n:1 view:1 arxiv:1 financial:1 consistent:1 conventions:1 second:1 result:2 fail:1 transitions:2 eq:1 out:2 brazil:1 fails:1 since:1 rev:3 while:1 its:1 state:1 does:1 between:1 boundary:2 conditions:2 method:2 tomio:3 gives:2 recently:1 ba:1 prescriptions:1 ısica:1 however:1 wi:2 bt:1 step:1 iw:1 depend:1 violate:1 suggested:2 both:1 instituto:1 ǫx:1 prescription:8 dividing:1 shift:2 turn:1 comment:2 br:1 h0:2 wii:2 dimensional:1 cx:1 cancel:1 precisely:2 perturbation:5 support:1 relations:1 their:2 intermediate:3 usp:1 ph:1 was:1 energy:3 pm:1 obtained:1 formally:1 definition:1 validity:1 discrepancy:1 ref:1 iv:1 case:3 ii:1 pacs:1 equation:1 depends:1 value:1 remain:1 accordance:1 contrary:1 abandon:1 more:1 example:3 performed:1 claim:2 rewrite:1 calculation:2 ao:2 general:1 states:4 numbers:1 need:1 ic:2 hamiltonian:1 occupied:1 universidade:1 faithful:1 zero:1 author:1 virtual:2 paulo:2 instance:1 potential:1 quant:1 pauli:4 massless:3 fma:1 used:1 see:1 opposite:1 nogami:3 λa:2 levels:1 purpose:1 recent:1 acknowledges:1 observation:1 calculated:1 sp:1 coutinho:5 feynman:9 solve:1 principle:6 model:2 4a:1 order:3 2ǫa:2
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