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quant-ph9902065.txt |@word consider:2 chain:1 splitting:1 ga:1 consists:1 denotes:1 gr:2 whose:1 calculate:2 superspace:1 ts:1 finally:1 petersburg:2 participants:1 rise:1 geometrical:2 every:2 condition:8 entire:1 presented:1 discrete:12 vector:2 uef:1 direct:1 imply:1 theory:3 universities:1 established:1 richard:1 sum:3 brief:1 expressed:1 birkhoff:2 version:2 subspaces:2 international:2 consisting:1 satisfy:1 troduced:1 degree:1 component:1 atoms:5 simplices:3 explore:1 represented:1 obtained:1 orthomodular:1 institute:1 vectors:3 action:1 makes:2 useful:1 dimakis:4 patience:1 boolean:1 unit:1 use:1 feb:1 prove:1 positive:1 contains:1 bundles:1 doubt:1 call:1 therefore:5 survive:1 theoretical:3 more:1 becomes:3 operators:2 envelope:1 particular:3 cardinality:1 join:1 recall:2 work:2 following:3 making:6 endow:1 deg:12 claim:1 dual:2 give:1 organized:1 cartan:2 spb:1 rather:1 verify:5 acts:1 liaison:2 sic:1 numerous:1 obius:1 product:5 algebra:25 may:2 mapping:2 collection:1 multiplication:1 fo:1 natural:1 outline:2 third:2 whenever:2 element:5 so:3 fundamental:1 representation:1 acknowledges:1 order:1 sd:3 help:1 over:5 symbols:2 paper:3 still:1 its:5 forms:4 a98:1 violette:2 into:2 maximal:3 non:5 good:1 outlined:1 introduce:3 they:1 now:1 possess:1 several:1 dirac:3 always:3 side:1 associative:2 referred:1 subset:2 differential:40 financial:1 quantum:5 laboratory:1 operation:1 space:8 since:5 induces:1 research:5 combinatorial:2 contained:1 eprint:3 formula:1 foundation:2 reformulation:1 linear:5 associate:2 hull:1 zapatrin:4 admits:3 put:1 card:2 definition:1 pairs:1 geometry:11 correctness:1 nonnegative:1 turn:1 length:1 generalizations:1 first:3 features:1 powerful:1 will:2 directly:2 introduction:2 adjoint:2 tata:1 their:4 ordered:5 posets:4 jordan:3 authors:1 than:2 accordance:1 acknowledgement:1 second:3 were:2 treated:2 russia:3 result:1 disjoint:1 st:2 border:6 any:13 seminar:1 built:2 thoroughly:1 instance:2 take:3 calculus:7 incidence:9 most:1 said:2 pair:1 why:2 considered:2 sometimes:1 vertices:3 countable:1 finitary:1 physics:5 section:7 fact:1 show:6 supported:1 purely:2 spaces:1 d2:4 decade:1 d1:3 fibre:1 based:1 aω:4 enough:1 only:1 notation:2 means:1 dg:1 express:1 combinations:1 dr:5 ds:3 dp:10 dq:1 fields:1 arxiv:1 qc:2 qd:3 riemannian:2 moduli:1 set:16 differentials:6 module:4 namely:1 differentiable:6 eliminating:1 terms:1 analog:1 acquires:1 polyhedral:1 satisfying:1 written:1 between:3 conditions:3 triples:1 extend:2 confusion:1 attention:1 however:1 ket:1 both:3 last:1 many:1 according:1 roman:2 context:1 logic:6 otherwise:5 conclude:1 dimensional:2 respect:1 hoissen:4 gratitude:1 commutative:11 basis:1 union:1 due:3 rhode:1 calculi:3 pd:3 basic:2 ph:1 algebras:10 empty:1 define:2 surjective:1 cotangent:1 offered:1 wahrscheinlichkeitstheorie:1 noncommutative:2 general:5 manifolds:6 case:1 subsets:2 empirical:1 value:1 ǫs:4 while:1 koszul:6 property:1 studied:1 almost:1 endowed:3 thus:1 them:1 equal:1 exterior:2 grant:3 lengths:1 belong:1 same:1 complex:8 quant:1 split:1 proved:2 finite:5 subalgebra:1 see:5 hand:2 build:2 older:4 object:1 obviously:1 sets:3 position:1 possesses:1 tha:1 manifold:7 graded:10 mistakes:1 atomic:6 uller:4 yet:1 captured:1 lattice:1 δpq:1 relevance:1 guarantees:1 gave:1 possible:1 spanned:1 integer:2 unique:2 poset:13 formal:2 like:2 follows:7 arbitrary:5 rota:3 mathematical:2 right:1 classical:3 some:1 rffi:1 specified:1 proper:5 nonempty:2 providence:1 decomposition:1 bra:2 prof:1 chains:1 who:1 journal:4 bi:10 bj:1 stem:1 simplex:4 although:1 properties:3 injective:1 complexes:1 island:1 carries:1 extensions:1 block:6 bimodule:2 inclusion:1 dubois:2 square:1 references:1 operator:13 greechie:10 bombay:1 unambiguous:1 logics:7 span:8 support:1 there:2 class:3 way:1 resulted:1 was:5 naturally:1 interest:1 form:2 but:3 atom:1 partially:3 versions:1 smooth:4 us:5 ur:1 below:1 ωm:8 ωn:6 ωa:3 ωb:1 called:10 simplicial:7 associated:3 defined:4 pseudo:1 abstract:1 linearity:1 denote:3 our:3 formalism:3 ina:1 friedmann:2 functions:4 no:1 when:2 scalars:5 other:1 elements:9 models:2 symbol:1 bundle:1 important:1 structure:7 algebraic:3 dω:5 modules:1 notion:2 dds:1 starting:1
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quant-ph9902066.txt |@word marinescu:1 represent:1 consider:1 interatomic:4 tomasi:1 focus:1 integration:1 leads:1 quasibound:5 gb:5 ga:5 gn:1 gm:1 contributions:1 gj:1 optical:1 compact:1 whose:3 collisions:1 γr:4 quasi:6 under:1 γc:9 cm2:1 hill:1 p2:1 supported:2 6p1:1 6p3:2 far:1 frequencies:2 rise:3 wave:3 indication:1 electron:1 ical:1 resonant:1 matrices:1 gg:2 induced:2 vibrational:8 hamiltonian:5 mb:1 solution:3 large:2 solved:1 convenience:1 vector:2 ml:2 dimer:1 schroeder:2 antinodes:1 galanti:1 estimates:1 prediction:1 likely:1 populating:1 further:1 dynamics:4 chem:1 blue:4 kinetic:2 morse:1 diag:2 section:3 dr2:2 near:4 expressed:3 consistently:1 experiment:1 poles:3 above:1 increasing:1 coefficient:1 supporting:1 wavefunctions:1 σ3i:1 exchange:2 respectively:2 even:1 spacing:1 aσ:2 κb:5 hundreds:1 ranges:1 desired:1 diatom:3 andrews:1 separation:6 along:4 strong:7 equations:2 transformation:1 courteille:1 antisymmetric:1 institute:1 losses:2 amount:1 periodic:1 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quant-ph9902067.txt |@word concept:1 consider:1 global:2 results:3 scalar:3 comments:15 talks:1 expressions:4 improperly:1 whose:4 depend:1 calculate:1 equivalence:1 acting:3 tm:1 th:1 under:3 γa:1 include:1 abelian:4 geometrical:2 print:10 every:2 redefinition:1 difference:3 matrices:1 inrne:2 presented:4 notes:2 applicable:1 leave:1 vector:2 indices:1 application:1 version:1 consistent:2 second:3 rigorous:5 further:2 dynamics:1 linear:4 index:2 what:5 plays:1 section:3 near:1 expressed:1 sequential:1 above:5 new:3 construction:1 order:1 ever:1 acknowledgments:1 paragraph:1 respectively:2 realizations:1 component:2 here:6 met:1 objects:3 free:1 address:1 active:3 path:2 november:1 quite:2 equations:16 appears:2 change:3 deduced:1 obtained:1 remark:1 rigorously:1 institute:1 involved:1 vectors:6 allows:1 homeomorphism:1 products:3 opinion:1 suitable:2 makes:1 massage:1 uniquely:1 formulated:1 regardless:3 family:2 explained:1 odinger:3 apply:1 linearly:1 derivatives:1 conventional:4 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quant-ph9902068.txt |@word replacing:1 limited:1 concept:1 consider:2 represent:1 global:10 results:5 four:3 rˆ:8 follow:1 expressions:2 localized:1 gr:1 devoted:1 whose:8 inverse:1 depend:1 calculate:1 reformulate:1 graph:1 mutatis:2 equivalence:3 corrections:1 tm:1 preserved:1 th:2 under:5 reuter:2 tg:6 analogous:2 include:1 presentation:1 worth:2 applied:1 abelian:3 returning:1 very:1 implicitly:1 conditions:1 choice:5 print:11 isomorphism:1 every:4 summarized:1 difference:3 exact:1 look:1 leads:1 azc:1 intersections:6 riemann:2 presented:4 did:1 positions:2 solution:1 t0:17 mutandis:2 vector:10 prevent:1 version:1 dealing:1 consistent:1 split:1 second:3 equal:1 rigorous:1 further:5 dynamics:1 situated:2 linear:9 even:1 established:1 what:2 plays:2 section:6 near:1 expressed:1 current:1 sequential:1 bernhard:1 above:2 dtγ:4 new:12 journal:2 full:1 transportation:2 gravitation:1 respectively:3 realizations:2 nena:1 here:8 understanding:1 behaviour:1 evident:1 objects:6 tangent:1 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quant-ph9902072.txt |@word 2m2:1 concept:1 partial:1 dx:3 just:1 show:1 developed:1 distinctly:1 results:1 paper:1 using:1 trivial:1 its:1 ground:2 whose:1 4m2:1 quasi:1 energies:2 produces:1 preprint:1 5m:1 only:1 th:2 indeed:3 jacobi:2 main:1 solvable:6 transformation:1 real:1 case:3 them:1 aspects:1 3m:4 bands:2 bound:2 band:6 they:1 half:1 oxford:1 dw:1 now:1 down:1 february:1 continuum:2 immediately:1 systematically:1 parameter:1 university:1 arxiv:1 discrete:1 yields:2 2b:3 further:1 2m:7 2k:1 differential:1 financial:1 computed:1 lam:1 sukhatme:3 energy:2 feinberg:2 direct:1 related:1 zero:1 result:1 scarcity:1 quantum:3 our:3 eq:4 out:2 even:1 said:1 proceeding:1 eigenfunctions:3 chicago:2 dn:7 since:1 rev:2 eigenstates:1 state:2 does:1 various:1 hill:1 provides:1 new:6 avinash:1 ref:3 acknowledged:1 d57:1 correctness:1 corresponding:4 superpotential:2 here:2 gratefully:1 khare:3 york:1 although:2 substitution:1 checked:1 exciting:1 suppressed:1 bhubaneswar:1 obtained:1 both:1 dunne:2 cn2:2 extension:1 institute:1 taking:1 discussed:1 agree:1 turn:1 amount:1 periodic:10 hence:1 shifting:1 expression:1 bloch:1 comment:3 winkler:1 via:1 followed:1 cn:6 manuscript:1 point:1 pergamon:1 into:1 period:2 analytically:1 three:1 dimensional:1 en:1 references:1 isospectral:7 table:3 given:5 marg:1 feb:1 additional:1 equations:1 support:1 there:1 limit:1 sech2:2 msn:1 noting:1 ψn:7 way:2 m2:2 ph:1 extreme:1 gives:1 function:4 generating:1 supersymmetric:6 elliptic:6 clearly:1 exactly:3 odinger:2 susyqm:5 basically:1 somewhat:1 particular:1 known:3 translation:2 applied:2 equation:4 see:1 mj:2 preparation:1 un:1 values:2 dn2:2 more:1 example:3 mechanics:3 claim:1 seven:1 constant:2 give:1 defined:1 ip:1 abstract:1 india:1 argument:1 general:1 sn2:9 sense:1 claimed:1 partner:4 formalism:2 any:1 functions:2 magnus:1 self:7 length:1 same:2 illinois:2 write:1 application:1 potential:10 quant:1 department:2 modulus:1 uic:1 higher:2 upto:1 simplicity:1 generates:1 wiley:1 problems:2 different:1 6m:2 edges:2 purpose:1 potentials:13 nothing:1 cooper:1 wave:2 cases:1 class:1 involving:1 recent:1 focused:1 schr:2 reflection:1 considered:1 onedimensional:1 clear:1 well:1 edge:3 so:1 sn:6 physics:2 original:1 fact:1 normalized:1
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quant-ph9902073.txt |@word concept:1 consider:3 pointing:1 rev:7 forbidden:2 particular:1 results:2 leads:1 scalar:2 grateful:1 whose:3 nonlocal:24 those:4 excluded:1 worth:1 applied:2 straightforward:1 orthogonal:1 far:1 choice:1 difference:1 matrices:1 turns:1 vector:1 upper:1 hillery:1 second:2 biproduct:1 even:1 what:2 stands:1 expressed:2 indian:1 above:4 shared:3 consisting:1 simultaneously:2 ρai:6 here:3 test:1 along:2 obtained:1 institute:2 study:1 larger:3 products:1 implement:1 suitable:2 useful:2 requiring:1 scaled:4 apply:1 unit:1 use:5 takes:1 would:1 prove:1 positive:1 next:1 comparing:2 therefore:4 type:1 more:5 introducing:1 becomes:3 normalized:3 varying:1 cases:1 hold:2 producing:1 originally:1 obvious:1 den:1 following:4 stated:1 calculation:1 share:2 states:17 sense:2 inseparability:5 information:1 requirements:2 buzek:6 six:2 feature:1 write:3 how:2 pair:4 pure:3 optimal:17 parameter:2 product:1 may:1 ancilla:6 snl:4 earlier:1 produce:5 broadcasting:17 so:3 decreasing:1 bipartite:1 operations:10 produces:1 indeed:1 pointed:1 satisfied:2 course:1 paper:1 london:1 statistical:1 fidelity:6 still:1 its:3 perfect:1 machine:5 thank:1 interesting:1 actually:1 better:1 systems:2 maximal:1 non:1 greater:2 practice:1 scaling:2 compound:1 now:5 represents:1 gets:2 always:2 iff:1 inequality:1 each:4 macchiavello:2 constraints:1 subsystem:1 domain:1 square:1 obtains:1 measure:1 quantum:42 organised:1 out:11 divincenzo:1 shown:4 matrix:1 since:2 crucial:1 investigate:1 denotes:3 particles:2 re:2 performs:1 ref:1 shows:1 inevitably:1 theory:1 ρin:1 pairs:7 introduction:1 isotropic:1 hence:1 first:7 separable:8 initial:2 symmetry:4 vedral:1 number:2 intuitively:1 blank:2 carry:2 quality:1 given:15 unitarity:2 unknown:1 system:3 construct:1 their:1 wootters:1 broadcast:7 hillary:3 authors:1 haven:1 coefficients:2 showed:2 fuchs:1 distinguishes:1 transferred:1 were:1 india:2 result:1 manuscript:1 seen:3 seem:1 any:1 subsystems:6 ρout:6 cloners:11 note:2 potential:1 objective:1 unless:1 though:2 most:4 device:1 acknowledgements:1 surprising:1 considered:1 clear:1 later:2 mechanical:3 physics:2 fact:1 show:3 supplied:1 attainable:1 threshold:2 find:3 writes:1 state:27 than:9 only:16 factor:10 local:36 do:1 goes:1 get:1 zurek:1 simplest:2 cannot:2 despite:1 copying:14 him:1 arxiv:1 optimally:2 require:1 requirement:1 set:2 achieved:1 correlations:1 see:1 individual:3 sec:1 cloning:33 discussions:1 satisfies:1 best:3 satisfying:1 knight:1 symmetric:1 written:2 between:1 subscript:1 conditions:4 email:1 available:1 recently:1 nature:1 qubits:4 inseparable:7 bose:1 both:1 essentially:1 many:1 equal:1 plenio:1 exceeds:2 qubit:8 whole:1 comes:1 otherwise:2 point:1 corresponds:1 werner:2 simply:1 applicability:1 wider:1 considering:1 described:3 transformations:3 locally:1 copier:3 copies:5 been:2 defined:10 reduction:10 much:2 replicate:1 copied:4 universal:23 corresponding:2 restrictions:1 observe:1 understand:1 maximally:3 spin:2 former:1 present:1 case:7 value:3 will:2 suppose:1 error:1 procedure:1 unitary:1 thus:8 them:1 according:1 sity:1 im:1 ernet:1 lengthy:1 perform:1 same:6 complex:2 quant:2 pauli:1 largest:2 constructed:1 difficult:1 used:8 uses:1 purpose:1 entanglement:33 identity:1 lower:2 nevertheless:1 well:1 calcutta:2 ekert:2 know:2 possibilty:2 just:1 less:6 being:3 obtain:2 distant:2 density:9 conclude:1 5m:1 belongs:4 lett:4 easy:1 theorem:4 input:4 transformation:7 real:2 easily:1 possible:7 possibly:1 entangled:16 using:8 prominent:1 loss:1 necessary:1 helpful:1 follows:4 reduces:1 isotropy:4 separately:1 communications:1 arbitrary:1 output:28 reduced:1 accessible:1 because:3 classical:1 some:5 choosing:1 home:1 happens:2 provided:1 lead:1 replicas:1 refer:1 bc:2 bi:4 bj:3 comparison:1 massar:1 discussed:2 range:9 mean:1 bloch:1 road:2 own:1 into:8 obtaining:1 bound:3 three:3 retaining:1 references:1 parties:3 operator:10 lastly:1 transfer:1 there:2 question:2 way:1 was:2 function:4 form:7 smolin:1 jun:1 but:5 cloned:1 clones:1 cloner:21 ph:2 made:1 applying:3 evident:1 horodecki:6 whether:2 prevents:1 maximum:4 gisin:1 bruß:4 ac:1 ab:2 separability:1 ai:6 abstract:1 meaningless:1 general:9 peres:4 single:4 our:1 defines:1 again:1 nl:1 no:3 whereas:3 when:7 field:2 role:1 details:1 outputs:1 department:1 mathematics:1 conclusion:1 dhom:1 prepared:1 a1:10 a2:11 values:4 together:1 requires:1 original:4
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quant-ph9902074.txt |@word partial:1 consider:8 funct:1 rev:4 results:11 four:2 roy:1 entropy:9 parametrisation:1 computation:1 fawcett:1 expressions:2 contributions:8 row:2 regularize:1 depend:2 illustrates:1 containing:1 compensate:1 stable:10 tg:1 robaschik:3 divergent:2 brown:1 g0:4 very:1 wave:3 ultraviolet:3 hck:1 experimentally:1 difference:1 condition:2 opher:2 entire:1 presented:2 turns:2 list:1 solution:2 large:7 small:8 noted:2 force:9 monotonous:1 oscillation:2 divergencies:1 approximation:4 zero:2 enclosed:1 insertion:1 qualitatively:1 situated:1 linear:2 even:2 established:1 errors:3 section:6 3k:1 experiment:1 above:1 waals:1 net:2 increasing:1 3g:1 3f:1 annalen:1 κm:2 wieczorek:2 here:6 behaviour:1 tangent:1 relaxation:1 alone:1 const:1 along:1 quite:1 equations:1 change:2 every:1 broken:2 involved:2 changed:1 allows:3 ravndal:1 periodic:1 products:1 poisson:1 akb:2 narrow:2 changes:1 der:1 plotted:1 appropriately:1 useful:2 prefer:1 scaled:1 austria:1 decrease:1 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quant-ph9902086.txt |@word dsu:1 sci:1 consider:2 desirable:1 results:3 leads:1 consists:2 expressions:1 a45:1 simon:1 const:2 paris:1 technique:5 young:1 program:1 under:3 anharmonic:4 case:10 straightforward:2 wave:3 putting:2 exact:1 condition:2 solves:1 presented:1 dif:1 solution:2 large:1 solved:1 science:1 c00:1 eigenvalues:8 c02:1 noted:1 zh:3 sukhatme:2 dealing:1 sign:1 approximation:4 go:1 zero:2 chen:1 further:1 folk:1 scientific:1 nonlinear:2 appear:1 xσ:1 expressed:1 version:1 poles:1 new:5 principal:1 method:5 contrast:1 nδ1:1 equals:1 here:1 behaviour:1 pub:1 address:1 represented:2 consideration:4 equations:6 logarithmic:10 obtained:4 fernandez:2 published:2 usually:1 conveniently:1 suitable:4 eks:3 exited:2 involves:1 useful:1 hermite:1 weniger:1 addressed:1 apply:1 circumvent:1 planck:2 readily:1 conventional:1 feb:1 asymptotic:1 would:1 sake:1 cho:1 a51:1 few:1 therefore:1 relativistic:1 taken:2 theoretical:2 more:4 nauka:1 becomes:4 odinger:5 particular:1 known:3 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quant-ph9903001.txt |@word secondly:3 measurements:1 partial:1 consider:15 represent:1 rev:3 results:2 leads:1 comments:1 computation:1 go:14 follow:1 jqi:3 contributions:1 row:18 particles:5 c0:23 violate:1 transferred:2 graph:4 concerned:1 similarity:1 tr:4 rightmost:15 swap:14 under:7 arranged:2 bunches:3 overlaps:2 applied:3 rational:1 advantage:3 orthogonal:16 very:3 assuming:1 unfamiliar:1 coloured:7 overlay:1 manipulated:3 every:6 difference:1 condition:3 illustrated:1 redistribute:1 swapping:2 solves:1 did:1 positions:4 t2:1 solution:4 t1:1 large:7 solved:9 vector:1 minimal:1 small:1 rk:17 originally:1 degeneracy:1 smaller:6 grateful:1 consistent:3 consists:4 likely:3 wmax:2 manipulating:9 implemented:1 will:114 what:8 appear:1 advantageous:1 giving:1 section:2 selected:1 expressed:1 anywhere:1 goes:3 shared:1 net:19 ˆl:1 method:22 filled:3 movement:23 satisfy:1 full:2 led:1 chose:1 nonmaximal:2 exchange:1 never:1 teleportation:1 here:4 plenio:2 compressed:1 meet:5 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quant-ph9903002.txt |@word sci:1 rev:6 dynamic:1 results:1 eds:3 consists:1 relationships:2 inverse:4 calculate:1 marcos:1 fokker:1 technique:1 tn:4 under:2 analogous:2 kν:28 applied:1 supported:1 ured:1 wave:5 difference:2 exact:2 presented:1 positions:1 t2:11 t3:2 t1:11 math:1 optics:1 der:1 employing:2 approximation:5 second:1 aim:1 nonlinear:3 han:1 expressed:3 new:6 method:2 satisfy:1 respectively:1 june:1 possibility:1 eikx:1 path:13 z2:1 obtained:4 institute:2 study:4 studied:1 accomplished:1 alamos:1 action:8 fourier:2 makes:1 via:1 merwe:1 marginal:19 namely:4 greenbelt:1 scaled:1 planck:1 use:3 probabilities:1 contains:1 substitutions:1 nucl:1 approach:7 taken:1 type:1 introducing:1 knows:2 odinger:11 correspondingly:1 riesenfeld:1 known:2 andreev:2 must:1 states:7 account:1 vladimir:1 integrating:2 science:1 equation:22 oscillator:5 reads:1 cat:1 labeled:2 obvious:1 arrive:3 example:3 give:1 reconstructed:1 dm:1 needs:1 goal:1 provide:1 till:2 pure:2 instead:1 sin:16 map:2 product:1 mar:1 mat:1 mendes:1 may:1 after:3 derived:4 dx2:1 dx1:1 data:1 man:26 quasiclassical:7 explicit:2 goddard:1 green:16 fundamental:1 representation:12 order:1 wigner:4 produces:1 over:11 paper:1 y1:1 y2:1 ieee:1 its:4 sciences:1 derive:2 malkin:4 trieste:2 fiz:1 systems:3 main:1 introduce:1 framework:2 yz:1 hamilton:1 symposium:2 multidimensional:1 now:2 2t:3 term:1 2s:4 invariants:1 hamiltonian:1 ensemble:3 trap:2 found:5 oviedo:1 series:2 energy:1 solution:2 used:7 obtains:5 quantum:35 eq:10 ru:1 tombesi:2 matrix:6 space:3 since:1 lagrangian:1 research:5 eprint:1 print:1 formula:12 gos:1 foundation:1 linear:1 free:5 standard:2 completely:3 york:1 publication:1 determining:1 transition:4 nonnegative:1 motion:5 fleck:2 teor:1 onto:2 top:1 first:1 initial:4 xn:5 probability:14 variables:6 relations:1 another:5 given:4 πf:7 rewritten:2 introduction:1 eqs:1 πi:1 system:6 approximately:1 their:1 intermediate:2 πt:1 final:4 gives:4 ictp:2 calculations:1 relationship:10 trapped:4 academy:1 moscow:3 optical:6 x2:23 x3:4 july:2 x1:19 determines:1 was:14 see:3 tomographic:2 determined:5 amplitude:1 were:2 russia:1 symmetries:1 mind:1 paramaters:1 angle:1 studying:1 k2:6 generalized:1 formulas:1 phase:2 measured:2 considered:7 coincides:1 feynman:2 proceedings:3 points:2 principle:1 exp:14 quadratic:1 kx:1 physics:1 fact:1 lebedev:3 lewis:1 random:1 relation:3 hungary:1 fifth:1 parameters:4 elucidated:1 analytic:1 only:3 hamiltonians:1 do:1 his:1 dk:6 notation:4 means:3 dependent:2 express:1 da:8 dz:7 dx:8 dy:8 report:1 dt:2 aν:1 ds:2 evolution:19 x21:1 arxiv:1 acknowledgments:1 dodonov:2 16th:1 view:8 exists:1 frame:3 depends:1 result:8 terms:16 dµ:3 paul:1 analog:1 satisfying:1 µt:3 label:1 state:6 between:1 µa:5 x22:1 available:1 dν1:1 dν2:1 recently:1 august:1 manko:1 jetp:2 suggested:2 observable:1 cos:5 last:1 cot:7 olga:2 taking:1 uncertainty:1 according:1 conference:3 connection:1 symplectic:6 contribution:1 expression:8 elaborating:1 point:3 corresponds:1 consideration:2 bν:2 cp:1 considers:1 ferrero:1 pr:1 described:3 trajectory:3 due:1 describes:3 maryland:1 basic:1 ph:3 arises:1 flight:1 iµ:1 coherent:3 noncommutative:1 spie:1 spin:1 spain:1 case:2 eis:1 laser:4 eix:1 appearance:2 value:1 will:1 harmonic:5 squeezed:1 cats:1 nonstationary:1 property:4 iy:1 ix:1 iz:1 vogel:1 vol:2 5th:1 thus:4 ik:6 ic:1 bargmann:4 different:2 atom:1 member:1 complex:1 quant:3 several:1 arrives:2 singapore:1 πit:1 hand:1 ion:5 levels:1 kim:1 reference:6 schr:11 center:1 well:1 analysis:1 academic:1 components:2 coordinate:1 position:6 safonov:3 being:2 rotated:1 obtain:2 bµ:2 world:1 alternative:1 rotation:1 previous:1 preprint:1 kluwer:1 density:6 iϕ:2 rosa:2 signals:1 lett:6 dµ1:1 dµ2:1 trifonov:2 euler:1 real:1 iν:2 homodyne:1 know:1 press:4 using:3 moshinsky:2 mod:1 like:1 particle:2 signal:1 δs:1 integrals:1 arbitrary:1 classical:49 lagrange:1 examples:2 describing:1 integration:6 provides:1 proc:1 minimal:1 measuring:1 vitale:2 eiϕ:2 scientific:1 problems:1 equivalent:1 processing:1 expansion:1 substitution:1 bx:2 properties:3 extension:1 discussed:2 o:3 kµ:6 introduced:1 own:1 into:1 integral:15 functional:5 variable:8 references:1 frames:3 statistics:1 van:3 there:1 nova:1 los:1 ixy:1 sections:1 propagator:44 vienna:1 function:30 form:5 but:1 aµ:1 delta:6 russian:3 partially:1 infn:1 us:1 below:1 frequency:1 russ:4 distribution:23 similar:1 called:1 mechanics:9 mails:1 nauka:1 ko:26 abstract:1 dν:2 formulation:4 tomography:13 ax:1 distributions:1 physical:4 functions:1 no:1 na:1 other:1 gran:1 conclusion:1 nonclassical:1 meaning:2 important:1 dissipation:1 sharma:1 risken:1 penning:1 lanl:1 diffraction:2 mancini:2 nasa:2 time:5 international:3 having:1
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quant-ph9903003.txt |@word represent:1 consider:7 remarkable:1 similarity:5 caused:1 yamamoto:1 lack:1 amplifier:1 results:8 quadrature:29 per:1 edu:1 go:2 amplified:2 weakly:1 issues:1 looking:3 amplification:5 calculate:1 re:1 arthurs:1 graph:5 technique:2 ts:5 nonlocal:1 tq:18 finally:1 efficiencies:1 squeezing:20 preserved:2 under:5 sent:3 applied:2 fax:1 amplitudes:2 vcv:10 straightforward:1 orthogonal:2 very:15 frequencies:2 rise:1 splitting:1 summarized:1 mixing:1 experimentally:1 difference:1 exact:1 al3:1 condition:3 entire:1 modulator:2 level:1 transmission:11 ref:3 correct:2 try:1 discrete:2 small:5 optics:1 still:2 upper:1 penalties:1 sin2:1 direct:3 second:2 further:1 port:4 even:1 what:2 goodman:1 adds:1 giving:3 ˆb:7 version:6 reconstruction:2 values:1 ηe:6 increasing:1 method:1 coefficient:2 simultaneously:3 submitted:1 implying:1 respectively:4 like:2 component:1 teleportation:37 here:6 aˆa:1 behaviour:1 desired:2 operating:4 cos2:1 situation:1 alone:2 ratio:2 strong:4 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quant-ph9903004.txt |@word partial:1 caused:1 entropy:14 computation:1 calculate:1 ohya:4 tr:2 tk:4 tc:1 case:2 conjecture:1 very:1 ρtk:2 wave:1 every:1 stays:1 resonant:1 difference:1 matrices:1 trj:1 hamiltonian:1 tra:1 knight:1 ρf:1 t2:2 t3:2 damped:1 eigenvalues:1 optics:1 oscillation:2 sin2:1 approximation:1 plays:1 appear:1 expressed:1 above:2 ever:1 method:1 dem:10 degree:12 respectively:1 component:1 teleportation:1 plenio:1 cos2:1 appears:1 studied:2 reason:1 eberly:1 makes:1 apr:1 marginal:1 iet:3 apply:2 use:5 takes:2 commun:1 call:1 therefore:2 becomes:3 operators:1 envelope:1 excellent:1 known:2 cases:1 ρa:7 tokyo:2 science:2 ρk:2 reviews:1 ρt:4 following:3 example:1 initial:1 indicated:1 bennett:1 states:10 minimum:2 numbers:1 want:2 verlag:1 information:2 s2:2 s1:2 rippin:1 feature:1 pure:6 parameter:2 sin:2 classify:1 map:1 product:1 may:1 after:1 sk:1 shore:1 so:3 sa:3 sf:2 ith:1 developed:1 over:1 mentioned:1 japan:2 belavkin:1 yamaguchi:2 jaynes:11 its:3 sciences:1 interesting:1 degrees:1 choose:1 rabi:3 now:1 bigger:2 february:1 2s:1 university:2 level:1 inequality:2 each:1 2n:4 higher:1 mean:2 en:3 gaussian:1 frequency:2 measure:6 quantum:12 our:1 trf:1 divincenzo:1 matrix:1 rep:3 since:1 interference:1 research:1 math:3 shows:6 theory:1 approaches:1 formation:1 e4:6 e1:8 e0:2 e3:4 e2:4 definition:1 interaction:1 transition:4 times:1 yamazaki:1 features:1 probability:4 number:2 done:1 city:2 given:1 revival:4 system:5 2ωn:2 returns:1 wootters:1 collapse:2 continuous:1 than:2 distance:2 ktr:1 annihilation:1 tret:1 seen:1 mins:1 any:1 convenient:1 note:1 instance:1 take:1 exactly:1 trace:1 though:1 trσ:3 measures:3 most:5 cummings:13 letter:4 analytically:1 considered:1 later:1 coincides:1 points:1 exp:8 quantifying:1 fact:1 quantity:1 phenomenon:1 rotating:1 find:2 ha:1 parameters:1 state:20 constant:3 araki:1 gea:1 closely:1 dv:1 during:2 evolution:2 arxiv:1 twice:1 fixed:1 view:1 computed:1 relative:3 namely:1 result:1 sem:1 closer:1 tensor:1 ieee:1 written:1 various:1 between:5 subscript:1 petz:1 recently:1 initially:2 however:1 banacloche:1 many:2 taking:1 equal:2 minus:1 σz:2 conclude:2 simple:1 corresponds:1 dephase:1 moreover:3 due:2 been:7 damping:1 ph:2 fig:9 θl:1 sufficient:1 photon:3 coherent:1 spin:2 applied:1 uncertain:1 pacs:1 solid:1 kodai:1 value:2 will:3 suppose:1 jaynescummings:1 unitary:2 von:4 t1:2 thus:2 sity:1 quant:2 pauli:1 φj:3 several:2 difficult:1 development:2 functions:1 entanglement:15 eigenvectors:1 model:21 researchers:1 know:1 entanglements:2 onoda:1 resp:2 atomic:1 chiba:1 grounded:1 readers:1 lett:2 iσ:2 solvable:1 excited:3 around:4 inversion:1 increases:1 entangled:12 using:1 mod:1 follows:1 yields:1 night:1 reduced:3 because:1 neumann:4 creation:1 some:2 strongest:1 entropic:1 describing:1 proc:1 refer:1 rephase:1 periodically:2 bz:1 mixed:3 lieb:1 rev:4 disentangled:3 three:1 operator:3 often:1 log:12 there:2 vedral:2 analyze:2 function:3 form:2 smolin:1 sequel:1 hi:1 atom:9 highest:1 hf:2 collapses:1 ut:6 us:1 below:1 ωn:5 called:2 adopt:1 associated:1 defined:7 pseudo:1 yoo:1 mutual:5 compared:1 dotted:1 no:1 dashed:1 when:2 field:6 other:1 role:1 details:1 department:1 noda:1 superposition:1 prepared:1 generated:1 important:2 correlated:2 coupling:3 interval:2 curve:3 time:11
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quant-ph9903005.txt |@word consider:1 results:2 hyperboloid:1 tn:2 finally:2 hibbs:1 straightforward:1 transitively:1 wishes:1 hamiltonian:5 turns:1 solution:10 a123:1 upper:1 sign:1 approximation:1 consists:1 odd:2 even:2 section:1 celebrated:1 sheeted:1 above:2 new:4 method:8 sinh:2 path:15 obtained:3 ref:1 ixed:1 institute:1 changed:1 ourself:1 resulting:2 action:1 symmetrical:1 changes:1 jalan:1 apr:1 integrations:1 derivatives:2 proceed:1 recalling:1 next:1 mckean:2 type:3 theoretical:1 grosche:6 introducing:3 becomes:1 dxµ:4 basically:1 cases:6 iii:1 extension:1 integrating:1 equation:11 work:1 det:2 values:1 following:4 compare:1 give:2 preserving:1 axis:1 s2:7 acts:1 pure:1 parameter:1 express:1 plane:1 fi:1 constants:1 explicit:2 so:6 representation:2 integrand:1 order:2 over:1 itb:1 y2:4 its:1 group:1 thank:1 acknowledge:1 ln:2 coordinates:9 him:1 differently:1 derivative:4 13b:1 13a:1 motivated:1 yn:3 yz:1 equidistant:1 half:1 yr:1 always:1 presented:1 2y:2 by1:1 form1:1 2a:2 2b:1 2m:1 repeating:1 2i:1 related:1 nostrand:1 poincare:1 quantum:1 laboratory:1 eq:7 out:5 space:4 since:4 hill:1 denoted:1 formula:1 evaluation:3 math:1 8b:1 8a:1 free:8 york:3 derivation:1 r2:5 could:1 hyperbolic:7 ds2:2 times:2 first:4 reversing:1 variables:2 xd:1 restrict:1 another:1 angular:1 given:3 sheet:1 similarly:1 introduction:1 πt:4 final:1 gives:4 x2:1 cosh:12 distance:6 unfortunately:1 double:1 providing:1 treated:1 minus:1 7b:1 7a:1 lim:2 able:1 note:2 take:2 begin:1 murphy:1 trace:1 significant:1 nothing:2 acknowledgements:1 xµ:4 especially:1 feynman:1 points:4 symmetrically:1 exp:13 physics:3 fact:1 12a:1 12b:1 spaces:1 relation:1 solutions:1 substituting:2 find:2 d1:1 x1:1 based:1 steiner:1 should:1 explicitly:2 factor:3 integrate:2 do:1 dl:2 dk:7 get:2 zen:1 simplest:1 overall:1 straightforwardly:1 dz:4 dx:1 dy:7 dt:10 dr:2 ds:4 differentiating:1 alexander:1 arxiv:1 fixed:2 kernel:1 multiplying:1 achieved:1 result:3 tensor:1 closed:1 between:4 invariant:3 xµn:1 email:1 recently:1 however:2 comm:1 lb:3 limits:1 taking:3 equal:1 expression:1 groups:1 simple:1 margenau:1 cd:1 dimensional:10 respect:8 considering:1 been:2 basic:1 ph:1 6a:1 6b:1 corresponding:2 θr:1 gab:3 present:2 case:8 evaluated:2 will:5 euclidean:2 evaluating:2 geometric:1 almost:1 refs:1 thus:2 iv:1 ii:1 im:1 rid:1 technology:1 id:1 different:2 author:1 same:2 quant:1 singapore:1 hand:6 kubo:3 purpose:1 hans:1 indonesia:1 well:1 analysis:1 academic:1 solve:1 components:1 chemistry:1 left:3 spherical:1 just:1 obtain:3 transforms:1 using:5 facts:1 4m2:2 now:1 had:1 parametrization:1 lett:1 transformation:1 euler:1 read:1 advances:1 immediately:1 necessary:2 particle:1 obvious:1 reduces:1 separately:1 integrals:1 arbitrary:1 mcgraw:1 beltrami:2 pertaining:1 right:3 methods:1 integration:4 manipulations:1 assuming:1 prog:1 prof:1 scientific:1 carried:1 world:1 pseudosphere:7 side:6 discard:1 gamma:1 helgason:2 h2:1 into:3 integral:25 functional:1 appropriate:1 references:1 operator:5 abel:3 fortsch:1 van:1 initial:1 appl:1 encouragements:1 was:3 propagator:10 function:3 kronecker:1 but:2 heat:1 delta:1 applying:1 up:2 us:4 freddy:1 discretized:2 2πt:3 problem:1 laplace:2 mechanics:1 ac:1 ab:2 defined:1 selberg:1 abstract:1 dξ:3 dλ:1 formulation:2 metric:3 other:1 department:1 mathematics:1 theor:1 polar:1 deriving:1 variable:4 pseudometric:1
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quant-ph9903006.txt |@word measurements:1 partial:4 consider:1 rev:8 global:1 results:2 leads:1 scalar:1 broader:1 consists:1 follow:1 causes:1 compact:1 young:2 finally:3 subbasis:2 case:7 orthogonal:10 very:1 rise:4 choice:1 corollary:1 manipulated:1 every:3 mixing:4 condition:1 nonselective:1 incoherent:1 presented:2 turns:1 make:1 leave:1 vector:15 indices:1 diu:1 noted:1 eiϑ:4 version:1 10b:1 dealing:2 10a:4 second:8 pass:2 incidentally:1 further:9 goes:1 spectral:6 index:1 what:4 appear:2 sum:1 slight:1 expressed:1 experiment:10 establishes:1 values:6 subtracting:1 satisfy:1 full:1 notions:1 degree:1 respectively:5 realizations:1 answers:2 reported:2 explore:1 selective:1 address:1 concluding:1 path:3 along:1 observing:1 appears:2 extreme:1 box:1 suitably:1 study:1 vectors:15 published:1 usually:1 suitable:4 uniquely:2 via:3 spatially:1 family:1 9a:3 9b:3 polarizers:2 herzog:1 establish:1 takes:6 would:1 entities:2 positive:1 contains:2 next:2 call:4 memory:3 more:5 henneberger:1 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quant-ph9903007.txt |@word secondly:2 evidence:3 consider:3 represent:3 saves:1 results:2 existing:1 leads:3 commute:4 invariably:1 go:2 remarkably:2 involved:3 saved:2 localized:4 restrictions:3 whose:2 careful:2 eigenbasis:1 dp:1 bordered:1 presents:1 finally:1 does:10 those:2 smallness:1 under:6 ontological:2 norm:1 ta:1 belonging:1 protective:49 very:7 wave:15 electron:11 untenable:1 decide:2 experimentally:1 exact:4 condition:4 arrange:1 entire:1 obvious:1 hamiltonian:20 altering:1 suffices:2 applicable:3 large:2 discrete:1 vector:2 avoiding:1 small:3 inspection:2 der:1 degeneracy:2 measuring:1 smaller:1 force:1 dealing:1 pass:1 direct:1 approximation:12 second:4 concludes:1 further:2 copenhagen:4 distance:1 canonical:1 even:8 established:2 what:4 stands:1 apparatus:9 incompatible:2 section:8 dass:1 expressed:1 experiment:5 suspect:1 above:9 shared:1 appeal:3 contrast:3 full:1 respectively:1 never:2 equals:1 here:6 perpendicular:1 following:1 asymmetry:1 test:1 free:4 address:1 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quant-ph9903008.txt |@word magnetic:1 reversibility:4 extends:1 four:3 consists:11 forget:1 whose:8 const:1 calculate:10 gcd:4 presents:1 under:1 worth:1 replication:1 every:4 rec:2 manin:5 believed:1 basics:2 supports:1 solution:1 vector:2 markov:2 methane:1 deutsch:3 estimates:2 direct:4 pulse:1 approximation:1 second:5 invariant:1 implemented:2 machines:8 blue:2 iterating:1 specification:1 selected:1 supplied:2 above:9 new:8 contributes:1 consisting:5 simultaneously:4 notions:2 here:11 atoms:2 represented:6 obtained:4 balance:1 study:1 changed:2 fourier:4 rϕ:1 projection:6 tensored:1 explained:3 highly:7 unitary:13 hindsight:1 total:2 unit:1 dna:1 would:7 substitutions:1 call:7 therefore:6 type:8 decomposable:1 tk:4 successful:1 naive:1 reversibly:2 berlin:1 reversible:5 midst:1 must:18 springer:2 word:5 setup:2 work:6 mu:2 grover:5 exceptions:1 example:11 mumford:3 organized:2 stressing:1 generically:1 involve:1 want:4 david:1 end:2 provide:1 machine:4 far:2 answer:1 gate:12 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quant-ph9903011.txt |@word concept:1 partial:6 consider:15 global:1 idealised:1 existing:1 leads:2 proposition:3 per:1 cooperative:1 consists:1 expressions:2 issues:1 gr:1 whose:9 paris:1 disposal:1 equivalence:4 tn:2 finally:2 petersburg:2 th:4 atlas:1 eprint:6 eories:1 sorkin:11 division:1 lack:1 straightforward:1 far:1 reader:2 results:8 every:1 summarized:1 experimentally:1 zeitschrift:1 bringing:1 entire:2 o4:3 did:1 irreducible:4 list:1 solution:1 try:1 solved:2 registers:1 team:9 referred:2 neighborhood:1 version:2 krasnikov:1 dealing:1 uef:1 direct:1 balachandran:1 approximation:1 crts:1 zero:2 pass:1 dynamics:1 substitute:6 linear:11 even:2 established:1 what:7 section:23 expressed:3 networks:1 cell:1 experiment:4 subspaces:3 deal:1 new:1 journal:8 satisfy:1 respectively:2 rudimentary:1 ranges:1 refinement:1 objects:1 address:1 represented:3 respect:1 differential:6 obtained:6 remark:2 antisymmetric:1 technical:1 hartle:1 study:1 studied:2 reason:1 products:1 masuda:1 δqr:1 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quant-ph9903012.txt |@word partial:11 consider:7 crucial:1 results:8 leads:1 ρt2:1 lewenstein:1 ρt1:5 fmrx:1 compact:1 dimensionality:3 depend:1 eˆ:14 ts:1 finally:1 include:1 norm:1 ta:9 g2:5 g1:5 ρta:52 very:4 account:1 corollary:6 difference:1 matrices:1 condition:6 dim:12 level:1 tra:1 ref:1 solution:3 try:1 vector:22 science:1 equation:3 sign:1 second:8 theory:2 even:1 remain:2 expressed:1 a232:1 full:2 degree:1 respectively:4 gemeinschaft:1 understanding:1 desired:1 nonsingular:1 equations:4 obtained:3 vectors:15 allows:2 suggests:1 resulting:1 hospitality:1 specialize:1 involves:1 useful:1 family:1 austria:1 apply:1 should:1 linearly:4 use:8 proceed:1 working:1 prove:5 positive:8 contains:4 readable:1 few:1 ψi:2 therefore:12 taken:2 a58:1 until:3 more:4 composite:1 operators:7 surprisingly:1 normalized:1 particular:6 cases:3 iv:1 iii:2 must:1 keeping:1 recall:1 der:1 work:1 det:2 ρn:3 ρs:11 values:1 ρt:1 erb:1 concepts:4 following:5 fulfill:1 arrive:2 example:2 proof:17 f0:2 f1:2 give:3 bennett:3 states:10 numbers:3 information:3 quantph:2 orthogonal:3 write:8 how:2 criterion:10 instead:2 product:26 mar:1 algebra:1 may:2 max:2 after:2 applications:2 plane:1 physik:2 fi:4 fk:1 transposed:1 hannover:3 lemmas:2 deutsche:1 ones:2 so:4 fundamental:1 definitions:1 order:6 indeed:1 paper:2 existence:2 its:5 derive:3 thank:1 chosen:1 interesting:1 fruitful:1 systems:15 main:1 might:1 non:5 introduce:2 they:4 acta:1 now:6 easily:3 february:1 vidal:3 always:6 hermitian:1 possibilities:1 sufficiently:1 iff:5 2b:2 found:2 universit:2 european:1 subsystem:1 ei:4 formulate:1 reduce:6 idea:1 related:2 quantum:8 our:6 happen:1 out:3 large:1 network:1 space:1 quantify:1 furthermore:1 since:6 rev:6 increase:2 acting:1 reader:1 induction:2 math:2 shows:1 linear:3 written:1 clarify:1 reason:2 e1:2 e2:1 definition:1 could:1 turn:1 terhal:1 a223:1 first:12 separable:29 already:1 variables:1 powerful:2 rank:3 theoretische:2 construct:1 directly:2 carry:1 given:11 necessarily:1 reference:1 forschung:1 similarly:2 system:9 least:3 their:3 assumption:2 statement:4 similary:1 proving:1 part:1 wissenschaftlichen:1 than:2 specify:1 showed:1 transposes:1 imply:1 contrary:2 fˆ:1 were:1 f15:1 well:1 need:1 any:6 relatively:1 lie:1 generalizes:1 realm:1 zero:2 min:1 note:4 take:2 spectral:2 play:1 unless:1 allow:2 tarrach:2 simplify:1 germany:1 but:2 letter:3 claims:1 pair:2 sfb:2 class:1 dordrecht:1 coincides:1 braunstein:1 fact:6 12a:1 12b:1 show:13 supported:13 spaces:1 solutions:1 find:7 symmetric:1 based:5 situations:1 state:5 separability:10 lemma:30 only:1 summarizing:1 writen:1 do:2 notation:1 cannot:4 despite:1 combinations:1 transposition:5 arxiv:1 fulfilling:1 contain:3 kernel:8 set:3 exists:4 depends:1 result:1 discussions:1 close:1 wonder:1 αa:2 enough:1 invariant:2 subscript:1 conditions:2 importance:1 complement:1 transpose:6 wi:3 unnormalized:2 distinguish:1 both:4 last:1 2n:1 ua:3 taking:1 according:13 otherwise:1 cn:1 bell:1 simple:5 ca:1 corresponds:1 dimensional:4 werner:1 simply:1 polynomial:2 moreover:1 throughout:1 basis:12 locally:1 three:2 responds:1 ai:4 certain:1 ph:5 define:5 arises:1 families:1 sufficient:6 subspace:2 denote:5 present:1 case:16 intriguing:1 look:2 will:14 situation:1 property:3 unitary:3 vi:8 thus:8 them:1 equal:3 ii:6 ia:1 fonds:1 different:2 perhaps:1 make:3 same:1 tells:1 complex:1 quant:5 proved:1 several:1 higher:1 independent:3 extended:1 see:2 dimk:1 i2:4 hand:1 entanglement:5 a2i:1 no:2 epr:1 analysis:1 obviously:3 academic:1 without:1 sets:1 position:1 dimension:5 usual:1 just:2 obtain:7 thanks:1 immediately:1 λi:6 yet:1 previous:1 kluwer:1 density:7 conclude:2 mathematically:1 lets:1 valid:3 conjugated:1 lett:6 easy:2 theorem:9 generalized:1 real:8 innsbruck:2 decomposed:2 know:1 sanpera:3 using:14 advanced:1 apart:1 like:1 follows:1 either:7 arbitrary:1 accessible:1 methods:1 some:9 back:1 respect:4 proofs:1 orthonormal:2 tmr:1 describing:1 dimensions:1 does:2 decomposition:7 demonstrated:1 refer:1 rep:1 bi:1 step:1 although:1 hilbert:2 bz:1 zur:1 would:4 most:2 practical:1 range:6 ensure:1 woronowicz:1 mixed:1 introduced:3 automatically:1 statements:1 into:1 appropriate:1 been:1 determine:1 operator:14 institut:2 there:16 question:1 specifically:1 why:1 physicists:1 way:2 forward:1 was:1 2ρs:1 complete:2 form:5 converse:1 denoting:1 fore:1 true:4 coefficients:1 horodecki:11 whether:5 us:8 ur:2 problem:1 similar:2 called:1 mechanics:1 fulfills:1 ab:1 constant:1 defined:2 implications:1 general:2 peres:9 proves:1 exist:1 corresponding:2 check:1 constructed:1 paradox:1 locality:1 when:2 nf:2 ng:2 other:5 role:1 er:10 conclusion:2 completes:1 divincenzo:1 prepared:1 substract:2 important:2 structure:1 matrix:1 implies:3 assume:3 original:1 far:1 decoherence:1 4b:2 having:1 4a:2
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quant-ph9903013.txt |@word chinese:1 splitting:1 leads:1 roy:1 finally:3 squeezing:1 choice:1 fan:1 pacs:1 try:2 joshi:1 optics:1 direct:2 zero:1 chen:1 further:1 nonlinear:60 expressed:1 ˆa:1 above:8 a233:1 new:1 lee:2 here:8 china:3 obtained:4 remark:4 institute:2 study:2 matsuo:1 real:1 matos:1 via:1 aphy:1 replace:1 prove:1 positive:1 negative:18 next:2 a51:1 comparing:3 a54:1 a58:1 type:3 theoretical:1 more:2 brings:1 operators:1 known:4 valued:2 ma:1 science:1 equation:6 work:3 fock:1 following:2 beijing:1 wang:1 give:5 expanding:1 states:60 numbers:1 tan:1 buzek:1 srinivasan:1 answer:1 acta:1 ordinary:1 parameter:3 product:1 fu:4 algebra:3 ladder:6 different:3 changchun:1 man:5 realized:1 natural:1 explicit:1 su:4 stimulate:1 so:2 order:2 pointed:1 paper:1 japan:1 still:6 excitations:2 derive:1 d36:1 d35:1 d32:1 boson:1 into:3 non:2 ya:2 rasetti:3 nov:1 now:3 eigenvalue:1 february:1 university:1 2n:1 displacement:6 quantum:2 laboratory:1 eq:26 special:1 out:1 shown:2 since:1 rev:10 ref:2 math:5 shows:1 foundation:1 guess:1 plex:1 nonnegative:1 motion:1 think:1 already:1 xn:1 features:1 laguerre:1 number:3 directly:3 given:2 similarly:1 jex:1 their:3 identity:1 realization:3 recovered:1 trapped:1 academy:1 part:1 than:1 coefficients:2 annihilation:1 solomon:2 determined:1 a43:1 a41:1 exhibit:1 affirmative:1 viewed:1 lie:3 self:1 note:1 sciences:1 k0:2 analogy:1 scripta:1 normal:1 gallardo:1 multiply:2 class:1 ko:5 physica:1 typeset:1 dattoli:1 optical:1 exp:11 holstein:2 physics:3 fact:2 show:4 supported:1 relation:2 substituting:3 d2:3 find:1 northeast:1 based:1 ment:1 state:38 explicitly:2 greenberg:2 hope:1 therefore:1 get:3 de:1 db:1 dv:1 gen:3 arxiv:1 summary:1 dodonov:2 multiplying:2 physically:1 national:1 j0:2 morosi:1 see:2 result:5 satisfying:1 commutation:1 currently:1 marmo:2 αa:3 written:7 various:1 barranco:1 approach:1 email:1 αn:4 terms:1 key:1 both:5 equal:1 context:1 filho:1 lm:3 cn:6 conclude:1 semiclassical:1 polynomial:1 been:1 much:1 interest:2 pj:1 ph:2 abstract:1 define:1 ariano:2 corresponding:4 photon:3 coherent:64 c0:8 present:1 exponential:7 tanh:1 eigenstate:1 will:1 stoler:1 opt:3 vogel:1 vk:1 xiao:1 zaccaria:2 agarwal:1 hong:1 verified:1 d11:3 multiphoton:5 grant:1 recursion:1 radiation:2 quant:2 sudarshan:1 hand:1 ion:1 supposing:1 sivakumar:2 normalization:1 recent:1 center:1 primakoff:2 acknowledgement:1 well:4 greatest:1 left:4 teich:1 guang:1 less:1 obtain:3 using:4 eigenstates:1 katriel:1 setting:1 lett:4 excited:18 gave:1 identical:2 ama:1 decomposed:2 displace:1 integer:4 mod:1 like:1 reduces:1 yields:1 arbitrary:1 stationary:1 reduced:1 right:1 classical:1 b2:1 confirm:1 assuming:1 expansion:1 step:1 binomial:28 revtex:1 although:1 ηj0:1 commun:1 o:2 soc:2 ηm:1 ηk:1 ηj:2 references:1 determine:1 operator:21 iphy:1 a50:1 there:2 question:1 was:1 naturally:1 function:11 form:22 construction:1 torre:1 up:1 us:1 limit:1 verification:1 called:2 vourdas:1 aa:1 ac:1 constant:1 af:1 defined:9 certain:2 ak:7 am:2 general:3 exist:1 saleh:1 bishop:1 sasaki:3 again:1 functions:1 na:1 tara:1 when:1 arctan:2 field:2 other:1 theor:1 superposition:1 ξj:1 ξk:1 sides:4 brandt:2 mancini:1 mass:1
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quant-ph9903014.txt |@word represent:1 homomorphism:5 consider:6 undecidable:1 saves:1 activated:1 results:1 generalize:1 subclass:1 computation:18 consists:1 maxσ:1 causes:1 whose:2 inverse:12 chain:4 failed:1 deterministic:3 canonical:1 languages:62 finally:6 behave:1 tj:5 those:2 under:29 qacc:22 stochastic:4 unions:2 presentation:1 ta:2 summarizes:1 applied:3 amplitudes:5 string:14 continues:1 none:1 focus:1 replication:1 corollary:4 p1:8 every:17 decide:1 affect:2 difference:3 matrices:22 condition:43 partitions:1 dim:1 38th:1 unlike:4 immediately:1 proc:1 array:1 enon:2 leave:1 solved:1 vector:8 small:2 eigenvalues:4 noted:1 configurations:7 prevent:1 zn:2 averaged:1 zi:4 renormalized:1 dealing:1 requirements:1 among:1 direct:2 sweeps:1 located:1 second:9 cyclic:1 3a:1 further:1 emptiness:1 machines:1 shma:2 even:1 what:3 sub:5 xσ:1 section:4 expressed:1 pippenger:1 access:1 3i:10 version:3 run:1 localized:1 watrous:11 new:14 unrestricted:3 nicholas:2 ever:2 equivalent:12 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quant-ph9903015.txt |@word concept:3 consider:3 forbidden:2 particular:1 splitting:8 existing:2 leads:1 scalar:1 poorly:1 whose:1 ρxi:1 essentials:1 nonlocal:2 under:1 applied:1 fax:1 advantage:1 outside:2 rise:1 results:3 matrices:6 turns:2 upper:2 hillery:2 second:6 qualitatively:1 employ:1 what:4 stands:2 section:3 negates:1 indian:1 above:5 3b:1 3a:1 increasing:1 consisting:3 satisfy:1 ρad:5 hasn:1 simultaneously:1 respectively:1 ρai:6 here:2 plenio:1 along:1 change:1 obtained:1 institute:3 changed:2 allows:1 resulting:1 ρx1:1 apr:1 ηmax:1 scaled:1 decrease:1 apply:1 unit:1 use:4 takes:1 would:1 massar:1 remains:2 positive:2 give:1 comparing:1 therefore:3 criteria:1 type:2 more:2 sharing:1 composite:3 india:3 operators:5 normalized:1 varying:1 known:1 cases:1 hold:3 producing:1 keeping:2 ρi:2 recall:2 originally:1 remain:2 values:3 following:3 ρx:1 example:1 stated:1 process:6 share:1 belonging:1 states:12 his:1 want:2 allowed:2 tal:1 inseparability:2 information:1 respective:1 requirements:1 thing:1 rather:3 discussion:2 machine:5 how:8 pure:18 answer:2 optimal:12 parameter:2 product:5 tried:1 ancilla:3 clone:1 after:9 produce:2 unentangled:1 third:1 broadcasting:7 so:5 definitions:1 buzek:4 operations:2 terno:3 produces:1 developed:2 closeness:2 satisfied:1 course:1 already:1 statistical:1 fidelity:8 still:1 its:4 before:2 perfect:1 till:1 bandyopadhyay:2 actually:1 forms:1 anirban:1 systems:2 main:1 non:1 good:2 scaling:1 framework:2 now:8 discuss:3 lies:4 always:1 inequality:2 each:3 macchiavello:1 mean:1 subsystem:8 domain:1 schemes:4 disentanglement:31 there:1 related:1 investigated:1 obtains:1 measure:1 quantum:21 our:4 operation:1 eq:2 special:1 really:1 divincenzo:1 shown:3 matrix:5 since:5 rev:5 denotes:2 re:1 acting:1 performs:1 rj:4 earlier:1 possibility:2 besides:1 definition:3 pairs:1 r1:1 r2:1 unitarity:1 explored:1 isotropic:7 undergo:1 first:9 separable:8 xi:1 symmetry:1 vedral:1 will:2 xy:2 done:1 blank:1 impossible:2 precisely:1 quality:1 given:10 introduction:1 system:6 their:2 scheme:3 final:1 gives:2 part:2 x2:3 copy:8 than:2 coefficients:1 showed:4 fuchs:1 require:1 transferred:1 result:2 motivation:1 unchanged:4 mind:1 say:1 close:3 seen:1 any:11 subsystems:19 cloners:4 able:2 note:6 ideal:1 take:1 objective:1 though:1 kar:1 pair:1 clear:4 later:1 bipartite:6 principle:1 physics:3 particularly:1 random:1 implying:1 supplied:1 ρbd:2 x1:2 written:3 should:2 only:2 black:1 factor:4 local:20 achieve:3 meant:1 dm:5 cannot:2 words:1 shared:1 becomes:2 disentangling:3 arxiv:1 requirement:3 constructing:1 exists:1 achieved:3 maximum:2 see:1 individual:4 cloning:14 discussions:2 unaltered:1 best:4 said:1 tensor:2 knight:1 state:38 smallest:1 between:1 probably:1 justified:1 conditions:3 email:2 ends:1 recently:1 qubits:11 inseparable:8 wi:3 bose:2 both:3 ρent:6 cow:1 equal:1 etc:1 qubit:16 otherwise:1 werner:1 better:4 described:2 transformations:2 basis:1 locally:6 copier:2 copies:7 been:1 ai:1 reduction:3 interest:1 basic:1 ph:6 abstract:1 corresponding:4 observe:2 those:1 case:4 look:2 value:2 aim:1 suppose:2 thus:5 telephone:1 according:1 ernet:2 ie:1 author:1 same:1 tells:2 complex:1 quant:6 copying:5 party:2 used:3 entanglement:17 totally:1 lower:1 possibly:1 nevertheless:2 preceeding:1 well:3 know:1 calcutta:3 ekert:1 usual:1 possibilty:4 less:5 being:3 obtain:1 via:1 distant:1 transforms:4 previous:2 density:18 belongs:5 lett:3 easy:1 theorem:3 transformation:4 real:1 mor:3 possible:10 department:2 entangled:20 using:4 particle:3 follows:2 isotropy:2 arbitrary:6 become:1 reduced:15 dhom:2 sketch:1 some:2 choosing:1 specified:1 provided:5 bd:1 disentangle:9 bi:4 bj:3 although:2 output:7 working:2 tracing:2 summarise:2 distinct:1 range:2 important:1 constraints:1 road:3 mixture:1 own:1 into:9 within:4 disentangled:4 bound:3 three:2 nothing:1 references:1 parties:3 operator:3 initial:1 question:2 approximate:1 way:1 form:3 smolin:1 but:6 cloned:1 construction:1 cloner:16 copied:4 he:1 made:1 applying:6 horodecki:6 whether:1 up:1 us:4 problem:1 gisin:1 bruß:2 ab:1 ad:1 defined:4 certain:1 universal:13 describe:1 meaningless:1 general:3 peres:4 single:2 exist:1 constructed:1 again:1 compared:1 whereas:3 when:3 other:3 outputs:1 test:1 mathematics:1 out:10 conclusion:1 poor:2 briefly:2 a1:4 a2:4 transfers:1 required:1 weights:1 original:2
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quant-ph9903016.txt |@word replacing:2 partial:2 consider:1 chinese:1 leads:1 ihep:1 whose:1 depend:2 tail:6 critical:19 niemi:1 inwards:2 nodes:1 discontinuously:1 worth:1 case:57 very:1 tends:4 wave:13 polytechnic:1 difference:2 condition:12 vidensk:1 hamiltonian:1 tanh:1 solution:25 large:2 discrete:1 small:8 der:1 smaller:3 sturm:8 direct:1 cosh:1 past:1 zero:58 equal:8 further:1 odd:21 even:21 established:2 plays:1 trivial:1 section:4 expressed:2 version:1 goes:3 new:4 method:3 satisfy:3 simultaneously:1 ibid:1 respectively:5 here:1 understanding:1 ranges:5 κx:3 cos2:1 sinh:1 address:1 implicit:1 logarithmic:17 box:3 property:3 institute:3 shift:23 study:3 studied:2 ignoring:1 published:1 suitable:1 changes:15 jackiw:1 useful:1 rosenberg:3 replace:1 d31:1 total:3 establish:4 readily:1 derivatives:3 asymptotic:1 usa:1 commun:1 always:4 positive:9 finally:6 next:2 nucl:1 approach:1 call:1 therefore:9 a57:1 a56:1 more:3 introducing:1 becomes:6 hauge:1 odinger:20 needed:1 employed:1 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quant-ph9903017.txt |@word consider:1 four:3 compact:1 amplification:3 depend:1 does:2 γn:22 th:3 marks:1 cm3:1 indicating:2 far:2 connects:1 every:1 summarized:1 difference:1 condition:2 illustrated:2 large:1 solved:1 small:4 optics:3 smaller:3 direct:1 approximation:1 rate:21 dynamics:5 even:3 expressed:1 current:23 above:6 pioneering:1 edited:2 relaxation:8 based:3 equations:2 obtained:2 thirty:1 holger:1 larger:7 allows:1 commonly:1 usually:1 via:1 apply:3 total:2 conventional:3 haken:1 takes:2 would:1 lasing:1 predictions:1 few:1 therefore:6 taken:1 more:3 separated:1 thus:6 stable:2 emission:20 validity:1 hofmann:1 normalized:1 particular:2 must:2 account:1 ma:3 equation:1 remain:1 minimum:1 values:1 transparency:8 concepts:1 following:2 drops:1 spontaneous:20 thermally:1 cited:1 high:2 assumptions:1 numbers:1 occur:1 lamb:1 needs:1 rather:1 describes:2 acts:1 very:1 lamp:1 instead:1 product:1 mar:1 may:4 lax:1 physik:2 dynamical:1 light:18 correspond:2 fundamental:2 definitions:2 order:1 typical:8 saturated:2 indeed:3 over:1 mainly:1 machida:1 years:1 thermal:12 lasers:12 still:2 excitations:2 derive:1 lc:1 located:1 scully:1 fig:4 dubois:1 maximal:1 greater:1 material:1 diodes:10 walls:1 half:4 now:1 easily:1 february:1 always:2 drop:1 γ2n:1 2d:1 sufficiently:1 magnitude:1 mode:5 2b:1 electrically:3 entirely:1 characterized:1 referred:1 disregarding:1 significantly:1 energy:2 frequency:2 measure:2 quantum:4 operation:3 beyond:1 factors:1 since:6 rev:4 semiconductor:12 shows:1 turning:1 theory:3 8b:1 8c:1 8a:1 8d:1 quite:1 nth:2 estimate:1 milburn:1 definition:2 βv:1 interaction:1 derivation:1 could:1 transition:1 days:1 times:2 technische:1 place:1 consequence:1 major:1 ff:1 relate:1 variables:1 number:50 directly:1 reached:1 size:4 given:6 necessarily:1 introduction:1 approximately:3 their:1 assumption:5 rates:1 observations:1 part:1 eliminated:2 than:19 holland:2 depends:1 matter:2 determined:1 providing:1 fluctuation:9 ann:1 spectrum:1 clearly:1 relatively:1 mechanism:1 note:2 internal:1 though:1 reach:1 most:1 germany:1 device:6 analytically:1 fluctuate:1 δn2:2 considered:1 average:2 optical:2 principle:1 schulz:1 physics:1 notion:1 fact:2 slope:2 shot:1 show:2 τsp:18 threshold:43 line:1 ratio:4 parameters:4 should:1 only:2 black:2 factor:11 achieve:2 do:1 get:1 express:1 dt:3 adiabatically:3 processes:1 arxiv:1 twice:2 fixed:1 qn:3 body:1 requirement:2 statistical:1 lifetimes:1 j1:4 relative:2 intensity:2 eliminating:1 close:1 definitely:1 fails:1 yamamoto:1 missing:1 µm:1 dlr:1 pump:1 jth:12 between:5 progress:1 approach:1 terms:4 nature:1 importance:2 emitted:1 however:3 fluctuations:19 distinguish:2 suggested:1 both:2 instant:1 equal:1 quantization:1 stuttgart:1 contribution:1 expression:1 finds:1 cm:1 point:3 corresponds:2 respect:2 2nt:6 described:1 px:1 been:2 reduction:2 much:5 basic:1 ph:1 box:1 corresponding:2 excita:1 photon:42 coherent:1 those:1 case:1 laser:43 pacs:1 value:1 will:3 near:1 viii:1 situation:1 property:2 procedure:1 resolved:1 adjusts:1 almost:1 tions:1 reads:2 currents:2 different:1 radiation:1 indistinguishable:1 stimulated:5 quant:1 units:1 physical:1 higher:1 effect:1 possible:2 purpose:1 lower:3 nevertheless:1 arising:1 less:3 obtain:1 sources:2 hess:1 density:1 photons:2 conclude:1 seems:1 wiseman:2 identical:1 radiator:1 read:2 louisell:1 breaks:1 term:1 early:1 immediately:1 meaning:1 loss:1 reduces:1 δn:7 works:1 stationary:3 often:1 back:1 moreover:1 vol:2 cavity:12 efficiencies:1 assuming:1 2a:1 noise:20 reasonable:2 acronym:1 2c:1 agreement:1 originated:1 properties:6 discussed:1 dependence:2 o:2 wolf:1 equally:1 into:2 down:1 arecchi:1 einstein:1 amsterdam:2 statistics:4 institut:1 springer:1 question:1 long:1 conservation:1 handbook:1 low:2 was:1 naturally:1 function:6 medium:8 north:2 complete:1 but:1 volume:1 pfaffenwaldring:1 link:1 gain:9 injection:7 coupling:2 made:2 intuitive:1 characteristic:2 inside:1 ωr:9 devices:3 ur:1 below:3 limit:2 emissions:1 pumped:3 demonstrate:1 defined:4 ah:1 contribute:1 general:1 single:3 ar:1 formulation:1 lifetime:4 defines:1 dotted:1 no:1 field:5 valid:5 nt:26 conclusion:1 excitation:14 generated:2 studied:1 risken:1 ago:1 regime:5 longer:1 required:2 berlin:1 time:1 requires:2 original:1
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quant-ph9903018.txt |@word partial:17 consider:7 activated:1 results:11 four:3 generalize:4 computation:1 amplified:1 fmrx:1 whose:1 amplification:1 violate:1 disposal:2 tr:1 send:1 thapliyal:1 estructura:1 spain:1 under:3 worth:1 ingredient:1 supported:1 departament:1 ρta:3 rise:2 none:1 mixing:2 condition:6 partitions:3 leads:1 level:4 turns:1 large:1 eigenvalues:1 round:2 lewenstein:3 deutsch:1 murao:1 second:3 concludes:1 greenberger:1 even:2 abc:2 phaseshift:1 analogously:1 above:3 new:2 satisfy:1 bruß:1 full:1 respectively:4 teleportation:2 here:2 understanding:2 respect:18 change:3 convert:2 institute:1 allows:2 simultaneous:1 resulting:2 hospitality:1 via:1 projection:1 family:7 extra:2 brought:1 austria:1 analyzing:1 apply:4 readily:2 use:2 proceed:1 would:2 prove:1 remains:1 positive:15 contains:1 negative:9 ψj:6 ψk:1 noting:1 therefore:5 type:1 more:3 linden:2 organized:1 operators:1 particular:2 known:2 cases:1 must:2 states:54 keeping:1 science:1 der:1 work:1 ρn:5 values:2 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quant-ph9903019.txt |@word dewitt:2 consider:4 remarkable:2 rev:3 davies:1 results:2 illustrated:1 eds:1 scalar:11 contributions:2 whose:2 bremsstrahlung:1 calculate:1 equivalence:2 finally:2 does:1 excluded:1 x02:2 x01:2 include:1 straightforward:1 casadio:3 frequencies:1 wave:4 every:1 difference:1 condition:2 leads:1 x0i:2 hamiltonian:2 did:1 notes:1 tanh:3 list:1 solution:1 small:4 upper:1 force:4 zi:1 mi:6 divergencies:1 cosh:12 second:2 value:1 further:2 sum:1 uniform:1 poles:1 above:7 increasing:1 degree:3 respectively:1 desired:1 smearing:1 sinh:6 along:1 change:7 obtained:4 2aτ:1 generalizing:1 study:1 survey:1 action:1 changes:1 examining:1 via:1 followed:1 requiring:1 imagine:1 modifying:1 decrease:1 planck:2 unit:3 use:2 identifies:1 positive:3 negative:1 few:1 nucl:1 ψi:12 m1:4 therefore:2 m2:6 possible:1 more:1 separated:1 flat:1 israel:1 giovanni:1 odinger:1 validity:1 transient:1 particular:3 hole:13 analogous:1 must:2 zi2:1 equation:2 mn:1 oscillator:2 modified:1 mp:1 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quant-ph9903020.txt |@word secondly:1 consider:2 represent:2 crucial:1 derr:2 existing:1 scalar:9 generalize:2 edu:2 expressions:1 contributions:1 issues:1 depend:1 calculate:2 interact:2 preserved:2 under:2 maryland:2 p2:7 schrieffer:1 very:1 plaga:1 wave:2 electron:1 replaces:2 every:1 condition:4 irreducible:1 erratum:1 angelis:1 small:2 khalatnikov:1 upper:1 demille:2 direct:1 odd:5 linear:1 even:3 established:1 appear:1 brackets:1 cycle:1 sum:3 celebrated:1 d3:2 experiment:2 above:1 new:3 body:2 degree:1 respectively:1 equals:1 here:3 atoms:4 mev:1 separation:1 address:2 equations:1 change:2 baron:1 antisymmetric:7 changed:1 products:2 permutation:4 anticommutators:1 composed:1 emerge:1 replace:1 neutrons:2 amherst:3 apply:1 linearly:1 use:1 takes:1 commun:2 probabilities:2 positive:1 contains:1 tightly:1 few:1 taken:1 type:2 theoretical:1 more:4 preserving:1 composite:13 operators:20 inguscio:1 ramberg:3 cases:3 analogous:1 must:6 md:1 ma:1 henri:1 recall:1 der:2 work:1 protons:2 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quant-ph9903021.txt |@word partial:1 consider:8 chain:1 lagrangian:1 results:1 four:4 eds:2 scalar:2 sci:1 scr:2 devoted:1 whose:1 depend:2 tr:4 quasi:1 preserved:1 under:2 p2:9 frequencies:2 connects:1 induce:1 wave:16 summarized:1 husimi:2 difference:1 matrices:5 deformations:2 condition:1 treating:1 smithey:1 hamiltonian:16 irreducible:5 leave:2 discrete:1 vector:7 indices:4 dealing:1 past:1 dynamics:7 implemented:1 canonical:9 established:1 appear:1 invertible:4 brackets:6 section:7 labeled:3 expressed:1 below:1 bαβ:1 lifshitz:1 international:2 consisting:1 submitted:1 degree:1 component:1 here:3 diagonal:4 canonically:1 hki:1 groups:1 represented:1 along:1 equations:7 obtained:2 scienze:1 institute:1 study:2 vectors:4 completely:1 δqq:1 poisson:5 stressed:1 usually:1 hospitality:1 quotient:1 mimicked:1 formulated:1 projection:2 family:3 extra:1 marginal:11 namely:1 vii:1 plenum:2 till:1 austria:2 ipq:2 ipu:1 summation:3 univ:1 relating:1 seligman:1 use:3 takes:2 would:1 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quant-ph9903024.txt |@word monte:7 consider:4 interference:20 excellent:2 theoretical:1 results:21 leads:1 ghrist:1 scalar:1 generalize:1 per:1 broader:1 consists:1 expressions:1 research:1 increase:2 calculate:1 sinatra:1 γt:1 environment:1 topic:1 according:3 th:1 under:3 analogous:2 worth:1 norm:1 applied:1 g4:1 orthogonal:1 very:7 rise:2 springer:1 wave:2 every:1 2γt:2 experimentally:1 emphasized:1 difference:8 exact:17 condition:1 dominate:1 presented:1 positions:6 t2:3 solution:13 t0:14 occurs:2 large:3 2κt:1 small:15 optics:1 equation:2 prevent:2 ruostekoski:1 dilute:1 slower:1 lewenstein:1 consistent:1 literature:1 approximation:21 generalisations:1 rate:5 timescales:2 value:8 substitutes:1 carlo:7 substitute:1 even:7 established:3 what:1 nonlinear:1 plays:1 section:7 analogously:1 expressed:1 find:4 access:1 above:1 new:1 acknowledgments:1 contrast:1 satisfy:1 condensed:1 full:1 simultaneously:1 κk:1 respectively:3 never:1 here:2 atoms:87 andrews:2 based:1 change:1 obtained:8 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quant-ph9903025.txt |@word slope:2 consider:1 snyder:3 results:3 leads:1 reinserting:1 mesons:2 contributions:1 reasoning:1 localized:2 feeding:2 depend:2 violate:1 integral:1 re:1 spin:1 preserved:1 under:4 tf:2 analogous:1 te:1 indicating:1 divergent:1 applied:3 provides:1 orthogonal:3 very:2 rise:2 translations:4 wave:1 dummy:1 normalizability:1 electron:1 repulsion:3 affect:1 exact:4 condition:2 treating:1 disturb:2 steeper:2 quantized:8 presented:1 positions:7 solution:2 t0:1 correct:1 try:1 assignments:1 convenience:1 differential:4 manifestly:1 eigenvalues:2 drop:1 regain:1 smaller:3 force:5 m4:1 oscillation:8 insignificant:1 consistent:4 d3:1 direct:2 approximation:10 imply:3 pass:1 further:4 dynamics:7 xf2:1 substitute:1 obey:1 even:3 established:2 xψ:1 nonlinear:4 giving:2 section:1 interactions:1 analogously:1 uniform:1 cell:2 version:1 en:2 tenable:2 above:2 method:3 increasing:3 consisting:1 satisfy:2 exchange:10 pushing:2 component:5 atoms:1 ranges:3 believed:1 objects:22 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