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quant-ph9809016.txt |@word magnetic:4 four:2 consists:4 relationships:1 whose:11 violate:5 swap:2 under:1 worth:2 digit:2 rise:1 differently:1 tantalizing:1 experimentally:1 vast:1 squares:1 suffices:3 conceive:1 solution:6 convenience:1 vector:25 indices:1 deutsch:4 consistent:1 estimates:1 direct:2 pulse:1 ǫn:3 approximation:2 likely:8 complicates:1 qualitatively:1 implemented:2 machines:2 even:17 errors:16 iterating:1 euclidean:1 selected:1 negates:1 decoding:4 reconstruction:3 designing:1 new:17 ever:2 consisting:3 simultaneously:2 reliably:3 never:1 preserves:1 here:6 hundreds:1 pratt:1 represented:3 calculate:1 digits:2 items:1 leaves:1 changed:2 approaches:2 reports:1 credit:1 permit:1 couple:1 fourier:43 changes:6 cancellation:1 appropriately:1 secure:3 tensored:2 explained:5 highly:2 visible:1 e4:2 brams:1 total:1 unit:8 plot:1 would:14 likelihood:1 chooses:1 call:1 therefore:8 recommend:1 25th:1 type:1 until:4 fractions:3 conclusions:1 odinger:1 reversibly:1 berlin:1 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quant-ph9809020.txt |@word represent:1 consider:4 ali:1 rev:3 results:5 leads:1 eds:1 ga:2 consists:1 expressions:5 commentaries:1 devoted:4 kowalski:2 inverse:1 depend:2 tn:14 finally:7 spain:2 under:4 analogous:1 te:1 case:14 belonging:2 supported:1 straightforward:2 orthogonal:1 far:1 none:1 wave:3 corollary:2 every:1 dispersions:1 nieto:1 difference:1 entire:6 obvious:1 immediately:1 presented:1 try:1 discrete:2 convenience:1 progress:1 quasiperiodicity:1 equation:2 zn:1 smaller:2 det:1 za:6 nski:1 approximation:1 go:11 canonical:1 even:3 aim:1 plays:1 minimize:1 d2:1 section:11 lengthy:2 version:1 above:1 values:29 method:3 compactness:1 compact:1 whose:1 rembieli:1 equals:1 here:6 understanding:1 behaviour:7 simon:2 eikz:1 making:3 represented:1 quite:2 equations:2 z2:1 ωa2:3 obtained:9 search:1 study:11 studied:2 allows:1 krieger:1 experience:1 suggests:1 periodic:10 published:2 usually:1 suitable:3 orthonormality:1 regardless:2 projection:2 family:10 put:1 iz:1 apply:1 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quant-ph9809021.txt |@word vila:2 consider:1 extensively:1 leads:2 quadrature:1 contributions:1 relationships:1 whose:2 inverse:2 aug:1 alamos:1 technique:1 quasi:1 spain:1 applied:1 amplitudes:1 wave:1 witten:2 socorro:1 nieto:1 hussin:1 hamiltonian:1 transmission:1 solution:15 dealt:1 subindex:1 deleting:1 sukhatme:3 zero:3 dynamics:1 even:1 nonlinear:5 appear:1 henceforth:1 above:2 obvious:1 method:6 led:1 respectively:1 nena:1 here:1 nodeless:1 ansatz:1 alone:1 equations:4 logarithmic:2 obtained:1 instituto:1 wλ1:1 superpotential:2 fernandez:2 equivalence:1 family:2 univ:1 derivatives:1 use:1 finally:2 nucl:2 archives:1 type:2 more:2 furthermore:1 solitons:1 particular:7 known:4 fermionic:4 springer:1 equation:7 work:2 oscillator:1 values:1 following:3 my:1 example:2 stimulating:1 performed:1 dwp:1 darboux:7 discussion:1 write:4 samsonov:2 dwg:3 instead:1 parameter:6 simplicity:1 may:4 wg2:3 singularities:1 fj:2 correspond:1 wishes:1 so:1 enter:1 order:4 interpretation:1 mielnik:4 duke:1 pointed:1 dv:1 its:2 le:1 thank:1 ln:7 gto:1 derivative:1 supersymmetry:1 susyqm:3 combination:1 bernoulli:1 noticing:1 now:1 name:1 mode:2 found:1 differential:2 energy:2 haley:1 obtains:1 quantum:5 out:1 factors:1 wλ:1 nuovo:3 since:1 rev:6 reader:1 math:4 ısica:1 free:4 cari:1 khare:2 pairs:1 inspection:1 iterative:1 turn:1 u20:2 universidad:1 davis:1 first:2 another:1 electronic:1 given:1 guanajuato:1 introduction:1 unknown:1 eqs:1 system:3 their:2 returns:1 bagrov:1 scheme:1 unbroken:2 relationship:1 part:1 somewhat:1 x2:2 x3:2 x1:2 than:1 double:2 iteration:1 second:1 limiting:1 project:1 symmetries:1 ann:1 generalization:1 distorted:1 intertwining:1 seen:2 any:5 note:1 potential:5 salle:2 multiple:1 shall:1 4u0:1 collaboration:1 riccati:19 most:1 why:1 considered:1 hierarchical:1 principle:4 abraham:3 physics:1 fact:1 dover:1 show:1 supported:1 solutions:5 ground:4 based:1 parameters:2 appended:1 written:5 should:1 analytic:1 only:2 factor:1 moses:3 borrowed:1 do:1 goes:1 notation:1 get:1 dependent:1 de:2 stop:1 dx:8 dy:1 combinations:1 procedures:1 freedman:1 arxiv:1 factorization:3 summary:1 common:1 fixed:2 cimento:3 unpublished:1 j1:1 see:4 w3:6 w2:5 w1:4 w0:1 terms:2 review:1 marmo:1 state:4 between:1 invariant:5 subscript:1 wg:5 notice:3 triplet:1 recently:1 matveev:2 however:1 wp:8 last:1 called:3 connection:3 apdo:1 schroedinger:5 reasons:1 continuation:1 harmonic:1 dimensional:1 respect:1 writing:1 considering:1 pv:1 transformations:1 basis:1 due:1 been:5 pb:1 workshop:1 ph:4 generating:1 supersymmetric:2 covariance:1 kw1:1 optics:1 those:1 case:3 pacs:1 employ:2 ǫu:1 report:1 property:1 procedure:4 mexico:1 thus:3 susy:3 partner:3 author:3 make:1 same:4 quant:4 gets:1 independent:1 used:3 i0:9 hand:1 v3:1 purpose:1 potentials:6 normalization:1 recent:1 reflection:1 well:3 without:1 parametric:3 burgos:1 less:1 obtain:2 reviewed:1 λj:1 λi:2 scattering:1 previous:1 postal:1 character:1 simple:2 other:2 conacyt:1 lett:3 rosu:8 transformation:2 identical:1 possible:2 admitting:1 using:2 unique:1 mod:1 like:1 follows:3 manifest:1 either:1 arbitrary:3 works:1 mathematical:1 because:1 methods:2 deal:1 sequence:1 moreover:1 confusing:1 provided:1 cooper:2 lead:1 integration:2 asking:1 prof:1 rep:1 step:3 although:1 dictated:1 carried:1 constraint:2 introduced:1 therein:1 into:1 within:1 integral:1 three:2 down:3 references:2 isospectral:6 bosonic:5 λj2:2 λj1:1 strictly:4 initial:4 u0:7 los:1 way:1 was:1 therefore:1 function:3 boya:2 form:5 but:1 construction:2 hb:2 true:1 adler:2 partially:1 directed:1 up:1 us:1 problem:1 display:1 mechanics:3 fulfills:1 constant:1 worthwhile:1 int:1 am:2 general:12 families:1 functions:1 no:2 whereas:1 when:1 book:1 details:1 theor:1 superposition:5 june:1 variable:1 2d2:3 original:1
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quant-ph9809022.txt |@word volta:1 measurements:1 partial:1 consider:2 helstrom:1 tamagawa:1 amplifier:1 results:2 entropy:17 grateful:1 research:2 row:1 certainly:1 amplification:2 calculate:1 z1t:2 environment:6 tk:11 under:1 analogous:1 tr2:1 case:4 far:1 conjectured:1 isomorphism:1 matrices:2 condition:2 impressive:1 presented:1 transmission:2 irreducible:2 notes:1 large:1 vector:9 eigenvalues:3 trr:1 optics:1 computation:1 second:1 rigorous:1 further:2 linear:3 aim:1 subadditivity:1 diag:2 section:2 agrees:1 abs:2 above:2 new:1 reynaud:1 acknowledgments:1 contrast:1 satisfy:3 degree:2 exchange:3 component:1 here:2 represented:1 z1:12 z2:12 obtained:1 sending:3 algebra:1 institute:1 study:3 studied:1 survey:1 schumacher:1 action:1 hospitality:1 via:1 ipj:1 diagonalizable:2 should:1 unit:1 use:5 feb:1 distinct:1 positive:2 negative:2 transactions:1 call:2 therefore:1 ip:1 mysterious:1 reflects:3 more:1 initiated:1 becomes:1 operators:6 interaction:1 particular:4 known:1 negativity:1 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quant-ph9809024.txt |@word limited:2 since:2 discards:1 caused:3 particular:2 splitting:1 existing:1 avalanche:1 code:2 c2:1 consists:3 perturbations:1 research:1 correc:1 weakly:1 devoted:1 whose:3 amplification:11 disposal:1 deterministic:1 acting:1 send:2 created:1 supported:1 finally:1 prolonging:2 device:3 protocols:4 th:4 analogous:1 attenuated:1 worth:1 sent:3 case:12 digit:3 probe:1 string:4 confidential:1 orthogonal:4 very:2 choice:2 polystyrene:1 trouble:1 parameter:6 electronics:2 dim:1 reciprocal:1 presented:1 transmission:14 positions:5 notes:2 eve:25 occurs:1 large:1 admissible:1 phase:4 small:8 relation:2 path:1 shows:2 optics:2 equation:2 prevent:2 smaller:1 lenz:1 10m:1 jungnickel:1 tolerate:3 d3:2 boca:1 literature:1 second:13 cost:1 design:1 pass:5 rigorous:1 further:1 implemented:2 machines:1 even:5 employ:1 material:5 errors:7 appear:2 apparatus:1 impasse:1 section:2 selected:7 while:2 agrees:1 current:1 abs:5 suspect:1 above:5 utkenhaus:3 shared:11 3a:1 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quant-ph9809028.txt |@word limited:5 externally:1 measurements:2 sci:1 represent:1 caused:1 garching:1 computation:4 follow:1 factorizing:1 devoted:2 whose:3 depend:1 alamos:1 technique:2 tr:19 young:1 factoring:1 tr1:5 tr2:5 applied:4 advantage:3 very:1 frequencies:1 conditions:1 electron:1 manipulated:1 experimentally:1 emphasized:1 exact:1 level:1 positions:1 solution:1 standards:3 large:6 differential:1 small:4 ueda:3 optics:1 force:1 miller:1 htm:1 pulse:8 rate:1 invention:1 further:1 kitagawa:2 even:2 what:1 advantageous:2 clock:2 selected:3 labeled:1 current:1 version:1 fortschritte:1 above:2 shared:1 avenues:1 method:3 contrast:1 here:1 atoms:10 ramsey:13 focused:4 address:1 ratio:2 strong:2 appears:1 obtained:1 spite:1 institute:2 study:1 goldwasser:1 step:1 accomplished:5 resulting:1 resonance:1 implement:2 fourier:1 makes:1 york:1 composed:1 useful:2 projection:2 stray:1 requiring:2 offset:1 apply:2 total:3 univ:1 planck:1 sympathetic:1 use:8 superpositions:1 would:4 army:1 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quant-ph9809029.txt |@word consider:5 dynamic:1 results:1 leads:1 computation:1 edu:1 query:13 sin2θ:2 technique:2 finally:1 helps:1 th:9 under:1 norm:1 orthogonal:3 very:2 induce:1 print:2 difference:3 exact:1 notes:1 list:6 solution:1 fewer:1 item:6 vector:11 caltech:1 upper:6 focs:1 sign:1 zero:1 substituting:1 implemented:1 appear:1 section:1 axes:2 fortschritte:1 above:1 new:1 margolus:1 led:1 respectively:1 component:8 desired:4 selective:1 separation:2 along:2 change:2 extreme:1 vazirani:1 search:14 involved:1 elaborate:1 vectors:19 approaches:1 amount:4 changes:1 elaborated:1 apr:1 total:1 unit:10 use:1 takes:1 would:2 army:1 positive:2 therefore:8 becomes:5 aware:1 rigid:1 normalized:2 known:2 weaknesses:1 der:1 work:1 grover:4 values:1 concepts:1 following:6 root:1 proof:12 weaker:1 figure:4 give:1 calculation:2 beals:1 bennett:2 states:2 minimum:1 refine:1 guarantee:1 needs:3 quantph:1 holds:2 how:2 optimal:4 parameter:1 sin:11 brassard:2 may:1 after:4 derived:1 produce:2 physik:1 improving:1 parallel:5 attempt:1 summing:1 complexity:1 so:1 order:7 office:1 developed:2 over:1 years:2 paper:3 through:5 mentioned:1 satisfies:1 y2:2 before:6 chosen:1 writing:1 systems:1 main:1 alter:1 return:1 greater:1 material:1 bound:21 framework:1 they:6 rotation:2 now:1 2t:1 easily:1 dirac:2 ensemble:4 possibilities:3 magnitude:1 each:3 2n:19 referred:1 square:1 retrieve:1 idea:3 related:2 measurement:1 quantum:23 operation:3 out:4 maximizes:1 shown:2 space:3 quantify:1 since:4 rev:1 research:1 increase:3 maximized:1 denoted:4 lecture:2 induction:2 shows:5 earlier:1 theory:1 given:1 standard:2 labs:1 reason:1 remainder:1 could:1 computers:2 length:1 first:5 zal:3 initial:1 manuscript:1 number:2 improvements:1 relations:2 precisely:4 zalka:2 differ:9 introduction:1 system:3 least:7 their:4 intermediate:1 too:1 calculations:1 siam:1 john:1 final:1 gives:1 hoyer:1 behind:1 needle:1 part:1 somewhat:1 x2:1 than:4 cosθ:1 showed:1 accesses:1 determined:1 identical:1 pre:2 say:2 close:1 need:3 seen:1 clearly:1 nents:1 note:1 take:1 finding:1 algorithms:1 strengths:1 calculus:1 multiple:1 compo:1 most:4 fore:1 phase:2 acknowledgements:1 intrinsic:1 why:2 clear:1 later:1 proceedings:1 refining:1 mechanical:5 particularly:1 show:3 supported:1 attempts:1 relation:1 solutions:1 subtle:1 find:1 tapp:1 based:1 shuffling:1 state:12 should:1 lemma:6 only:3 indeed:2 attained:1 bernstein:1 oct:1 do:1 notation:2 cannot:1 despite:1 stoc:3 evolution:1 expansions:1 tth:3 queries:16 ponents:1 fixed:1 reference:3 com1:1 undergoes:1 frame:1 bounds:3 relative:2 differs:2 see:1 computer:4 result:4 simultaneously:2 subject:1 subsequent:1 written:1 various:4 between:5 terms:2 initially:3 however:1 distinguish:1 improve:2 suggested:1 both:4 cos:8 last:2 many:2 taking:1 according:1 contract:1 context:1 com:1 comes:2 bell:1 simple:2 asymptotically:1 dimensional:2 pol:2 anti:2 considering:1 described:1 transformations:2 due:1 been:1 ph:6 choose:1 corresponding:4 observe:2 θt:10 case:3 value:2 will:12 items:2 property:1 real:1 unitary:3 surprisingly:1 equal:5 converts:1 different:6 develop:1 make:1 same:6 any:7 complex:1 quant:6 units:2 several:1 development:1 erence:1 used:3 http:1 upon:1 effect:1 v3:1 tighter:3 lower:5 charlie:1 without:2 boyer:1 components:9 coordinate:1 just:6 less:1 being:2 obtain:1 transforms:1 immediately:1 patel:1 point:1 spread:15 lett:1 theorem:21 haystack:1 remaining:1 resolved:3 mos:2 possible:5 increases:2 using:7 apoorva:1 follows:4 steps:3 become:2 preskill:2 classical:1 people:1 some:2 searching:4 choosing:2 specified:1 proofs:2 happens:2 orthonormal:1 inequality:4 journal:1 step:7 variation:1 properties:1 simpler:1 chapter:1 about:1 constraint:1 prove:3 o:8 mutually:1 range:1 unsorted:2 slightly:2 own:1 into:1 within:1 refines:1 three:2 references:1 elementary:1 refined:1 additional:1 prepare:1 there:3 fast:3 pages:1 lov:1 way:1 was:5 considerably:1 but:3 lows:2 maximum:3 quantitatively:1 limit:1 highlight:1 problem:3 mechanics:2 lanl:2 proved:6 computing:2 defined:2 certain:1 denote:3 proves:1 mosca:1 no:5 when:7 tight:1 other:4 papers:1 gro:3 christof:1 deviation:1 time:1 problems:2 polynomials:2 bounded:3 sides:1 implies:1 algorithm:10 4t:5 required:3 equivalently:1 portion:1 searched:1 oracle:2 requires:2 original:1
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quant-ph9809030.txt |@word represent:2 footing:1 consider:3 suggests:1 alternatives:2 results:10 four:1 known:1 scalar:1 gb:1 ga:1 talks:1 follow:1 moon:1 localized:13 devoted:1 whose:2 repetition:2 const:1 calculate:1 yngvason:2 nonlocal:2 gromes:3 indicate:1 under:2 analogous:2 norm:2 case:4 straightforward:1 far:4 implicitly:1 translations:1 springer:2 wave:10 experimentally:2 difference:2 condition:1 usp:1 clouds:3 hamiltonian:4 transmission:1 ref:5 notes:1 large:5 vector:6 eigenvalues:1 optics:1 noted:2 solutions:1 application:2 approximately:1 james:1 direct:1 sign:1 past:1 zero:6 concludes:1 rigorous:2 further:1 spectral:3 what:3 nonlinear:1 appear:1 section:1 interactions:1 brief:1 expressed:1 find:2 current:1 experiment:1 above:6 new:5 slabs:3 counters:1 compact:1 notions:1 implying:1 exchange:1 never:2 equals:1 here:2 atoms:4 heitler:1 desired:1 simon:1 separate:1 others:1 represented:1 consideration:1 strong:3 equations:1 change:1 ensembles:1 great:1 involved:1 larger:1 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quant-ph9809031.txt |@word gw:7 gv:16 sch:7 particular:1 results:4 leads:2 commute:1 expressions:2 gl:1 consider:4 increase:1 etching:1 tv:7 tw:9 answered:1 indicate:1 those:1 under:1 include:1 case:1 amplitudes:2 presently:1 g0:10 very:2 translations:1 induce:1 wave:6 figs:1 experimentally:1 matrices:1 impressive:1 hamiltonian:3 transmission:6 issue:1 large:3 tang:1 pˆ2:1 science:1 small:6 optics:5 dimer:5 smaller:6 second:7 value:2 insertion:1 incidentally:2 further:2 estimated:1 alt:2 even:5 what:1 appear:1 section:5 above:2 learned:1 increasing:2 consisting:1 body:7 edited:1 outgoing:1 modify:2 here:2 atoms:6 directions:1 µev:1 equations:5 change:2 obtained:2 incoming:2 technical:1 until:1 changed:1 allows:1 resulting:1 pick:1 decouple:1 plotted:1 diameter:3 ekstrom:2 private:1 esry:1 visible:1 turchette:1 summation:1 apply:1 counts:2 total:4 planck:1 use:4 hegerfeldt:2 would:3 breakup:5 contains:1 negative:1 nonsymmetric:2 next:1 few:5 nucl:1 therefore:1 taken:5 goettingen:2 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quant-ph9809033.txt |@word four:4 controversial:3 consists:1 poorly:1 relationships:3 whose:5 auc:2 presents:2 under:2 worth:1 alternating:1 void:14 connects:1 every:3 encounter:1 solution:2 vector:9 guiding:1 force:1 consistent:2 bubbling:1 direct:1 surrounding:2 second:5 rigorous:1 implemented:1 expressive:1 even:7 neo:1 specification:3 revolves:1 near:1 above:11 supplies:1 increasing:1 evolving:1 simultaneously:8 never:1 residual:1 here:15 granularity:1 represented:2 path:1 quark:1 interpret:1 obtained:2 changed:3 changes:8 divide:1 explained:1 replace:1 glance:1 total:1 unit:1 charge:8 would:2 coins:8 call:7 therefore:5 tell:1 separated:1 hold:1 must:10 work:1 theories:3 lincei:1 guise:1 example:2 indicated:2 give:2 relativistic:2 stressing:1 indicates:3 end:7 provide:3 verify:1 machine:1 how:18 adjacent:1 answer:5 ordinary:1 preferable:1 abstraction:9 description:3 turing:2 ladder:9 after:4 diagram:2 misfit:1 law:1 parallel:1 types:1 attempt:4 third:4 helsinki:1 baggage:1 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quant-ph9809035.txt |@word magnetic:7 consists:2 whose:7 calculate:1 paris:1 under:2 γa:8 worth:1 every:5 figs:4 experimentally:2 34a:1 34b:1 34c:1 solution:1 vector:42 ueda:6 heidmann:2 force:3 direct:1 pulse:7 approximation:4 second:18 tangential:1 implemented:1 even:3 employ:1 errors:5 ˆu:1 ˆz:7 selected:1 ˆa:2 ˆf:1 ˆi:4 increasing:1 ˆn:2 27a:1 27b:1 27c:1 evanescent:1 never:10 here:4 atoms:174 ionization:2 obtained:15 sjx:2 sjy:1 study:1 eiδt:1 projection:2 replace:1 brought:2 unitary:5 counts:1 total:7 linearly:1 plot:4 would:2 negative:6 call:1 therefore:15 type:3 glass:1 excellent:2 must:7 me:1 ih:2 setup:1 γf:9 dn2:2 example:7 give:2 organized:1 indicates:6 degenerate:1 magnitudes:2 feasible:1 provide:1 how:3 isotropic:3 minimums:1 replacing:2 after:2 third:4 imα:2 correlation:1 acknowledges:1 order:21 satisfied:1 oven:3 affect:3 japan:3 satisfies:3 before:1 37a:3 37b:1 exhibits:1 tilts:1 fig:56 schmidt:1 bunching:1 maximal:2 them:4 combination:2 pegg:4 heinzen:3 diodes:1 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quant-ph9809037.txt |@word ideality:2 code:12 schumaker:1 consider:6 represent:1 rev:8 varying:1 ptc:1 results:1 leads:1 computation:4 assessment:1 consists:1 causes:3 amplification:1 calculate:1 antinode:1 illustrates:1 γt:1 environment:2 finally:1 under:4 applied:1 amplitudes:3 straightforward:1 orthogonal:6 very:3 choice:2 difference:1 exact:2 condition:2 υl:1 school:1 υk:4 level:2 suffices:2 solution:1 damped:1 large:4 small:7 markov:1 optics:4 force:3 insignificant:1 variables:1 pulse:1 approximation:1 zero:5 summer:1 dynamics:2 implemented:1 odd:9 linear:4 even:11 what:1 errors:3 appear:3 advantageous:1 giving:1 interactions:1 remain:2 above:4 3b:1 3a:1 increasing:2 method:6 satisfy:1 supporting:1 evolving:2 led:1 degree:2 respectively:2 here:1 desired:3 test:1 others:1 ratio:4 appears:1 change:1 antisymmetric:1 shift:2 leaves:2 reason:1 amount:4 knill:1 implement:3 king:2 appropriately:1 via:1 useful:3 although:2 extra:1 9a:4 9b:3 logical:26 apply:1 manipulate:1 standing:1 use:5 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quant-ph9809040.txt |@word consider:2 holthaus:1 magnetic:3 global:1 results:6 island:2 microwave:2 grateful:1 follow:1 issues:1 whose:1 depend:1 subjected:1 canonical:1 quasi:1 does:1 indicate:2 under:4 stochastic:3 presentation:1 indicating:1 case:9 conjecture:1 consequently:1 very:1 frequencies:1 rise:2 springer:2 wave:4 lyapunov:6 kcr:2 experimentally:2 difference:1 vast:2 inset:4 squares:1 steeper:1 hamiltonian:1 positions:1 large:2 arndt:1 small:1 hcm:1 optics:4 challenge:1 upper:5 smaller:1 force:1 oscillation:1 consistent:1 located:1 zero:5 displays:1 chen:1 further:1 dynamics:8 implemented:1 situated:1 haake:1 even:1 plays:2 trivial:1 experiment:9 localized:1 above:6 new:1 abele:1 contrast:3 kicked:3 evanescent:3 behavior:1 respectively:3 here:6 atoms:11 2kg:2 focused:1 κz:1 address:3 represented:1 along:3 equations:2 logarithmic:1 obtained:3 spite:1 study:1 larger:3 allows:1 approaches:1 reports:1 later:1 suggests:1 resulting:1 sokol:1 published:1 cesium:1 della:1 changes:2 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quant-ph9809043.txt |@word secondly:1 partial:1 consider:6 results:5 leads:1 ciudad:1 generalize:2 computation:4 consists:1 faster:1 fmrx:1 forget:1 increase:1 depend:1 knill:5 subjected:1 tr:13 misses:1 environment:4 finally:2 does:4 present:1 th:3 under:1 analogous:1 include:1 norm:8 case:17 worse:2 straightforward:1 very:1 rise:1 connects:1 primed:1 worst:2 decompostion:1 specific:1 difference:1 exact:3 condition:2 four:4 wolfgang:1 presented:1 discrete:1 vector:1 science:2 small:3 equation:1 proof:11 solutions:1 upper:11 smaller:1 fout:2 deutsch:2 10b:4 10a:3 maximization:3 α2n:1 matrices:1 second:4 enclosed:1 rigorous:1 dynamics:4 implemented:2 repeaters:1 theory:2 even:6 errors:27 xor:1 apparatus:1 projectors:1 section:8 sequential:1 3n:4 above:3 expresses:2 increasing:5 equivalent:1 satisfy:2 erb:1 degree:1 respectively:1 error:16 teleportation:2 here:4 diagonal:10 following:5 plenio:1 free:4 others:2 consideration:1 equations:1 imperfections:2 interpret:1 every:2 remark:1 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quant-ph9809044.txt |@word secondly:1 emch:1 consider:6 aids:1 magnetic:1 lack:2 amplifier:4 results:7 roy:1 computation:1 expressions:7 sch:1 whose:1 certainly:1 calculate:6 concerned:1 shanghai:3 james:1 finally:2 squeezing:11 those:3 th:1 include:1 pte:2 case:2 eigenstate:1 comm:1 thermalize:1 very:1 soni:1 rise:2 springer:1 additional:3 husimi:1 nieto:3 difference:1 matrices:2 indicate:1 hamiltonian:3 knight:5 who:1 strayer:1 convenience:1 vector:1 epstein:1 optics:4 related:1 leibfried:1 employing:4 oscillation:1 iα1:2 consistent:10 za:2 literature:5 cosh:9 past:1 imply:1 equal:1 further:2 dynamics:12 iα2:4 canonical:2 index:1 section:9 chaotic:2 expressed:1 find:3 version:1 above:5 new:2 acknowledgments:1 contrast:1 coefficient:1 hasn:1 ibid:1 respectively:3 component:1 here:9 understanding:1 cancelled:1 china:2 sinh:12 address:4 xβ:27 respect:1 z1:2 z2:1 knowledge:1 box:1 great:1 bu:1 studied:3 experience:1 vogt:1 suggests:1 products:1 situations:1 action:5 raab:1 suitable:1 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quant-ph9809045.txt |@word transitions:1 systematic:1 magnetic:3 results:12 four:2 scalar:6 commute:2 edu:1 reson:1 sci:1 consider:1 whose:1 tr:1 corrections:1 αeff:9 finally:2 program:1 indicate:1 present:3 under:11 norm:5 case:22 methyl:1 advantage:2 zhang:1 very:1 frequencies:4 recursively:1 springer:1 induce:1 general:1 difference:2 exact:7 treating:1 entire:1 school:1 4n2:4 positions:1 liss:1 solution:2 convenience:1 vector:1 small:2 chuang:2 specially:1 deutsch:1 dealing:1 consistent:1 equalized:1 sin2:3 pulse:12 approximation:6 zero:1 rigorous:2 further:5 dynamics:3 implemented:2 linear:1 what:1 nonlinear:1 bspin:1 above:7 new:2 net:1 contributes:1 acknowledgments:1 contrast:1 eω1:1 margolus:1 full:1 required:3 compound:1 component:7 residual:3 here:3 desired:3 selective:3 cos2:2 relaxation:1 directions:1 ratio:1 along:7 strong:2 sinc:9 obtained:9 rigorously:1 institute:1 increasing:1 precede:1 amount:1 simultaneous:1 resulting:1 pictorial:1 eigenvalues:2 resonance:43 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quant-ph9809050.txt |@word ibid:6 gt:1 consider:2 magnetic:1 results:2 ξq2:9 entropy:6 computation:1 consists:1 osc:10 contributions:1 als:1 devoted:1 depend:1 calculate:2 producing:1 tr:1 uniqueness:1 squeezing:39 under:1 worth:1 evolves:1 very:2 wave:1 govern:2 experimentally:1 nieto:1 exact:1 condition:4 entire:1 hamiltonian:10 solution:1 deals:1 solved:1 small:2 optics:1 possibility:1 oscillation:3 direct:1 pulse:1 sign:1 second:1 dynamics:2 estimated:1 odd:1 even:3 employ:1 what:1 appear:1 sum:2 version:1 subspaces:5 method:2 simultaneously:1 degree:2 exchange:6 here:4 atoms:2 cancelled:2 ramsey:4 ramon:2 address:1 represented:1 appears:3 change:1 obtained:3 institute:1 involved:1 study:3 studied:2 approaches:1 published:1 suitable:1 changes:1 cancellation:2 plotted:1 examining:1 marginal:4 namely:1 scaled:1 decrease:1 total:2 use:3 prove:1 remains:2 positive:1 hilbert:1 few:1 approach:1 call:1 m0:11 ψl:3 m2:1 permanently:1 type:1 more:2 lowering:1 israel:2 vpr:1 becomes:2 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