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quant-ph9803066.txt |@word saturating:1 consider:1 pointing:1 results:3 leads:4 scalar:1 entropy:1 computation:1 follow:1 expressions:1 latorre:2 compact:1 whose:1 spin:7 finally:3 monotonically:1 spain:1 departament:1 advantage:2 orthogonal:3 rotational:1 every:2 summarized:1 vast:1 four:2 level:3 skills:1 turns:2 solution:16 try:1 solved:1 manifestly:4 smaller:3 second:3 evaluated:1 odd:1 zr:1 linear:1 even:5 ˆr:1 stands:1 brackets:1 giving:1 sum:2 contracted:1 uniform:2 3n:3 above:3 ˆi:3 increasing:1 zrk:2 consisting:1 satisfy:2 justification:1 respectively:2 realizations:1 component:1 here:5 b2i:2 directions:1 equations:15 obtained:3 rigorously:2 study:1 larger:1 allows:1 amount:1 products:1 proof:1 makes:1 sci:1 useful:1 elaborated:2 highly:2 analyzing:1 modus:1 cirit:1 select:1 use:1 y2:1 projector:1 would:3 massar:2 ψr:31 positive:3 estructura:1 hilbert:4 therefore:3 wondering:1 taken:1 type:1 more:6 becomes:1 clue:1 normalized:1 known:2 cases:2 must:3 valued:2 extension:2 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quant-ph9803071.txt |@word nwu:1 limited:1 magnetic:2 reversibility:1 four:2 circuitry:1 neighbours:3 whatsoever:1 under:1 worth:1 misunderstanding:1 logarithmically:1 vast:1 vibrational:13 solution:2 vector:1 c00:1 c01:1 force:5 deutsch:2 miller:1 pulse:1 approximation:10 likely:2 even:7 trapping:3 above:8 supplies:1 net:2 increasing:1 ever:1 consisting:1 evolving:1 simultaneously:2 here:4 atoms:1 met:1 plenio:2 represented:2 digits:1 study:2 ignoring:1 fourier:3 turchette:1 hindsight:1 total:8 unit:2 would:10 definiteness:1 noting:2 call:1 therefore:4 25th:1 type:4 until:1 relax:1 composite:1 naive:1 odinger:1 correspondingly:1 hole:1 hold:1 must:10 me:1 work:3 3l2:1 concepts:1 akin:1 example:5 give:4 bennett:1 table:5 implementations:1 end:3 provide:2 machine:3 how:5 answer:7 gate:13 description:3 earlier:1 wrong:2 minimizes:1 law:1 constants:1 third:2 complexity:2 algorithms:4 ultimate:1 keeps:1 order:9 operations:6 executed:2 interpretation:2 over:3 vary:2 london:1 fit:2 writing:1 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quant-ph9803073.txt |@word since:1 particularly:1 consider:1 just:2 among:2 unique:1 seen:1 mathematicians:1 grateful:1 wigner:18 its:5 academic:1 adv:2 mmax:1 now:1 group:1 proposed:1 instance:2 chosen:1 dr:1 lm:2 character:1 than:1 only:1 bases:1 mail:2 schmidt:6 defining:1 transformation:2 attribution:1 provides:1 easily:1 very:1 familiar:1 possible:1 choice:3 define:1 they:2 rm:2 press:1 immediately:1 thus:5 difference:1 procedures:6 naturally:1 school:1 equality:1 like:3 turns:1 university:1 arxiv:1 method:3 orthonormal:8 continue:1 gram:7 each:2 further:2 eigenvalues:1 referred:1 zl:3 correct:1 set:6 old:1 methods:1 discriminates:1 zk:1 some:1 related:3 up:1 matrices:1 operator:4 second:1 used:1 cyclic:1 obtains:1 measure:1 discussions:1 reformulation:1 chem:2 out:3 maximizes:2 kapoor:1 satisfying:2 matrix:9 invertible:1 quantify:1 footing:1 definite:1 extensively:1 vol:1 reformulate:2 inequality:1 various:2 wavelet:2 above:2 between:2 term:1 new:6 chelsea:1 numerous:1 email:1 math:1 refer:1 landshoff:2 pose:1 algorithmic:1 theory:1 nature:1 vi:1 attention:1 wk:1 diagonal:4 standard:1 wv:2 completely:1 owdin:2 members:1 ask:1 appears:4 physik:1 suggested:1 diego:1 essentially:1 enables:1 applications:1 many:1 taking:1 vectors:7 discussed:3 orthogonalization:11 eigenbasis:1 context:1 introduced:4 finds:1 york:1 origin:1 hyderabad:2 already:1 useful:1 cn:1 xl:1 upper:1 requiring:2 ca:1 prof:2 sign:1 corresponds:2 references:1 chemists:1 lies:1 hermitian:4 square:1 simply:1 least:1 directly:1 wider:1 table:1 mmin:1 linearly:7 constructing:2 diagonality:1 given:6 zj:1 basis:22 distinct:1 positive:2 arbitrary:1 question:3 been:2 their:3 cauchy:1 therefore:1 way:4 attribute:1 ph:1 was:3 historically:1 pl:1 select:1 introducing:3 form:2 quantity:7 brings:2 m2:2 triangular:1 but:1 chui:1 gantmacher:1 particular:4 known:2 natural:2 vl:1 maximally:2 themselves:1 vj:1 zi:1 srivastava:1 p1:1 applying:1 showed:2 pacs:1 2πi:2 pn:1 equation:1 work:5 maximum:2 us:1 choices:1 mu:1 kk:5 while:1 ij:1 obvious:1 ms:2 following:1 agarwal:1 problem:1 property:2 root:1 clear:1 procedure:18 perspective:1 motivation:1 unitary:3 associated:1 ad:2 defined:1 endowed:1 abstract:1 vk:2 india:1 vn:1 denote:2 vs:1 vt:1 manner:1 zu:1 follows:3 ernet:3 any:3 elements:1 defines:1 sequentially:1 extremal:2 mij:1 verified:1 hoc:2 no:2 rather:2 holds:1 off:3 same:2 poincar:1 srinivasan:1 democratically:2 other:2 quant:2 see:2 significance:1 answer:1 independent:9 literature:2 vup:2 trace:1 shall:1 rhs:1 minimum:1 what:3 paid:1 v1:1 vkl:3 value:3 letter:1 mzm:2 minimizes:3 acknowledgements:1 intrinsic:1 o:1 scsp:1 shortly:1 treats:3 attains:2 ss:1 requires:2 age:1 sp:1 analysis:1 mar:1 amounts:1 write:1 so:1 exp:2 san:1 quantitative:1 democratic:2 physics:1 notion:1 chaturvedi:1
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quant-ph9803081.txt |@word consider:2 caused:4 magnetic:7 splitting:11 gy:1 causes:1 increase:1 auf:1 compensate:1 blaze:1 th:1 cm2:3 case:1 advantage:1 very:3 results:6 resonant:1 experimentally:2 exact:1 splitter:1 level:3 nagel:1 standards:1 large:1 small:2 optics:2 der:3 consistent:2 direct:1 pulse:12 rate:1 correlator:1 further:1 spectral:2 trapping:1 section:8 cell:9 experiment:8 waals:1 increasing:1 method:3 edited:2 agreement:1 mea:1 d1:4 component:1 j2i:1 atoms:17 reported:1 cylindrical:1 operating:2 free:1 separation:1 relaxation:2 extreme:1 obtained:5 photomultiplier:2 shift:13 study:2 larger:1 experience:1 cesium:1 resonance:10 sealing:1 narrow:2 diameter:1 apr:1 plenum:1 electromagnetically:1 achievable:1 univ:2 use:2 chi:1 few:1 camera:1 therefore:2 bender:1 taken:2 train:1 varying:3 known:1 producing:1 me:1 topic:2 account:1 mf:9 locked:3 science:1 setup:3 work:1 values:1 transparency:1 νp:1 figure:3 lock:2 allowed:1 neglected:1 purposes:2 states:3 performed:1 magnitudes:1 information:1 respective:1 rather:1 s1:3 get:2 delay:1 far:1 pure:2 ensemble:1 modulation:1 physik:1 date:1 spectrometer:2 choice:1 data:1 parallel:1 lar:1 short:1 natural:1 third:1 whenever:1 light:11 spectra:1 ghz:4 negligible:1 affecting:1 order:3 typical:4 pulsed:8 over:4 mainly:2 years:1 experiments:5 pulses:5 lasers:2 sony:1 linewidth:11 fwhm:6 longitudinal:2 monitor:1 reflection:1 interesting:1 presence:1 detected:1 fig:9 lp:3 torr:1 mail:1 greater:2 matches:3 walls:1 effects:2 inversion:1 magnitude:1 l2:1 mode:4 each:1 universit:1 side:1 lorentzian:4 mean:2 heavy:1 happer:1 receipt:1 frequency:25 static:1 measure:4 quantum:2 our:10 operation:2 transitions:1 out:2 shown:5 literature:1 since:2 rev:7 periments:1 collisions:6 rf:3 rb:10 induced:2 ref:1 occurs:1 shows:1 xxxv:1 linear:1 isotope:2 franz:2 van:1 pairs:2 interaction:5 geometry:1 could:3 transition:6 length:1 first:4 chopped:1 manuscript:1 xe:2 chopper:2 fi:1 quality:1 passes:1 given:3 checked:1 synthesizer:1 introduction:1 system:2 approximately:2 surements:1 mandel:1 sealed:1 pump:1 relative:1 argon:6 part:1 ubingen:3 sublevels:1 than:3 population:1 diffusion:3 observed:2 kind:2 polarized:1 accordance:1 sections:2 second:2 boulanger:1 were:2 modulating:1 turned:1 spectrum:3 elsevier:1 orders:1 viewed:1 relatively:1 strength:1 so:1 hyperfine:10 mlynek:2 connected:1 phase:1 coil:2 measured:3 kilohertz:1 vapor:3 isotopic:1 considered:1 later:2 kr:2 subharmonic:1 velocity:1 typically:2 fitted:3 intensity:1 show:1 probe:1 attenuator:2 radio:1 earth:1 find:1 d0:1 ground:15 current:1 slow:1 state:15 should:1 only:9 enriched:1 factor:1 helmholtz:2 coherences:1 ger:1 lockin:1 mixture:1 means:3 de:1 da:1 beam:5 cannot:1 progress:1 contributes:2 transversal:1 crt:1 fields:3 arxiv:1 bandwidth:1 common:1 shg:2 through:2 thesis:2 reference:3 achieved:1 unpublished:2 detection:1 depends:3 result:1 coils:1 morgenstelle:1 µt:3 diode:5 simard:1 enough:1 smallest:1 between:6 tens:1 limit:1 recently:2 lange:1 mbar:6 both:2 last:1 taking:1 uncertainty:2 zeeman:2 bristol:1 uni:1 experimental:5 adjusted:1 jitter:1 cm:2 simple:1 corresponds:1 anti:1 cs:1 cw:3 broadening:5 described:1 publishing:2 acceptance:1 due:5 been:5 pc:1 reduction:1 describes:2 interest:1 synth:1 expected:1 ph:2 pm:2 j0i:1 sufficient:2 coherence:5 gas:26 precision:1 coherent:5 observe:1 external:1 hamburg:1 repetition:10 spin:1 applied:3 p0:3 p1:1 laser:21 pacs:1 solid:2 value:3 will:1 while:2 ar:3 error:1 sld:1 expander:2 thus:1 reads:1 helium:1 containing:2 circularly:1 locking:1 cross:10 serving:1 shifts:1 quant:1 several:1 noble:1 used:5 diploma:1 iop:1 inhomogeneities:2 levels:7 fourier:1 off:1 center:1 minimize:1 no:1 well:2 cco:1 without:2 epj:1 ccd:2 shape:1 atomic:2 arimondo:2 simi:1 monitored:1 absorption:1 lett:1 grating:2 c12:1 resolved:1 measurement:2 term:3 dark:12 possibly:1 increases:1 integer:4 correcting:1 mod:1 loss:1 necessary:1 like:1 ad0:1 signal:4 alkali:2 mhz:2 output:1 accuracy:1 rubidium:24 hartmann:1 duration:1 home:1 confirm:1 cavity:1 resonances:3 measurements:4 buffer:25 yielded:2 l3:1 power:2 ps:3 l1:1 conventional:2 linewidths:2 pressure:12 corp:1 bs:2 optimize:1 about:3 mutually:1 wolf:2 germany:1 own:1 j1i:1 into:1 within:1 three:3 down:1 appropriate:1 because:3 references:1 theoretically:1 institut:1 inserted:2 there:1 philadelphia:1 width:4 editor:1 fraction:5 was:5 hz:13 considerably:1 hp:1 atom:2 line:6 he:1 made:1 builds:1 polariser:1 cells:3 using:15 up:3 us:1 below:1 physikalisches:1 spectroscopy:1 autocorrelation:4 strongly:1 khz:4 carver:1 constant:2 ad:1 subtracting:1 abstract:1 describe:1 scanned:4 loschmidt:1 ing:2 pit:1 compared:1 nm:2 variety:1 tuebingen:1 when:2 ne:1 field:10 other:1 compares:1 poor:1 perpendicular:1 calculating:1 time:5 lens:1 structure:1 brandt:2 fluorescence:3 meschede:1 physics:1 ments:1 xenon:14 n0:2 decoherence:7 cpt:6
quant-ph9803082.txt |@word consider:6 ron:1 crucial:1 results:4 leads:2 consists:1 follow:1 expressions:1 denotes:1 scr:1 whose:4 preserves:3 depend:2 calculate:1 braginsky:1 quasi:1 infinitesimally:1 stable:2 stochastic:1 characterised:1 worth:1 norm:6 prigogine:1 division:1 orthogonal:1 very:1 pascazio:2 2re:2 rise:1 induce:1 geometrical:2 prof:1 cook:2 experimentally:1 condition:2 generalised:6 propagating:1 level:4 knight:1 prolonged:1 large:1 discrete:3 vector:9 succession:1 small:1 eigenvalues:2 der:1 inserting:1 prediction:1 past:1 zero:3 petrovsky:1 further:2 dynamics:3 linear:17 even:2 what:1 plays:1 apparatus:2 contemp:1 expressed:1 experiment:1 3n:1 above:3 solitonic:1 evolving:2 full:1 led:1 component:1 here:3 understanding:1 behaviour:9 nonunit:1 grundlagen:1 pati:5 path:3 along:2 quite:1 equations:7 change:1 involved:1 study:8 losses:1 2aω:1 identity:1 resonance:1 via:1 projection:2 explained:1 replace:1 addressed:1 inequality:1 viz:1 apply:1 total:3 univ:1 qze:20 unit:1 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quant-ph9803083.txt |@word represent:1 partial:3 consider:3 remarkable:1 equalities:2 results:5 gx:6 scalar:3 proposition:1 ga:1 consists:1 denotes:2 devoted:1 whose:4 preserves:1 dimensionality:2 depend:2 tv:1 mutatis:1 idπ:1 th:2 under:2 mutandis:1 analogous:2 sent:1 applied:1 implicitly:1 wave:2 corollary:1 every:3 matrices:3 condition:7 hamiltonian:12 turns:1 solution:1 t0:15 standards:1 vector:23 noted:1 ıu:3 neighborhood:1 consistent:3 past:1 second:4 further:1 defines:2 situated:2 substitute:1 theory:13 plays:4 section:9 analogously:1 version:1 above:4 new:7 increasing:1 drechsler:1 satisfy:1 transportation:3 respectively:2 component:1 here:11 selective:1 address:1 represented:4 path:13 along:37 equations:5 interpret:2 morphisms:5 obtained:1 admits:1 rigorously:1 institute:1 items:1 leaves:1 vectors:3 allows:1 γs:2 products:1 published:1 usually:1 suitable:2 uniquely:1 nents:1 via:10 regardless:2 projection:1 diffeomorphisms:1 assertion:1 viz:1 apply:4 total:1 univ:1 unit:1 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