Measures of Quantum Entanglement |
In General
> s.a. entanglement; quantum correlations.
* Idea: Two approaches to entanglement
measures are a geometric one and one based on fidelity; The standard geometric entanglement
measure for a pure state is sin2θ, where
θ is the angle between the state and the closest separable (unentangled) one.
@ Reviews: Bruß JMP(02);
Myhr MSc(04)qp;
Plenio & Virmani QIC(07)qp/05;
Das et al a1701;
Haddadi & Bohloul IJTP(18)-a1805 [and multipartite].
@ General references: Popescu & Rohrlich PRA(97)qp/96 [entropy];
Schulman & Mozyrsky qp/97;
Vedral et al PRL(97)qp;
Nielsen PRL(99)qp/98 [partial order];
Virmani & Plenio PLA(00)qp/99;
Rudolph JMP(01)mp/00;
Blanchard et al JPA(01) [decoherence-based];
Majewski qp/01-conf;
Życzkowski & Bengtsson AP(02)qp/01;
Vidal & Werner PRA(02) [computable];
Nagel & Raggio qp/03;
Partovi PRL(04)qp/03;
Yukalov PRL(03)qp [as operator action];
Christandl & Winter JMP(04);
Cavalcanti et al PRA(05)qp [maximal entanglement and purity];
Mintert et al PRP(05)qp [and dynamics];
Pawłowski & Czachor PRA(06)qp/05 [ambiguity, photon];
Datta et al PRA(07)qp/06 [bounds];
Ostapchuk et al a0707 [interpretation];
Gour & Roy PRA(08)-a0711;
Yang et al PRL(08) [conditional entanglement of mutual information];
Sperling & Vogel PS(11)-a0908 [Schmidt number];
Walborn PRL(09) [entropic entanglement criteria];
Ma & Zhang a0910 [D-concurrence];
Caponigro & Giannetto a1206 [epistemic vs ontic classification, all states are entangled];
D'Arrigo et al AP(14)-a1207 [hidden entanglement and local operations];
Beigi a1405-conf [maximal entanglement];
Dugowson a1407 [connectivity order];
Dahlsten et al JPA(14) [typical entanglement];
Regula & Adesso PRL(16)-a1512 [polynomial measures];
Krynytskyi & Kuzmak a1811 [mixing];
Gudder a1902 [simple characterization];
Pathania & Qureshi a2012 [coherence].
@ And Bell inequalities:
Bartkiewicz et al PRA(13);
Bracken IJTP(14);
Datta et al PRA(17)-a1503 [Son-Lee-Kim inequality as a measure of entanglement].
@ Comparisons between measures: Streltsov a0911;
Ford et al OC(10)-a1005 [without heat bath];
Girolami & Adesso PRA(11)-a1111 [and other correlations].
@ Geometric: Blasone et al PRA(08)-a0712;
Uyanik & Turgut PRA(10)-a0910;
Carrington et al JPA(10)-a1004;
Ramšak EPL(11)-a1109;
Hu et al a1204;
Chen et al PRA(14)-a1308 [comparison];
Carrington et al JPA(15)-a1504;
Regula & Adesso PRA(16)-a1606 [polynomial measures];
> s.a. entanglement.
@ For fermions: Zander & Plastino PRA(10) [violation of uncertainty relations];
Johansson & Raissi PRA(16)-a1607;
> s.a. entangled systems.
@ Other systems: Eisert et al JPA(02)qp/01 [infinite-dimensional];
Hollands & Sanders a1702 [quantum field theory].
@ Entwinement: Erdmenger & Gerbershagen a1910;
> s.a. emergence.
@ Experimental: Shimizu & Morimae PRL(05)qp,
Kothe & Björk PRA(07)qp/06 [through local observable correlations];
Gühne et al PRL(07)qp/06 [estimate];
Badziag et al PRL(08) [experimentally friendly sufficient conditions];
Zhang et al PRA(08)-a0806 [for mixed states];
Singh et al NJP(13) [through heat capacity].
@ Uniqueness: Rudolph JMP(01)qp;
Donald et al JMP(02)qp/01.
> Related topics: see entropy;
examples of entangled systems; quantum vs classical
states [entanglement witnesses].
For Multipartite Entanglement
@ General references: Eisert & Briegel PRA(01)qp/00;
Meyer & Wallach JMP(02)qp/01;
Miyake PRA(03);
Heydari & Björk JPA(04)qp/04;
Pitowsky qp/06-wd [entanglement classes];
Adesso et al PRA(07)qp/06;
Facchi et al IJQI(07)qp/06;
Cardy EPJB(08)-a0708-conf [and von Neumann entropy];
Facchi et al JPA(09)-a0803,
JPA(10)-a1002 [statistical mechanics];
Teresi et al a0805;
Hassan & Joag PRA(09)-a0901;
Osterloh & Hyllus PRA(10)-a0908 [estimate];
Hillery et al PRA(10)-a1005 [sufficient conditions];
Streltsov et al NJP(10)-a1006;
Gühne & Seevinck NJP(10) [separability criteria];
Zhu et al NJP(10) [additivity];
Brunner et al PRL(12)-a1110;
Solomon et al JPA(13)-a1205;
Sperling & Vogel PRL(13);
Cianciaruso et al NpjQI(16)-a1507 [experimentally friendly method];
Hedemann QIC-a1611,
QIC-a1701;
Kraft et al PRL(18)-a1707 [multilevel entanglement];
Haddadi & Bohloul IJTP(18)-a1805 [rev];
Haddadi a1810;
Luo a2003 [new type].
@ Classification:
Walter et al Sci(13)jun-a1208 [entanglement polytopes];
Quinta & André PRA(18)-a1803 [based on topological links].
@ Geometric: Hilling & Sudbery JMP(10)-a0905;
Buchholz et al AdP(16)-a1412 [evaluation, analytical approach];
Sanz et al JPA(17)-a1606 [and algebraic geometry];
Mainiero a1901 [and homological algebra].
@ Special types of systems: Eltschka & Siewert SRep(12)-a1305 [GHZ entanglement in arbitrary three-qubit states];
Lücke et al PRL(14) [detection, in Dicke states];
Pepe IJQI(14)-a1404-proc [short-range and few-body interactions].
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