Quantum Correlations – Types and Bounds| Quantum Correlations – Types and Bounds |
Types of Correlations
> s.a. correlations [quantum discord, and causality, out-of-time-order];
quantum causality; quantum computation.
@ General references: Eckert et al AP(02) [indistinguishable particles];
Svozil PRA(05) [stronger than quantum];
Ozawa AP(06)qp/05 [perfect correlations];
Hastings & Koma CMP(06) [fermions in a lattice];
Brunner et al PRL(08)-a0802 [test of Hilbert space dimension];
Allcock et al PRA(09)-a0906 [information causality as principle to single out quantum correlations];
Seevinck QIP(10)-a0908 [monogamy and shareability];
Liang et al PRL(10)-a0909 [from randomly chosen local measurements];
Werlang et al PRA(11)-a1104 [and detection of quantum critical points];
Streltsov et al PRL(12)-a1112 [monogamy];
Nizama & Cáceres JPA(17)-a1512 [bath-induced correlations];
Wang a1906 [bipartite fluctuations, and quantum chaos];
Queisser & Schützhold a1909 [hierarchy];
Weilenmann & Colbeck a2003 [using correlations to self-test quantum theory].
@ Multipartite: Walczak PLA(10) [information-theoretic approach];
Xiang & Ren QIC(11)-a1101 [bound from information causality];
Brunner & Vértesi PRA(12)-a1207 [persistency];
Amico et al ed-IJMPB-a1211 [composite systems];
Jebaratnam QS:MF(15)-a1407 [tripartite];
Abbott et al PRA(16)-a1608 [the most general causal correlations];
Sawicki et al RPMP(18)-a1701 [symplectic and algebraic geometry approach];
Szalay JPA(18)-a1806 [classification];
Coiteux-Roy et al a2105
[Nature's non-locality is fundamentally multipartite].
@ In time: Nigmatullin TMP(74) [calculation];
Fedrizzi et al PRL(11)-a1011 [Hardy's paradox and Bell inequality];
Brierley et al PRL(15)-a1501 [non-classicality];
Mal et al a1510 [types];
Dall'Arno et al PRL(17)-a1609 [no-hypersignaling constraints on timelike correlations];
Ringbauer & Chaves Quant(17)-a1704 [non-classicality];
Costa et al PRA(18)-a1710,
Zhao et al a1711 [in spacetime, unified framework];
Zhang et al a2002 [different approaches];
Zhang a2101-PhD;
Vidick a2103 [almost synchronous].
Types of Systems
> s.a. composite systems; matter.
@ General references: Ivanov & Wallentowitz EPL(06)qp [atoms in a bosonic gas];
Caban & Rembieliński PRA(06)qp [EPR correlations for massive Dirac particles];
Massar & Spindel PRD(06) [accelerated oscillators];
Mori PRA(14) [system and thermal reservoir];
Gerasimenko MFAT-a1512 [many-particle systems].
@ In quantum field theory: Valentini PLA(91) [QED];
Redhead FP(95) [vacuum fluctuations];
Calzetta & Hu PRD(00)hp/99 [stochastic dynamics];
Shchukin & Vogel PRL(06) [of radiation, proposed measurement];
Vogel PRL(08)-a0706 [multimode radiation fields];
Buscemi & Compagno PRA(09)-a0904 [and detection];
Iemini et al QIP(12)-a1206 [in arbitrary systems of indistinguishable fermions];
Orszag et al JMO(14)-a1407 [in cavity QED networks];
Roussel & Feller a1906;
> s.a. N-point functions; bose-einstein condensates;
quantum field theory in curved spacetime; vacuum.
@ Across a horizon: Wald GRG(92) [cosmological];
Martín-Martínez & León PRA(10) [fermionic versus bosonic entanglement];
Schützhold & Unruh PRD(10)-a1002 [black hole, effect of modified dispersion relation];
Parentani PRD(10).
@ Applications, experiments: Clauser PRD(74)
[violation of Cauchy-Schwarz inequality in atomic two-photon cascade system];
Paterek PhD(07)-a0708 [application to communication];
Kheruntsyan et al PRL(12)-a1204
+ Macovei Phy(12)jun
[violation of Cauchy-Schwarz inequality with matter waves];
Lloyd et al a1510 [energy transport requires discord];
Postler et al Quant(18)-a1806 [spatial correlations in quantum dynamics];
Pusey Phy(19)
[quantum network with triangular geometry];
> s.a. experiments in quantum mechanics;
Hanbury Brown–Twiss Effect.
@ In quantum gravity: Neville PRD(99)gq/98 [quantum gravity];
> s.a. cosmological perturbations.
Bounds and Inequalities
> s.a. quantum correlations [measures].
* Tsirelson (Cirel'son) bound:
A bound on the strength of quantum mechanical correlations, that can be derived
using the principle of information causality; The absolute value of the combination
of quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH) inequality
is bounded by 2√2.
* Stronger-than-quantum correlations:
Note that work on these theories usually assumes that they are non-signaling.
* Clauser-Horne-Shimony-Holt inequality:
A combination of quantum correlations can give values between the classical bound,
2, and Tsire'son's bound, 2√2.
@ Tsirelson bound: Cirel'son LMP(80);
Filipp & Svozil PRL(04)qp [generalized];
Bovino et al PRL(04) [experiment];
Buhrman & Massar PRA(05) [and causality];
Choudhary et al PLA(07)qp/06 [origin, for spins],
PLA(07) [and causality];
Heydari JPA(06) [and Grothendieck's constant];
Toner PRS(09)qp/06 [technique];
Ghirardi & Romano PRA(12) [arbitrary violations];
Bub in(12)-a1208 [re information-causality derivation];
Cabello PRA(14)-a1406 [and the exclusivity principle];
Rohrlich in-a1507 [and causality];
Cuffaro SHPMP(18)-a1708 [motivation, information causality];
> s.a. entangled systems [photons].
@ CHSH inequalities: Saldanha & Vedral PRA(12) [and relativistic spinning particles];
Graft JAP(15)-a1409.
@ Other bounds: Cabello PRL(04)qp/03 [test];
Navascués et al PRL(07)qp/06;
Wolfe & Yelin PRA(12)-a1106 [algorithm for determining new bounds];
Brukner NJP(15)-a1404 [with indefinite causal order];
Frustaglia et al PRL(16)-a1511;
Fogel a1512
["multideviations" and a new method for finding tight Bell inequalities];
Kull et al npjQI(19)-a1807 [spacetime area law bound].
@ Stronger-than-quantum correlations:
Short & Barrett NJP(10)-a0909 [model violating the Tsirelson bound];
Gross et al PRL(10)-a0910 [triviality of reversible dynamics in maximally non-local theories];
Barnum et al PRL(10)-a0910 [quantum correlations from local quantum measurement and no signaling];
Ferrero & Sánchez-Gómez a1303 [classification of theories];
Rohrlich a1408
[and violation of relativistic causality];
Uzan a1602 [non-signaling ones cannot exist].
@ Almost-quantum correlations:
Navascués et al nComm(15)-a1403;
Ramanathan a2004 [inequality violations].
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