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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