Bell's Theorem and Inequalities – Applications and Generalizations  

Applications, Phenomenology and Tests > s.a. optics; wave-function collapse [gravity-induced].
@ General references: Flitney et al PLA(09)-a0803 [and game theory]; Chen & Deng PRA(09)-a0808 [for qubits, from the Cauchy-Schwarz inequality]; Brukner & Żukowski a0909-ch [and quantum communication]; Durham AIP(12)-a1111 [and the second law of thermodynamics].
@ Classical models: Barut & Meystre PLA(82); Palmer PRS(95) [spin]; Morgan JPA(06)cm/04 [random fields]; Matzkin JPA(08)qp/07, PRA(08)-a0709 [classical violation from random interactions]; Willeboordse a0804; Ferry & Kish FNL(10)-a1008, Gerhardt et al PRL(11)-a1106 [faking the violation with classical states]; Khrennikov a1111, JPCS(14)-a1404; Faber a1907 [violation of Mermin's version in a classical statistical model]; > s.a. spin.
@ Particle physics and cosmology: Benatti & Floreanini hp/97 [correlated Ks]; O'Hara ht/97 [particle couplings]; Campo & Parentani PRD(06)ap/05 [inflationary spectra]; Gallicchio et al PRL(14) [proposed test with cosmic photons]; Hiesmayr a1502-conf; Maldacena FdP(16)-a1508 [inflationary model with a Bell inequality violating observable]; Choudhury et al EPJC(17)-a1607 [massive particle creation, inflation], Univ(17)-a1612 [early-universe violation]; Kanno & Soda PRD(17)-a1705 [in inflation].
@ Other tests: Cabello a1303 [experimental test for higher-than-quantum inequality violations]; Hofer et al PRL(16)-a1506 [in electromechanics]; news PT(16)jan [two loopholes closed at once]; > s.a. EPR paradox and experiments.

Other Results and Generalizations > s.a. Leggett Inequalities; Leggett-Garg Inequality.
* Gisin's theorem: For any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model; A similar result holds for three-qubit pure entangled states.
@ Single particle: Tan et al PRL(91), Hardy PRL(94) [photon]; Basu et al PLA(01) [spin-1/2].
@ Multipartite: Mermin PRL(90), Chen et al PRA(08) [3-particle]; Cabello PRA(02) [n spin-s particles]; Laskowski et al qp/03; Shchukin & Vogel PRA(08) [and algebras of quaternions and octonions].
@ For mixed states: Popescu PRL(95).
@ Bounds on violations: Cabello PRL(02) [beyond Cirel'son]; Filipp & Svozil AIP(05)qp/04 [method]; Bohata & Hamhalter JMP(09); Palazuelos a1206 [largest attainable violation]; > s.a. quantum correlations.
@ Entropic Bell inequalities: Cerf & Adami PRA(97)qp/96; Durham qp/07-in, a0801.
@ Without inequalities: Cabello PRL(01), PRL(03)qp, PRL(03)qp, comment Marinatto PRL(03)qp, comment Cabello PRL(04)qp; Cabello FP(05)qp/04; Greenberger et al PRA(08), PRA(08)qp/05 [GHZ-type, using inefficient detectors]; Broadbent et al NJP(06)qp/05 [logical structure]; Ghirardi & Marinatto PLA(08)-a0711; Choudhary & Agrawal IJQI(16)-a1610 [rev]; > s.a. Hardy's Paradox.
@ Gisin's theorem: Choudhary et al PRA(10)-a0901 [for three qubits].
@ In more general settings: Panković qp/05 [general relativistic]; Loubenets FP(17)-a1612 [general non-signaling case].
@ Other generalizations: Braunstein & Caves PRL(88), AP(90) [information-theoretic]; Gočanin et al PRA(20)-a2001 [for trajectories].
@ Related topics: Franson PRL(89); Stapp PRA(94); Peres FP(99)qp/98; Razmi & Golshani qp/98; Vervoort EPL(00)qp [non-linear systems]; Collins et al PRL(02)qp/01 [high dimensionality]; Reid qp/01, qp/01 [continuous outcomes]; Larsson PRA(04)qp/03 [position]; Clover qp/04 [time ordering of measurements]; Christian a0806 [macroscopic domain]; Cabello PRL(10)-a0910 [with local violation]; Fedrizzi et al PRL(11)-a1011 [in time]; Fritz NJP(12)-a1206 [without free will]; Aravinda & Srikanth a1211 [Bell-type inequality encompassing both the spatial and temporal variants, and criterion for non-classicality]; Borges et al PRA(12) [continuous angular variables]; Harper et al PRA(17)-a1608 [causal networks and quantum correlations]; Szangolies et al PRL(17)-a1609 [inequalities free from the detection loophole, device-independent bounds on detection efficiency]; Te'eni et al a1902 [new multiplicative class]; Cabello a1904 [generalized Bell non-locality equivalent to Kochen-Specker contextuality]; Tavakoli & Gisin Quant(20)-a2001 [and Platonic solids].
> Related topics: see measure theory [quantum measure analog]; Penrose Dodecahedron; relativistic quantum mechanics.

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