Bell's Theorem and Inequalities – Applications and Generalizations| 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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