Bell's Theorem and Inequalities

In General > s.a. hidden variables; locality; realism.
* Idea: Bell's theorem and inequalities are the formal counterpart of the EPR paradox, and strengthen Einstein's argument by showing that either reality or locality must not hold ("Quantum mechanics is correct; Quantum mechanics is crazy; So nature is crazy"); Quantum mechanics predicts that "properties one cannot know anything about" (e.g., the value of spin along different directions) do not exist; Shown using entangled states.
* Bell's theorem: No physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.
* Bell inequalities: Inequalities (the orginal one by Bell and others derived later) among correlations between different quantum observables, that can be violated if quantum mechanics (as opposed to theories with local hidden variables) is correct.
* Consequences: Clauser et al proved that experiments on Bell's inequalities rule out all interpretations which assume locality, time-forwards causality and the existence of an objective real world.
@ Non-technical references: Jack PW(95)apr; Nadeau & Kafatos 00; Ekert pw(09)sep.
@ General references: Bell Physics(64); Wigner AJP(70)aug [simplification]; de Broglie CRAS(74); Lochak FP(76) [criticism]; Eberhard NCB(77), NCB(78); Clauser & Shimony RPP(78); Feingold & Peres JPA(80); Fine PRL(82) [hidden variables and probabilities], PRL(82); Stapp PRL(82), Eberhard PRL(82) [and determinism, locality]; Ballentine & Jarrett AJP(87)aug; Fine FP(89); Bertlmann FP(90); issues FP(90)#10, FP(90)#11, FP(90)#12, FP(91)#1, FP(91)#2, FP(91)#3; Home & Selleri RNC(91); Santos PRL(91); Stapp FP(91); Elby BJPS(93); Mermin RMP(93) [and Kochen-Specker]; Sudarshan & Rothman IJTP(93); Jones & Adelberger PRL(94); Ferrero et al AJP(90)jul; Ardehali qp/98; Aspect in(02)qp/04; Rosinger qp/04 [and George Boole]; Hess & Philipp FP(05)qp [Bass theorem]; Marlow qp/06 [and relationism]; Paterek a0708-PhD; Corbett & Home a0802; Norsen FP(09)-a0808 [and local causality]; Avis et al a0812 [for non-specialists]; Blaylock a0902 [pedagogical].
@ Proofs: Herbert AJP(75)apr; Gisin PLA(91) [non-product states]; Hess & Philipp qp/02, qp/02, qp/02, qp/02, qp/02, qp/04 [critiques], refuted by Mermin FP(05); Ryff qp/05 [simple]; Cabello PRL(05) [2-observer]; Argaman a0807 [and causality].
@ Loopholes: Brans IJTP(88); Werbos & Dolmatova qp/00 [backwards-time interpretation]; Volovich qp/00; Vaidman PLA(01)qp; Clover qp/05; Christian qp/07, qp/07, a0707 [failure for Clifford-algebra-valued local variables], Grangier a0707, Tung a0712 [criticisms]; Morgan a0801 [coincidence time]; LiMing & Tang a0807; Nieuwenhuizen AIP-a0812; Christian a0904 [entanglement as an illusion].
> Online resources: Wikipedia page.

Related Topics > s.a. collapse [gravity-induced]; EPR paradox and experiments; probability in physics [and quantum measure].
* 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.
@ And entanglement: Cereceda PLA(96)qp/98, PRA(02)qp; Werner & Wolf QIC(01)qp [review].
@ Bounds on violations: Cabello PRL(02) [beyond Cirel'son]; Filipp & Svozil qp/04-in [method]; Bohata & Hamhalter JMP(09); > s.a. correlations.
@ Applications: Benatti & Floreanini hp/97 [correlated K's]; O'Hara ht/97 [particle couplings]; Campo & Parentani PRD(06)ap/05 [inflationary spectra].
@ And covariance: Stapp AJP(01)aug-qp/00 [acausal propagation]; Kim & Noz qp/06-in [simultaneity].
@ Conceptual, interpretations: Dotson AJP(86)mar; Durt FP(94); Peres FdP(00)qp/99 [Bayesian].
@ Classical models: Barut & Meystre PLA(82); Palmer PRS(95) [spin]; Morgan JPA(06)cm/04 [random fields]; Matzkin JPA(08)-a0709, PRA(08) [classical violation from random interactions]; Willeboordse a0804.
@ Other topics: Berthelot NCB(80); Harrison AJP(82)sep [correlations]; Svetlichny et al PhSc(88)sep; Hacyan PLA(01) [invariance]; Rothman & Sudarshan IJTP(01) [assumptions]; Auberson et al PLA(02) [in phase space]; Lupo et al JPA(06)qp [in tomographic representation]; Matzkin JPA(08)qp/07 [classical distributions that violate the inequalities], AIP(09)-a0802, a0808; Flitney et al PLA(09)-a0803 [and game theory]; Chen & Deng PRA-a0808 [for qubits, from Hölder inequality]; Choudhary et al a0901 [Gisin's theorem for three qubits]; Brukner & Zukowski a0909-in [and quantum communication]; > s.a. CPT; optics; spin [classical models].

Generalizations > s.a. Penrose Dodecahedron; relativistic quantum mechanics.
@ 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).
@ 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-a0711.
@ Related topics: Braunstein & Caves PRL(88), AP(90) [information-theoretic]; Franson PRL(89); Stapp PRA(94); Peres FP(99)qp/98; Razmi & Golshani qp/98; Vervoort EPL-qp/00 [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]; Pankovic qp/05 [general relativistic]; Lapiedra & Socolovsky a0806 [arrow of time and Leggett inequalities]; Christian a0806 [macroscopic domain]; Cabello a0910 [with local violation].

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