On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site

Details On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site

2008-04-15

arxiv.org/abs/0804.2398v2

J. Phys. A: Math. Theor. 41 (2008), 445303 (23pp)

Physics

Quantum Physics

26 pages; added section Conclusions and some references for section 3

Scientific paper

10.1088/1751-8113/41/44/445303

We consistently formalize the probabilistic description of multipartite joint measurements performed on systems of any nature. This allows us: (1) to specify in probabilistic terms the difference between nonsignaling, the Einstein- Podolsky-Rosen (EPR) locality and Bell's locality; (2) to introduce the notion of an LHV model for an S_{1}x...xS_{N}-setting N-partite correlation experiment, with outcomes of any spectral type, discrete or continuous, and to prove both general and specific "quantum" statements on an LHV simulation in an arbitrary multipartite case; (3) to classify LHV models for a multipartite quantum state, in particular, to show that any N-partite quantum state, pure or mixed, admits an Sx1x...x1 -setting LHV description; (4) to evaluate a threshold visibility for a noisy bipartite quantum state to admit an S_{1}xS_ {2}-setting LHV description under any generalized quantum measurements of two parties. In a sequel to this paper, we shall introduce a single general representation incorporating in a unique manner all Bell-type inequalities for either joint probabilities or correlation functions that have been introduced or will be introduced in the literature.

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