Nonsignaling as the consistency condition for local quasi classical probability modelling of a general multipartite correlation scenario

Abstract

We specify for a general correlation scenario a particular type of a local quasi hidden variable (LqHV) model [J. Math. Phys. 53 (2012), 022201] -- a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single measure space with a normalized bounded real-valued measure not necessarily positive and random variables, each depending only on a setting of the corresponding measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition constituting the general nonsignaling condition formulated in [J. Phys. A: Math. Theor. 41 (2008), 445303]. This mathematical result specifies a new probability model that has the measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi classical probability model covers the probabilistic description of every nonsignaling correlation scenario, in particular, each correlation scenario on an multipartite quantum state.

11 pages

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• Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually
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• New concise upper bounds on quantum violation of general multipartite Bell inequalities
• Context-invariant and local quasi hidden variable (qHV) modelling versus contextual and nonlocal HV modelling
• Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement
• Full Bell locality of a noisy state for $N\ge 3$ nonlocally entangled qudits