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

Abstract

We specify for a general correlation scenario a particular type of local quasi hidden variable (LqHV) model (Loubenets 2012 J. Math. Phys. 53 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 being 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 Loubenets (2008 J. Phys. A: Math. Theor. 41 445303). This mathematical result specifies a new probability model that has a 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 each nonsignaling correlation scenario, in particular, each correlation scenario on a multipartite quantum state.