Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually

Abstract

Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model - the LqHV (local quasi hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)], incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities - Bell's nonlocality - in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically - in d and N. In view of our rigorous mathematical description of Bell's nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of "quantum realism".

10 pages, reported at the International Conference "Quantum and Beyond", June 2016, Sweden

References in corpus (5)

• Partial list of bipartite Bell inequalities with four binary settings
• "Local Realism", Bell's Theorem and Quantum "Locally Realistic" Inequalities
• Class of bipartite quantum states satisfying the original Bell inequality
• Reducing the number of inputs in nonlocal games
• New concise upper bounds on quantum violation of general multipartite Bell inequalities

Cited by in corpus (9)

• Conditional probability framework for entanglement and its decoupling from tensor product structure
• Entanglement of observables: Quantum conditional probability approach
• Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations
• Quantifying Bell nonlocality of a pure two-qudit state via its entanglement
• Geometric quantum discord of an arbitrary two-qudit state: the exact value and general upper bounds
• 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
• Quantifying tolerance of a nonlocal multi-qudit state to any local noise
• High-spin measurements in an arbitrary two-qudit state