On the existence of a local quasi hidden variable (LqHV) model for each N-qudit state and the maximal quantum violation of Bell inequalities

Abstract

We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of N-partite Bell inequalities of any type (either on correlation functions or on joint probabilities) for S observables per site. This new upper bound not only improves for all N, S and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables per site, reduces exactly to the attainable upper bound known for quantum violations of correlation 2x...x2-setting Bell inequalities in a dichotomic case.

14 pages, reported at the Conference "Quantum Theory: from foundations to technologies (QTFT)", June 8-11, 2015, Linnaeus University, Sweden, and at the Institute for Quantum Information and Matter (IQIM), July 2015, Caltech, USA

References in corpus (4)

• Grothendieck's constant and local models for noisy entangled quantum states
• Survey on Nonlocal Games and Operator Space Theory
• "Local Realism", Bell's Theorem and Quantum "Locally Realistic" Inequalities
• Context-invariant and local quasi hidden variable (qHV) modelling versus contextual and nonlocal HV modelling

Cited by in corpus (5)

• Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually
• New concise upper bounds on quantum violation of general multipartite Bell inequalities
• 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