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

TL;DR

This paper introduces a local quasi hidden variable model for N-qudit states, providing a tighter upper bound on quantum violations of Bell inequalities, which enhances understanding of quantum nonlocality in multi-partite systems.

Contribution

The paper develops a new LqHV model for N-qudit states and derives improved bounds on Bell inequality violations, advancing the theoretical framework of quantum nonlocality.

Findings

New upper bound on Bell inequality violations for N-qudit states

Model reproduces probabilistic descriptions of N-partite measurements

Bounds reduce to known limits in the N-qubit dichotomic case

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.