New concise upper bounds on quantum violation of general multipartite Bell inequalities

TL;DR

This paper introduces new upper bounds on the maximum quantum violation of general multipartite Bell inequalities using the LqHV framework, improving upon previous bounds and applicable for various system sizes and settings.

Contribution

It derives novel upper bounds on quantum violations of Bell inequalities for multipartite systems using the LqHV model, surpassing existing bounds.

Findings

New upper bound (2d-1)^{N-1} for all d and N.

Improved bounds for specific S, d, and N values.

Some bounds are attainable in certain cases.

Abstract

Last years, bounds on the maximal quantum violation of general Bell inequalities were intensively discussed in the literature via different mathematical tools. In the present paper, we analyze quantum violation of general Bell inequalities via the LqHV (local quasi hidden variable) modelling framework, correctly reproducing the probabilistic description of every quantum correlation scenario. The LqHV mathematical framework allows us to derive for all d and N a new upper bound (2d-1)^{N-1} on the maximal violation by an N-qudit state of all general Bell inequalities, also, new upper bounds on the maximal violation by an N-qudit state of general Bell inequalities for S settings per site. These new upper bounds essentially improve all the known precise upper bounds on quantum violation of general multipartite Bell inequalities. For some S, d and N, the new upper bounds are attainable.