Arbitrary Measurement dependence in tripartite non-locality

TL;DR

This paper investigates the minimal relaxation of measurement independence needed for local deterministic models to violate tripartite Bell inequalities, expanding understanding of non-locality in multipartite quantum systems.

Contribution

It introduces the minimum degree of measurement dependence required for tripartite Bell inequality violations and provides models achieving these violations.

Findings

Identifies the minimal relaxation needed for tripartite Bell violations.

Constructs local deterministic models that simulate these violations.

Extends the analysis of measurement dependence to multipartite scenarios.

Abstract

The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the assumption needs to be relaxed to achieve violation of some bipartite Bell inequalities, has been investigated recently in [Phys. Rev. Lett. 105, 250404(2010), Phys. Rev. A 99, 012121(2019)]. In this work, we study the minimum degree of relaxation required to simulate violations of various well-known tripartite Bell inequalities and opens the possibility of relaxation in multipartite scenario. Local deterministic models are also provided to achieve the violations of these Bell inequalities.