Hierarchy of multipartite nonlocality in the nonsignaling scenario

TL;DR

This paper introduces a hierarchy of Bell-type inequalities for n-partite systems to distinguish various degrees of nonlocality, from standard to genuine multipartite nonlocality, using nonsignaling models.

Contribution

It develops a hierarchy of inequalities that identify different nonlocality levels in multipartite systems, extending previous work and providing new tools for analysis.

Findings

Hierarchy of inequalities for multipartite nonlocality

Reduction to known inequalities at specific levels

Examples demonstrating the hierarchy

Abstract

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.