The definition of multipartite nonlocality

TL;DR

This paper explores different definitions of multipartite nonlocality, proposing new criteria and inequalities to better identify genuine n-way nonlocal correlations in quantum states.

Contribution

It introduces two alternative, more motivated definitions of n-way nonlocality and develops Bell-type inequalities to detect 3-way nonlocality, improving upon Svetlichny's approach.

Findings

All 3-way entangled pure states can produce 3-way nonlocal correlations.

New definitions are strictly weaker than Svetlichny's, offering broader detection.

Numerical evidence supports the presence of 3-way nonlocality in pure states.

Abstract

In a multipartite setting, it is possible to distinguish quantum states that are genuinely $n$-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely $n$-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of $n$-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of 3-way nonlocality. Numerical evidence suggests that all 3-way entangled pure quantum states can produce 3-way nonlocal correlations.