Single Bell inequality to detect genuine nonlocality in three-qubit genuinely entangled states

TL;DR

This paper introduces a refined Bell inequality that effectively detects genuine nonlocality in all three-qubit genuinely entangled states, advancing the understanding of quantum nonlocality in multipartite systems.

Contribution

It improves existing Bell inequalities to more effectively identify genuine multipartite nonlocality, including in all three-qubit genuinely entangled states.

Findings

Tighter Bell inequalities for GMNL detection

Detection of GMNL in all three-qubit genuinely entangled states

Generalization to nonlocality depth and multi-outcome scenarios

Abstract

It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in [F. J. Curchod, M. L. Almeida, and A. Acin, New J. Phys. 21, 023016 (2019) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver tighter Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.