Test of Genuine Multipartite Nonlocality Without Inequality

TL;DR

This paper introduces a new set of probability-based conditions to test for genuine multipartite nonlocality without using inequalities, demonstrating that all entangled symmetric n-qubit states exhibit this nonlocality.

Contribution

The authors propose a novel inequality-free test for genuine multipartite nonlocality and show its effectiveness on symmetric n-qubit states, also deriving Bell-type inequalities from it.

Findings

All entangled symmetric n-qubit states pass the test

The test distinguishes nonlocal states from non-signaling local models

Derived Bell inequalities whose violations confirm genuine multipartite nonlocality

Abstract

In this letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all non-signaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the non-signaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any non-signaling local models, i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit ($n \geq 3$) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.