Testing the Structure of Multipartite Entanglement with Bell Inequalities

TL;DR

This paper develops device-independent Bell inequalities to distinguish different types of multipartite entanglement, providing practical tests for nonlocality in complex quantum states like W and GHZ states.

Contribution

It introduces Bell inequalities that can differentiate between W and GHZ states without assumptions on measurement devices, advancing multipartite entanglement testing.

Findings

Bell inequalities for three qubits distinguish W and GHZ states.

Sub-correlation Bell inequalities applicable to any number of parties.

Violations of these inequalities reveal nonlocality of W states.

Abstract

We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by GHZ states, and vice versa. Next, we devise 'sub-correlation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of GHZ states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.