Device-independent witnesses of genuine multipartite entanglement

TL;DR

This paper introduces a device-independent method to detect genuine multipartite entanglement using an n-partite inequality that can be violated by entangled states like GHZ, without assumptions on the system or measurements.

Contribution

It presents a new inequality for device-independent detection of genuine multipartite entanglement and a semidefinite programming approach for identifying such entanglement.

Findings

The inequality is satisfied by all biseparable states.

Violations indicate genuine multipartite entanglement.

The method is independent of system dimension and measurement details.

Abstract

We consider the problem of determining whether genuine multipartite entanglement was produced in an experiment, without relying on a characterization of the systems observed or of the measurements performed. We present an n-partite inequality that is satisfied by all correlations produced by measurements on biseparable quantum states, but which can be violated by n-partite entangled states, such as GHZ states. In contrast to traditional entanglement witnesses, the violation of this inequality implies that the state is not biseparable independently of the Hilbert space dimension and of the measured operators. Violation of this inequality does not imply, however, genuine multipartite non-locality. We show more generically how the problem of identifying genuine tripartite entanglement in a device-independent way can be addressed through semidefinite programming.