Device-Independent Witnesses of Genuine Multipartite Entanglement

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 Greenberger-Horne-Zeilinger 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 nonlocality. We show more generically how the problem of identifying genuine tripartite entanglement in a device-independent way can be addressed through semidefinite programming.

Figure 1

A particular slice of the space of tripartite correlations with three settings and two outcomes representing schematically the sets of general quantum ($Q_3$), Svetlichny ($S_{2/1}$), and biseparable quantum correlations ($Q_{2/1}$). The point $\mathbb{1}$ corresponds to random correlations and $P$ to the GHZ correlations maximally violating the DIEW (5), which is represented by the straight line $I_3$; note that a DIEW can be violated by Svetlichny-local correlations. (The Svetlichny polytope $S_{2/1}$ can be determined exactly using linear programming, while $Q_3$ and $Q_{2/1}$ can be approximated efficiently using SDP techniques; see main text.)