Multisetting Bell-type inequalities for detecting genuine tripartite entanglement

TL;DR

This paper generalizes a Bell inequality for detecting genuine tripartite entanglement to multiple settings, achieving a threshold visibility close to 2/pi, and demonstrates the optimality of these device-independent witnesses.

Contribution

It extends a three-setting Bell inequality to an arbitrary number of settings and introduces a pseudo-telepathy Bell inequality with the same threshold.

Findings

Threshold visibility approaches 2/pi as settings increase

Generalized Bell inequalities detect genuine tripartite entanglement

Device-independent witnesses are proven optimal

Abstract

In a recent paper, Bancal et al. put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a lab without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a three-party three-setting Bell inequality which enables to detect genuine tripartite entanglement in a noisy 3-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as 2/3 in a device-independent way. In this paper, we generalize this inequality to an arbitrary number of settings, demonstrating a threshold visibility of 2/pi~0.6366 for number of settings going to infinity. We also present a pseudo-telepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that the above value cannot be beaten with three-party-correlation Bell inequalities.