In a recent paper, Bancal et al. [Phys. Rev. Lett. 106, 250404 (2011)] put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a laboratory 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 multiparty three-setting Bell inequality which makes it possible to detect genuine $n$-partite entanglement in a noisy $n$-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 pseudotelepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that for $n$ odd the above value cannot be beaten with $n$-party-correlation Bell inequalities.

• Received 21 February 2011

DOI:https://doi.org/10.1103/PhysRevA.83.062123