Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads

TL;DR

This paper demonstrates that randomly chosen triad measurements on multipartite GHZ states can reliably certify genuine multipartite entanglement in a device-independent manner, even with noise, without requiring a shared reference frame.

Contribution

It introduces a method using random triad measurements to certify multipartite entanglement device-independently, supported by numerical evidence up to eight parties.

Findings

Random triad measurements typically violate Bell inequalities.

Correlations reveal genuine multipartite entanglement even with noise.

Method applicable without shared reference frames in experiments.

Abstract

We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen triads, i.e., three mutually unbiased bases, on a multipartite Greenberger-Horne-Zeilinger state. Our main interest lies on investigating the feasibility of using these correlations to certify multipartite entanglement in a device-independent setting. In contrast to previous works, our numerical results up to the eight-partite scenario suggest that if each triad is randomly but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure zero) finds Bell-inequality-violating correlations. In fact, a substantial fraction of these is even sufficient to reveal, in a device-independent manner, various higher-order entanglement. In particular, for the specific cases of three parties and four parties, our results---obtained from semidefinite programming---suggest that these randomly generated correlations always reveal, even in the presence of a non-negligible amount of white noise, the genuine multipartite entanglement possessed by these states. In other words, provided local calibration can be carried out to good precision, a device-independent certification of the genuine multipartite entanglement contained in these states can, in principle, also be carried out in an experimental situation without sharing a global reference frame.