Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations

TL;DR

This paper demonstrates that Greenberger-Horne-Zeilinger states can produce fully genuine-multipartite nonlocal, monogamous, and random correlations through local measurements, with implications for advanced cryptographic protocols.

Contribution

It introduces a multipartite chained Bell inequality and proves GHZ states can generate optimal correlations for multipartite cryptography.

Findings

GHZ states produce fully genuine-multipartite nonlocal correlations

A multipartite chained Bell inequality detects genuine nonlocality

Results enable new cryptographic protocols like device-independent secret sharing

Abstract

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and associated to fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality that appears in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy and full random outcomes are thus highly desired properties for multipartite correlations in intrinsically genuine-multipartite cryptographic scenarios. We prove that local measurements on Greenberger-Horne-Zeilinger states, for all local dimension and number of parts, can produce correlations that are fully genuine-multipartite nonlocal, monogamous and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss the applications of our results for intrinsically genuine-multipartite cryptographic protocols such as device-independent secret sharing.