Anonymous Quantum Nonlocality

TL;DR

This paper demonstrates that certain multipartite quantum correlations, generated from GHZ states, exhibit anonymous nonlocality, meaning they are nonlocal but cannot be attributed to any specific subset of parties, with implications for secure quantum communication.

Contribution

It introduces the concept of anonymous nonlocality in multipartite quantum correlations and provides explicit decompositions, expanding understanding of nonlocality without identifiable subsets.

Findings

Existence of n-partite correlations from GHZ states exhibiting anonymous nonlocality

Explicit biseparable decomposition for any bipartition

Potential applications in device-independent secret sharing and quantum key distribution

Abstract

We show that for all $n\ge3$, an example of an $n$-partite quantum correlation that is not genuinely multipartite nonlocal but rather exhibiting anonymous nonlocality, that is, nonlocal but biseparable with respect to all bipartitions, can be obtained by locally measuring the $n$-partite Greenberger-Horne-Zeilinger (GHZ) state. This anonymity is a manifestation of the impossibility to attribute unambiguously the underlying multipartite nonlocality to any definite subset(s) of the parties, even though the correlation can indeed be produced by nonlocal collaboration involving only such subsets. An explicit biseparable decomposition of these correlations is provided for any partitioning of the $n$ parties into two groups. Two possible applications of these anonymous GHZ correlations in the device-independent setting are discussed: multipartite secret sharing between any two groups of parties and bipartite quantum key distribution that is robust against nearly arbitrary leakage of information.