Anonymous Quantum Nonlocality

Abstract

We show that for all $n\ge 3$, 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.

4 + 4 pages, 2 figures; comments welcomed!

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• Quantum Correlations in Connected Multipartite Bell Experiments
• Multipartite nonlocality and random measurements
• Quantifying multipartite nonlocality via the size of the resource
• Genuine multipartite entanglement detection with imperfect measurements: concept and experiment
• Single-copy activation of Bell nonlocality via broadcasting of quantum states
• Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames
• Almost quantum correlations and their refinements in a tripartite Bell scenario
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
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• Structure of quantum and broadcasting nonlocal correlations
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• Detecting genuine multipartite entanglement using moments of positive maps
• Unextendible product operator basis
• Nonlocality of Quantum States can be Transitive