Genuine $N$-partite entanglement without $N$-partite correlation functions

Abstract

A genuinely $N$-partite entangled state may display vanishing $N$-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd $N$ is to design an `anti-state' in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its anti-state then produces a mixed state with no $N$-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of `entanglement without correlations' involve an \emph{odd} number of particles. Here we further develop the idea of anti-states, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no anti-state to any pure even-$N$-party entangled state making the simple construction scheme unfeasable. However, as we prove by construction, higher-rank examples of `entanglement without correlations' for arbitrary even $N$ indeed exist. These classes of states exhibit genuine entanglement and even violate an $N$-partite Bell inequality, clearly demonstrating the non-classical features of these states as well as showing their applicability for quantum communication complexity tasks.

arXiv comment8 pages

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Cited by in corpus (11)

• Entanglement in indistinguishable particle systems
• Analysing quantum systems with randomised measurements
• Optimization of device-independent witnesses of entanglement depth from two-body correlators
• Characterizing quantum states via sector lengths
• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• Higher dimensional entanglement without correlations
• A Moment for Random Measurements
• Genuinely entangled symmetric states with no $N$-partite correlations
• Valid and efficient entanglement verification with finite copies of a quantum state
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Cooperation and dependencies in multipartite systems