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 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.