Genuine N-partite entanglement without N-partite correlations

A genuinely N-partite entangled state may display vanishing N-partite correlations measured for 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 “antistate” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate 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. We conjecture that there is no antistate to any pure even-N-party entangled state making the simple construction scheme unfeasible. However, higher-rank examples of entanglement without correlations for arbitrary even N indeed exist. These classes of states exhibit genuine entanglement and even violate a Bell inequality, demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.