We investigate genuinely entangled N-qubit states with no N-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of N-partite correlations. We show that symmetric states with no N-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no N-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd number of qubits.
@article{arxiv.1707.04103,
title = {Genuinely entangled symmetric states with no $N$-partite correlations},
author = {S. Designolle and O. Giraud and J. Martin},
journal= {arXiv preprint arXiv:1707.04103},
year = {2017}
}