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.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.

arXiv:1707.04103Physical Review ASep 12, 20177 citations

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.