Genuinely entangled symmetric states with no N -partite correlations

S. Designolle ^{1, 2} O. Giraud ² J. Martin ³

Physical Review A, American Physical Society, 2017, 96 (3), pp.032322. 〈10.1103/PhysRevA.96.032322〉

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-two states. We present a general procedure to construct families for arbitrary odd number of qubits.

• 1. Ecole Polytechnique – X
• 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Institut de Physique Nucl’eaire, Atomique et de Spectroscopie