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