Genuinely entangled symmetric states with no $N$-partite correlations

Abstract

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 comment9 pages, 2 figures

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Cited by in corpus (6)

• Entanglement in indistinguishable particle systems
• Majorana representation for mixed states
• Entanglement in highly symmetric multipartite quantum states
• Constraints on correlations in multiqubit systems
• Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States
• Cooperation and dependencies in multipartite systems