Best Separable Approximation of multipartite diagonal symmetric states

Abstract

The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a different route to the study of multipartite entanglement based on the closeness of a multipartite state to the set of separable ones. In particular, we analyze multipartite diagonal symmetric N qubit states and provide the analytical expression for their Best Separable Approximation (BSA [Phys. Rev. Lett. 80, 2261 (1998)]), that is, their unique convex decomposition into a separable part and an entangled one with maximal weight of the separable one.

8 pages, 1 figure

References in corpus (5)

• The structure of multidimensional entanglement in multipartite systems
• Device-independent entanglement quantification and related applications
• Four-qubit entangled symmetric states with positive partial transpositions
• Entangled symmetric states of N qubits with all positive partial transpositions
• Entanglement is not a lower bound for geometric discord

Cited by in corpus (14)

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• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Entangled states in the role of witnesses
• Internal Boundary between Entanglement and Separability Within a Quantum State
• The optimal approximation of qubit states with limited quantum states
• Symmetric extendibility of quantum states
• Heuristic for estimation of multiqubit genuine multipartite entanglement
• Derivation of the robustness from the concurrence
• The best approximation of an objective state with a given set of quantum states
• The best approximation of a given qubit state with the limited pure-state set