Best Separable Approximation of multipartite diagonal symmetric states

TL;DR

This paper derives an analytical expression for the Best Separable Approximation of multipartite diagonal symmetric states, aiding the understanding of entanglement by quantifying how close states are to being separable.

Contribution

It provides the first explicit formula for the BSA of multipartite diagonal symmetric states, advancing the operational analysis of multipartite entanglement.

Findings

Analytical expression for BSA of multipartite diagonal symmetric states.

Unique convex decomposition into separable and entangled parts.

Enhanced criteria for distinguishing entanglement properties.

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.