Degree of separability of bipartite quantum states

Abstract

We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified with the degree of separability of the state. In a recent work, the problem was solved for two-qubit states using semidefinite programming. In this paper, we describe a procedure to obtain the optimal decomposition of a bipartite state of any finite dimension via a sequence of semidefinite relaxations. The sequence of decompositions thus obtained is shown to converge to the optimal one. This provides, for the first time, a systematic method to determine the so-called optimal Lewenstein-Sanpera decomposition of any bipartite state. Numerical results are provided to illustrate this procedure, and the special case of rank-2 states is also discussed.

arXiv comment11 pages, 7 figures, submitted to PRA

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• Anomalies of weight-based coherence measure and mixed maximally coherent states
• Entangled states in the role of witnesses
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Internal Boundary between Entanglement and Separability Within a Quantum State