A Robust Semidefinite Programming Approach to the Separability Problem

Abstract

We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as Robust Semidefinite Programs (RSDP). We propose, using well known properties of RSDP, several new sufficient tests for the separability of mixed states. Our results are then generalized to multipartite density operators.

Revised version (minor spell corrections) . 6 pages; submitted to Physical Review A

References in corpus (6)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• A complete family of separability criteria
• Detection of entanglement with few local measurements
• A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
• Finding optimal strategies for minimum-error quantum-state discrimination

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