Title

The Structural Physical Approximation Conjecture

Department

Mathematics

Document Type

Article

Publication Date

2016

Abstract

It was conjectured that the structural physical approximation (SPA) of an optimal entanglement witness is separable (or equivalently, that the SPA of an optimal positive map is entanglement breaking). This conjecture was disproved, first for indecomposable maps and more recently for decomposable maps. The arguments in both cases are sketched along with important related results. This review includes background material on topics including entanglement witnesses, optimality, duality of cones, decomposability, and the statement and motivation for the SPA conjecture so that it should be accessible for a broad audience.

Comments

Fred Shultz, The structural physical approximation conjecture, J. Math. Phys. 57 (2016), 015218 Copyright (2015) American Institute of Physics. The published article may be found at may be found at http://dx.doi.org/10.1063/1.4938226

Version

Post-print

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