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Another dual formulation of the separability problem

D. Salgado·J. L. Sanchez-Gomez·M. Ferrero
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Abstract

We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several inmediate consequences are analyzed: (i) a sufficient criterion for separability for bipartite quantum systems, (ii) a complete solution to the separability problem for pure states also of bipartite systems independent of the classical Schmidt decomposition method and (iii) a natural generalization of these results to multipartite systems.

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D. Salgado, J. L. Sanchez-Gomez, M. Ferrero. 2005-09-19. Another dual formulation of the separability problem. https://arxiv.org/abs/quant-ph/0509124

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