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Fortschritte der Physik

Separability and Distillability of bipartite Gaussian States – the Complete Story

G. Giedke, Barbara Kraus, L.-M. Duan, P. Zoller, J. I. Cirac, Maciej Lewenstein

Published Oct 1, 2001• 15 citations
Publisher

Abstract

We present necessary and sufficient conditions for both the separability and the distillability of bipartite Gaussian states of an arbitrary number of modes. The conditions can be easily checked by direct calculations, thus providing operational criteria for both properties. This solves the separability and distillability problems for Gaussian states.

DOI
10.1002/1521-3978(200110)49:10/11<973::aid-prop973>3.0.co;2-b

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We present necessary and sufficient conditions for both the separability and the distillability of bipartite Gaussian states of an arbitrary number of modes. The conditions can be easily checked by direct calculations, thus providing operational criteria for both properties. This solves the separability and distillability problems for Gaussian states.
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PPP-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $\mathrm{Sp}(2,R)\ensuremath{\bigotimes}\mathrm{Sp}(2,R)$ locally invariant. Although this special class of states can be reached by a convenient $\mathrm{Sp}(2,R)\ensuremath{\bigotimes}\mathrm{Sp}(2,R)$ transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.