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Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

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, , Citation Otfried Gühne and Norbert Lütkenhaus 2007 J. Phys.: Conf. Ser. 67 012004 DOI 10.1088/1742-6596/67/1/012004

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1 Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, A-6020 Innsbruck, Austria

2 Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

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1742-6596/67/1/012004

Abstract

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.

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10.1088/1742-6596/67/1/012004