Partial Traces and the Geometry of Entanglement; Sufficient Conditions for the Separability of Gaussian States

• URL: http://arxiv.org/abs/2003.13190v1
• Date: Mon, 30 Mar 2020 02:22:08 GMT
• Title: Partial Traces and the Geometry of Entanglement; Sufficient Conditions for the Separability of Gaussian States
• Authors: Nuno Costa Dias, Maurice de Gosson, Joao Nuno Prata
• Abstract summary: We put an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We thereafter focus on Gaussian states and we give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states. Unlike the positive partial transposition criterion, none of these conditions is however necessary.

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