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

Dias, N. C.; Gossan, M. de; Prata, J. N.

http://hdl.handle.net/10400.26/57830

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Authors

Dias, N. C.

Gossan, M. de

Prata, J. N.

Abstract(s)

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.

Keywords

Quantum entanglement separability criteria Gaussian states Wigner functions

URI

http://hdl.handle.net/10400.26/57830

Citation

Dias, N. C., de Gosson, M., & Prata, J. N. (2022). Partial traces and the geometry of entanglement: Sufficient conditions for the separability of Gaussian states. Reviews in Mathematical Physics, 34(03).