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arXiv · 1310.6470

Minkowski structure for purity and entanglement of Gaussian bipartite states

Marcos C. de Oliveira·Fernando Nicacio·Salomon S. Mizrahi
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Abstract

The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode bipartite Gaussian state. We verify that the correlation matrix of arbitrary Gaussian states can be associated to a hyperbolic space with a Minkowski metric, which is divided in two regions - separablelike and entangledlike, in equivalence to timelike and spacelike in special relativity. This correspondence naturally allows the definition of two insightful invariant squared distances measures - one related to the purity and another related to amount of entanglement. The second distance allows us to define a measure for entanglement in terms of the invariant interval between the given state and its closest separable state, given in a natural manner without the requirement of a minimization procedure.

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Marcos C. de Oliveira, Fernando Nicacio, Salomon S. Mizrahi. 2013-10-24. Minkowski structure for purity and entanglement of Gaussian bipartite states. https://doi.org/10.1103/physreva.88.052324

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