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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Calculating the Gaussian relative entropy of entanglement

Li-zhen Jiang, Liang-neng Wu, Yun Zhou

Published Jan 11, 2005• 0 citations
Publisher

Abstract

We in this paper calculate the relative entropy between the bipartite Gaussian states. By evaluating the minimization of the relative entropy of an entangled Gaussian state with respect to the separable Gaussian states, we obtain the Gaussian relative entropy of entanglement of the state. The bipartite operations of squeezing and rotations on the separable states are also addressed. We prove that for bipartite symmetric Gaussian states the separable states we sought will be symmetric Gaussian states, and we get quite simple expressions of Gaussian relative entropy of entanglement for such states.

DOI
10.1117/12.575432

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We in this paper calculate the relative entropy between the bipartite Gaussian states. By evaluating the minimization of the relative entropy of an entangled Gaussian state with respect to the separable Gaussian states, we obtain the Gaussian relative entropy of entanglement of the state. The bipartite operations of squeezing and rotations on the separable states are also addressed. We prove that for bipartite symmetric Gaussian states the separable states we sought will be symmetric Gaussian states, and we get quite simple expressions of Gaussian relative entropy of entanglement for such states.
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Multipartite entanglement is quite difficult to deal with. In this paper, I will consider a particular kind of tripartite Gaussian states, which can be produced as the initial pure tripartite states undergo different noise for each party. I will make use of the relative entropy of entanglement to evaluate the entanglement properties of the states based on the fact that the separability of tripartite Gaussian states is well known. In addition, the procedure of calculating the relative entropy between Gaussian states have developed recently. All these make the evaluating the relative entropy of entanglement of tripartite Gaussian states possible.