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

The separability of the evolved tripartite Gaussian state

Xiaoyu Chen

Published Oct 26, 2007• 0 citations
Publisher

Abstract

We consider the time evolution of the tripartite three mode Gaussian state which is initially prepared in genuine entangled pure state. The state undergoes parametric amplification and amplitude damping as well as thermal noise. The correlation matrix of the evolved state is studied in the symmetrical case. The separability conditions are given.

DOI
10.1117/12.754810

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 11, 2005•0 citations
We consider the time evolution of the tripartite three mode Gaussian state which is initially prepared in genuine entangled pure state. The state undergoes parametric amplification and amplitude damping as well as thermal noise. The correlation matrix of the evolved state is studied in the symmetrical case. The separability conditions are given.
We give a simplified form of Simon's separability criterion for two-mode Gaussian states, showing that for systems whose unitary evolution is governed by arbitrary time-dependent quadratic Hamiltonians, the separability dynamics is completely described in terms of the determinant of the cross-covariance matrix. As concrete examples, we consider the evolution of the 'inverse negativity coefficient' (which gives a quantitative estimation of the 'degree of entanglement') for two initially uncoupled modes (each being in a squeezed thermal state) in the cases of parametric converter, parametric amplifier and for a cavity whose boundary oscillates in resonance with two field modes.
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.