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Conference: Bucharest University Faculty of Physics 2006 Meeting

Section: Quantum Mechanics and Statistical Physics Seminar

Title:

Separability of two-mode Gaussian states revisited

Authors:

Paulina Marian(1), Tudor A. Marian(2)

Affiliation:

(1) Department of Chemistry, University of Bucharest, Boulevard Regina Elisabeta 4-12,

R-030018 Bucharest, Romania

(2) Department of Physics, University of Bucharest, 405 Atomistilor St, R-077125 Bucharest-Magurele, Romania

E-mail

t.marian@b.astral.ro

Keywords:

radiation,two-mode Gaussian state, separability, classicality

Abstract:

We reexamine a necessary condition for separability of any two-mode state of the radiation field recently proposed by Lu-Ming Duan et al. [Phys.Rev. Lett. 84, 2722-2725 (2000)]. These authors established an inequality for the variances of a pair of EPR-like variables that holds if the state is separable. Then, by adequate local unitary transformations of the state, they succeeded to reduce the separability of a given Gaussian state to the classicality of the transformed one. In this way, they found in principle a sufficient condition of separability of any two-mode Gaussian state expressed in terms of an unknown solution of a system of two algebraic equations. However, the problem has been explicitly solved only for symmetric Gaussian states. In this work we present a minimization scheme that leads to the above-mentioned system of equations. The existence of a solution is proved. A careful discussion on its uniqueness follows. We give the analytic solution for squeezed thermal states and mode-mixed thermal states, as well as the explicit solution for any Gaussian state at the separability threshold.