Gaussian entanglement of symmetric two-mode Gaussian statesP. Marian1 and T.A. Marian2
1 Department of Chemistry, University of Bucharest, Boulevard Regina Elisabeta 4-12, 030018 Bucharest, Romania
2 Department of Physics, University of Bucharest, PO Box MG-11, 077125 Bucharest-Magurele, Romania
Published online: 18 June 2008
A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.
© EDP Sciences, Springer-Verlag 2008