Gaussian entanglement of symmetric two-mode Gaussian states

Details Gaussian entanglement of symmetric two-mode Gaussian states Gaussian entanglement of symmetric two-mode Gaussian states

2007-11-21

arxiv.org/abs/0711.3477v1

Eur. Phys. J. Special Topics 160, 281--289 (2008)

Physics

Quantum Physics

Submitted to European Physical Journal Special Topics as a contribution to CEWQO, Palermo 2007

Scientific paper

10.1140/epjst/e2008-00731-x

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.

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