Abstract.
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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Marian, P., Marian, T. Gaussian entanglement of symmetric two-mode Gaussian states. Eur. Phys. J. Spec. Top. 160, 281–289 (2008). https://doi.org/10.1140/epjst/e2008-00731-x
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DOI: https://doi.org/10.1140/epjst/e2008-00731-x