Bures distance as a measure of entanglement for symmetric two-mode Gaussian states

Details Bures distance as a measure of entanglement for symmetric two-mode Gaussian states Bures distance as a measure of entanglement for symmetric two-mode Gaussian states

2007-05-08

arxiv.org/abs/0705.1138v3

Physical Review A 77, 062319 (2008)

Physics

Quantum Physics

published version

Scientific paper

10.1103/PhysRevA.77.062319

We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was considerably simplified by using the remarkable properties of the Uhlmann fidelity as well as the standard form II of the covariance matrix of a symmetric state. Our result for the Gaussian degree of entanglement measured by the Bures distance depends only on the smallest symplectic eigenvalue of the covariance matrix of the partially transposed density operator. It is thus consistent to the exact expression of the entanglement of formation for symmetric two-mode Gaussian states. This non-trivial agreement is specific to the Bures metric.

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