  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.
