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The volume of Gaussian states by information geometry
We formulate the problem of determining the volume of the set of Gaussian
physical states in the framework of information geometry. That is, by
considering phase space probability distributions parametrized by the
covariances and supplying this resulting statistical manifold with the
Fisher-Rao metric. We then evaluate the volume of classical, quantum and
quantum entangled states for two-mode systems showing chains of strict
inclusion
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