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. This is done by considering phase space probability distributions parametrized by their covariances and endowing the resulting statistical manifold with the Fisher-Rao...

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Bibliographic Details
Published in:Journal of mathematical physics 2017-01, Vol.58 (1)
Main Authors: Felice, Domenico, Quang, Minh Hà, Mancini, Stefano
Format: Article
Language:English
Subjects:
Chain entanglement
Entangled states
Physics
Statistical analysis
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Summary:We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. This is done by considering phase space probability distributions parametrized by their covariances and endowing the 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 inclusions.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4973507