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Characterization of symmetric monotone metrics on the state space of quantum systems

Frank Hansen
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Abstract

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

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Frank Hansen. 2006-03-29. Characterization of symmetric monotone metrics on the state space of quantum systems. https://arxiv.org/abs/math-ph/0601056

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