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On the monotonicity of scalar curvature in classical and quantum information geometry

P. Gibilisco·T. Isola
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Abstract

We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries and Wigner-Yanase-Dyson information. Finally we show that this last conjecture implies the truth of the Petz conjecture about the monotonicity of the scalar curvature of the Bogoliubov-Kubo-Mori monotone metric.

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BibTeXRIS

P. Gibilisco, T. Isola. 2004-10-08. On the monotonicity of scalar curvature in classical and quantum information geometry. https://doi.org/10.1063/1.1834693

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