We study the monotonicity under mixing 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
Gibilisco, P., Isola, T. (2005). On the monotonicity of scalar curvature in classical and quantum information geometry. JOURNAL OF MATHEMATICAL PHYSICS, 46(2), 1-14 [10.1063/1.1834693].
On the monotonicity of scalar curvature in classical and quantum information geometry
GIBILISCO, PAOLO;ISOLA, TOMMASO
2005-01-01
Abstract
We study the monotonicity under mixing 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| File | Dimensione | Formato | |
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