On the monotonicity of scalar curvature in classical and quantum information geometry
arXiv:math-ph/0407007 · doi:10.1063/1.1834693
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.
20 pages, 2 .eps figures; (v2) section 2 rewritten, typos corrected