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Open AccessFeature PaperArticle

Canonical Divergence for Flat α-Connections: Classical and Quantum

by 1,* and 1,2,3
1
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
2
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
3
Faculty of Mathematics and Computer Science, University of Leipzig, PF 100920, 04009 Leipzig, Germany
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(9), 831; https://doi.org/10.3390/e21090831
Received: 25 July 2019 / Revised: 23 August 2019 / Accepted: 23 August 2019 / Published: 25 August 2019
(This article belongs to the Special Issue The Ubiquity of Entropy)
A recent canonical divergence, which is introduced on a smooth manifold M endowed with a general dualistic structure ( g , , * ) , is considered for flat α -connections. In the classical setting, we compute such a canonical divergence on the manifold of positive measures and prove that it coincides with the classical α -divergence. In the quantum framework, the recent canonical divergence is evaluated for the quantum α -connections on the manifold of all positive definite Hermitian operators. In this case as well, we obtain that the recent canonical divergence is the quantum α -divergence. View Full-Text
Keywords: information geometry; quantum relative entropy; alpha connections; canonical divergence; Kullback-Leibler divergence information geometry; quantum relative entropy; alpha connections; canonical divergence; Kullback-Leibler divergence
MDPI and ACS Style

Felice, D.; Ay, N. Canonical Divergence for Flat α-Connections: Classical and Quantum. Entropy 2019, 21, 831.

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