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Canonical divergence for flat α-connections: classical and quantum
Citation Link: https://doi.org/10.15480/882.3735
Publikationstyp
Journal Article
Date Issued
2019-08-25
Sprache
English
Author(s)
TORE-DOI
Journal
Volume
21
Issue
9
Article Number
831
Citation
Entropy 21 (9): 831 (2019-08-25)
Publisher DOI
Scopus ID
Publisher
MDPI
A recent canonical divergence, which is introduced on a smooth manifold M endowed with a general dualistic structure (g,∇,∇*), is considered for flat a-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.
Subjects
Alpha connections
Canonical divergence
Information geometry
Kullback-Leibler divergence
Quantum relative entropy
DDC Class
004: Informatik
Publication version
publishedVersion
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