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Publisher DOI: 10.3390/e21090831
Title: Canonical divergence for flat α-connections: classical and quantum
Language: English
Authors: Felice, Domenico 
Ay, Nihat 
Keywords: Alpha connections; Canonical divergence; Information geometry; Kullback-Leibler divergence; Quantum relative entropy
Issue Date: 25-Aug-2019
Publisher: MDPI
Source: Entropy 21 (9): 831 (2019-08-25)
Abstract (english): 
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.
DOI: 10.15480/882.3735
ISSN: 1099-4300
Journal: Entropy 
Document Type: Article
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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