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Canonical divergence for flat α-connections: classical and quantum

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Bibliographic Details
Published in: Entropy 21(2019), 9, Artikel-ID 831, Seite 1-14
Authors and Corporations: Felice, Domenico (Author), Ay, Nihat (Author)
Other Authors: Ay, Nihat [Author]
Type of Resource: E-Book Component Part
Language: English
published:
25 August 2019
Series: : Entropy, 21(2019), 9, Artikel-ID 831, Seite 1-14
, volume:21
Subjects:
Alpha connections
Canonical divergence
Information geometry
Kullback-Leibler divergence
Quantum relative entropy
Alpha connections
Canonical divergence
Information geometry
Kullback-Leibler divergence
Quantum relative entropy
Source: Verbunddaten SWB
Lizenzfreie Online-Ressourcen
ISSN: 1099-4300
License:
https://doi.org/10.15480/882.3735$xR$4LF
Description
Summary: 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.
ISSN: 1099-4300
DOI: 10.15480/882.3735
Access: Open Access