Fundamental properties of Tsallis relative entropy

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hi...

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Bibliographic Details
Published in:Journal of mathematical physics 2004-12, Vol.45 (12), p.4868-4877
Main Authors: Furuichi, S., Yanagi, K., Kuriyama, K.
Format: Article
Language:English
Subjects:
Entropy
Exact sciences and technology
Mathematical analysis
Mathematical methods in physics
Mathematics
Physics
Quantum theory
Sciences and techniques of general use
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Summary:Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible. The generalized Tsallis relative entropy is defined and its subadditivity is shown by its joint convexity. Moreover, the generalized Peierls–Bogoliubov inequality is also proven.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1805729