Fundamental properties of Tsallis relative entropy
By Shigeru Furuichi, K. Yanagi, K. Kuriyama. 2004
201 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/30ce7b7deb9005c4ee84fc1c5105fff135ed0338
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Information theoretical properties of Tsallis entropies (2004, background): “See [19, 20, 21, 23] for details of Tsallis relative entropy.”
- A note on operator inequalities of Tsallis relative operator entropy (2005, unknown): “ar X iv :m at h/ 05 02 33 8v 2 [ m at h. FA ] 5 A pr Keywords : Tsallis relative entropy, relative operator entropy, superadditivity, subadditivity and operator inequality 2000 Mathematics Subject Classification : 47A63, 94A17, 15A39”
- Convexity/concavity of renyi entropy and α-mutual information (2015, methodology): “The Schur-concavity of the Tsallis entropy was discussed in [7].”