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Fundamental properties of Tsallis relative entropy

By S. Furuichi, K. Yanagi and K. Kuriyama


Abstract. 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. The generalized Tsallis relative entropy is defined and its subadditivity in the special case is shown by its joint convexity. As a byproduct, the superadditivity of the quantum Tsallis entropy for the independent systems in the case of 0 ≤ q < 1 is obtained. Moreover, the generalized Peierls-Bogoliubov inequality is also proven

Topics: Tsallis relative entropy, relative operator entropy, monotonicity and generalized Peierls-Bogoliubov inequality
Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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