2 research outputs found
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 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
Information inequalities and Generalized Graph Entropies
In this article, we discuss the problem of establishing relations between
information measures assessed for network structures. Two types of entropy
based measures namely, the Shannon entropy and its generalization, the
R\'{e}nyi entropy have been considered for this study. Our main results involve
establishing formal relationship, in the form of implicit inequalities, between
these two kinds of measures when defined for graphs. Further, we also state and
prove inequalities connecting the classical partition-based graph entropies and
the functional-based entropy measures. In addition, several explicit
inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa