We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian’s Von Neumann entropy as a measure of bipartite entanglement present betw...

Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...

The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and entanglement measures can be realized from it. As such, there has been broad interest in generalizing the notion to further understand its most basic properti...

This paper discusses a possible program for improving the outer (converse) bounds on the finite-blocklength performance of multiple-access codes. The program is based on a certain conjecture involving Rényi entropy of a sum of two independent binary vectors. Some partial results towards showing the conjecture are presented. The problem of bounding the joint Rényi entropy in terms of the margina...

In this paper, we consider the problem of variable-length source coding allowing errors. The exponential moment of the codeword length is analyzed in the non-asymptotic regime and in the asymptotic regime. Our results show that the smooth Rényi entropy characterizes the optimal exponential moment of the codeword length. Index Terms ε source coding, exponential moment, the smooth Rényi entropy, ...

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdös-Rényi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm ...