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...

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 consider the Rényi entropy function for weakly ψ-mixing systems. The first main result proves existence and regularity properties. The second main result of the paper is to get the decay rate for the large deviation of the return time to cylinder sets. We show it to be exponential with a rate given by the Rényi entropy function. Finally we also obtain bounds for the free energy.

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 ...

This paper explores some applications of a twomoment inequality for the integral of the r-th power of a function, where 0 < r < 1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment c...

The work discussed in this presentation is motivated by the problem of decoding superposition codes when using {−1,+1}-valued dictionary elements. Under this encoding scheme, the output, Y , is a linear combination of independent Bernoulli random variables and noise. Statistical decoding then requires the study of the conditional distribution of the Bernoulli random variables given the output, ...