Probabilistic ‘distances’ (also called divergences), which in some sense assess how ‘close’ two probability distributions are from one another, have been widely employed in probability, statistics, information theory, and related fields. Of particular importance due to their generality and applicability are the Rényi divergence measures. This paper presents closed-form expressions for the Rényi...

1.1 Random (ER) graphs The Erdös-Rényi (ER) random graphs model, also called simply random graphs, was presented by Erdös and Rényi [4] in the 1950s and 1960s. Erdös and Rényi characterized random graphs and showed that many of the properties of such networks can be calculated analytically. Construction of an ER random graph with parameter 0 ≤ p ≤ 1 and N nodes is by connecting every pair of no...

The concept of classical f -divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory;...

Entanglement Rényi-α entropy is an entanglement measure. It reduces to the standard entanglement of formation when α tends to 1. We derive analytical lower and upper bounds for the entanglement Rényi-α entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rény...

The concept of classical f -divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory;...

We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller–Lennert et al. Recently, Müller–Lennert et al. [12] and Wilde et al. [15] modified the traditional notion of relative Rényi entropy and showed that their new definition has several desirable properties of a relative entropy. One of th...

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...

In this work, we examine the existence and the computation of the Rényi divergence rate, lim ( ), between two time-invariant finite-alphabet Markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions and , respectively. This yields a generalization of a result of Nemetz where he assumed that the initial probabilities under and are strictly p...