PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference between the marginal and joint entropies must be relinquished. The same inequality, relating the PAE to the Rényi entropy, when applied to the mean code length pr...

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. This generalizes the well-known duality relation...

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...

One of the most important properties of a cryptographic system is a proof of its security. In the present work, information-theoretic methods are used for proving the security of unconditionally secure cryptosystems. The security of such systems does not depend on unproven intractability assumptions. A survey of entropy measures and their applications in cryptography is presented. A new informa...

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibl...

Rényi entropies are compared to generalized log-Fisher information and variational entropies in the context of translation, scale and concentration invariance. It is proved that the Rényi entropies occupy a special place amongst these entropies. It is also shown that Shannon entropy is centrally positioned amidst the Rényi entropies.

Rényi entropy refers to a generalized class of entropies that have been used in several applications. In this work, we derive a non-parametric distance between distributions based on the quadratic Rényi entropy. The distributions are estimated via Parzen density estimates. The quadratic complexity of the distance evaluation is mitigated with GPUbased parallelization. This results in an efficien...