The squashed entanglement quantifies the amount of entanglement in a bipartite quantum state, and it satisfies all of the axioms desired for an entanglement measure. The quantum discord is a measure of quantum correlations that are different from those due to entanglement. What these two measures have in common is that they are both based upon the conditional quantum mutual information. In [Ber...

The classical entropy power inequality is extended to the Rényi entropy. We also discuss the question of the existence of the entropy for sums of independent random variables.

We investigate the large-time asymptotics of nonlinear diffusion equations ut = ∆u p in dimension n ≥ 1, in the exponent interval p > n/(n+ 2), when the initial datum u0 is of bounded second moment. Precise rates of convergence to the Barenblatt profile in terms of the relative Rényi entropy are demonstrated for finite-mass solutions defined in the whole space when they are re-normalized at eac...

Landsberg’s notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome deficiencies of entropy as a measure of disorder due to extensivity. We generalize Landsberg’s concept to three classes of extended entropies: Rényi, Tsallis and Landsberg-Vedral. Three examples are treated, including one based on the logistic ...

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...