where H(F)σ ≡ −Tr{σF log σF} is the von Neumann entropy of a state σF on system F and we unambiguously let ρC ≡ TrAB{ρABC} denote the reduced density operator on system C, for example. The CQMI captures the correlations present between Alice and Bob from the perspective of Charlie in the independent and identically distributed (i.i.d.) resource limit, where an asymptotically large number of cop...

Rényi entropy of order α is a general measure of entropy. In this paper we derive estimations for the Rényi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the Rényi entropy dimension of arbitrary order of a mixture of measures. The key for obtaining these results is our new definition of the weighted Rényi entropy. It is shown t...

We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner’s, which are based on quantum conditional Rényi entropy of order 1 + s. Using those theorems, we derive an exponential decreasing rate for leaked information and the asymptotic equivocation rate.

This paper studies bivariate distributions with fixed marginals from an information-theoretic perspective. In particular, continuity and related properties of various information measures (Shannon entropy, conditional entropy, mutual information, Rényi entropy) on the set of all such distributions are investigated. The notion of minimum entropy coupling is introduced, and it is shown that it de...

Two different distributions may have equal Rényi entropy; thus a distribution cannot be identified by its Rényi entropy. In this paper, we explore properties of the Rényi entropy of order statistics. Several characterizations are established based on the Rényi entropy of order statistics and record values. These include characterizations of a distribution on the basis of the differences between...

A short quantum Markov chain is a tripartite state ρABC such that system A can be recovered perfectly by acting on system C of the reduced state ρBC . Such states have conditional mutual information I(A;B|C) equal to zero and are the only states with this property. A quantum channel N is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Rényi divergence is related to Rényi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) 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 information divergence. We review the most important properties of Rényi divergence, including it...

The measure-theoretic definition of Kullback-Leibler relative-entropy (KL-entropy) plays a basic role in the definitions of classical information measures. Entropy, mutual information and conditional forms of entropy can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. These measure-theoretic defi...