We evaluate Rényi entropy flows from generic quantum heat engines (QHE) to a weakly coupled probe environment kept in thermal equilibrium. We show that the flows are determined not only by heat flow but also by a quantum coherent flow that can be separately measured in experiment apart from the heat flow measurement. The same pertains to Shannon entropy flow. This appeals for a revision of the ...

Recently, ε-almost dual universal2 hash functions has been proposed as a new and wider class of hash functions. This class well works even when the random seeds of hash function are subject to non-uniform distribution. This paper evaluates the security performance when we apply this kind of hash functions. We evaluate the security in several kinds of setting based on the L1 distinguishability c...

This paper investigates the privacy amplification problem, and compares the existing two bounds: the exponential bound derived by one of the authors and the min-entropy bound derived by Renner. It turns out that the exponential bound is better than the min-entropy bound when a security parameter is rather small for a block length, and that the min-entropy bound is better than the exponential bo...

We introduce novel information-entropic variables—a Point Divergence Gain (Ω α ), a Point Divergence Gain Entropy (Iα), and a Point Divergence Gain Entropy Density (Pα)—which are derived from the Rényi entropy and describe spatio-temporal changes between two consecutive discrete multidimensional distributions. The behavior of Ω α is simulated for typical distributions and, together with Iα and ...

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the re...

It was recently shown that estimating the Shannon entropy H(p) of a discrete k-symbol distribution p requires Θ(k/ log k) samples, a number that grows near-linearly in the support size. In many applications H(p) can be replaced by the more general Rényi entropy of order α, Hα(p). We determine the number of samples needed to estimate Hα(p) for all α, showing that α < 1 requires a super-linear, r...

We introduce a new family of continuous models called the beta odd log-logistic generalized family of distributions. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, reversed-J, unimodal and bimodal shaped, and has constant, increasing, decreasing, upside-down bathtub and J-shaped hazard rates. Five special models are discussed. W...