Related papers: On Relations Between the Relative entropy and $\ch…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
We study the relative entropy and the trace square distance, both of which measure the distance between reduced density matrices of two excited states in two dimensional conformal field theories. We find a general formula for the relative…
R\'enyi divergence is related to R\'enyi 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 R\'enyi as…
In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($\chi^2$),…
We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…
This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…
We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…