Related papers: A Novel Distance Matric: Generalized Relative Entr…
Given a compact metric space $X$ and a continuous map $T: X \to X$, the induced hyperspace map $T_\mathcal{K}$ acts on the hyperspace $\mathcal{K}(X)$ of nonempty closed sets of $X$, and the measure-induced map $T_*$ acts on the space of…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly…
Motivated by the approach of random linear codes, a new distance in the vector space over a finite field is defined as the logarithm of the "surface area" of a Hamming ball with radius being the corresponding Hamming distance. It is named…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular…
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
We summarize some results of geometric measure theory concerning rectifiable sets and measures. Combined with the entropic chain rule for disintegrations (Vigneaux, 2021), they account for some properties of the entropy of rectifiable…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
Generalized mutual entropy is defined for networks and applied for analysis of complex network structures. The method is tested for the case of computer simulated scale free networks, random networks, and their mixtures. The possible…