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The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…

Information Theory · Computer Science 2021-05-06 Saptarshi Chakraborty , Debolina Paul , Swagatam Das

We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…

Quantum Physics · Physics 2022-12-09 Jacob A. Barandes , David Kagan

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

Statistical Mechanics · Physics 2019-10-21 Piergiulio Tempesta , Henrik Jeldtoft Jensen

Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…

Quantum Physics · Physics 2025-10-21 Christopher Popp , Tobias C. Sutter , Beatrix C. Hiesmayr

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

Quantum Physics · Physics 2015-03-20 Marco Tomamichel

The paper considers a new quantitative-qualitative proximity measure for the features of information objects, where data enters a common information resource from several sources independently. The goal is to determine the possibility of…

Artificial Intelligence · Computer Science 2026-04-08 Volodymyr Yuzefovych

We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…

Quantum Physics · Physics 2018-10-02 Yi Peng , Heng Fan

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Information Theory · Computer Science 2026-05-28 Yanxiao Liu , Yijun Fan , Deniz Gündüz

We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…

Computation and Language · Computer Science 2007-05-23 Lillian Lee

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…

Statistical Mechanics · Physics 2023-08-21 Vladimir Zhdankin

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Statistics Theory · Mathematics 2022-03-03 Michel Broniatowski , Wolfgang Stummer

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…

Machine Learning · Computer Science 2025-06-24 Tao Yang , Chuang Liu , Xiaofeng Ma , Weijia Lu , Ning Wu , Bingyang Li , Zhifei Yang , Peng Liu , Lin Sun , Xiaodong Zhang , Can Zhang

Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…

Quantum Physics · Physics 2026-04-08 Johannes Jakob Meyer , Asad Raza , Jacopo Rizzo , Lorenzo Leone , Sofiene Jerbi , Jens Eisert

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…

Information Theory · Computer Science 2015-03-13 François Bavaud

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Mathematical Physics · Physics 2017-12-19 Roberto Franzosi , Domenico Felice , Stefano Mancini , Marco Pettini

Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…

Applications · Statistics 2025-06-17 Michael R. Powers , Jiaxin Xu

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…

Mathematical Physics · Physics 2018-03-02 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…

Methodology · Statistics 2024-08-06 Mohd. Arshad , Swaroop Georgy Zachariah , Ashok Kumar Pathak

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…

Statistical Mechanics · Physics 2018-04-10 D. Felice , C. Cafaro , S. Mancini

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

Statistics Theory · Mathematics 2019-11-12 Linda Altieri , Daniela Cocchi , Giulia Roli