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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…

This paper proposes to study neural networks through neuronal correlation, a statistical measure of correlated neuronal activity on the penultimate layer. We show that neuronal correlation can be efficiently estimated via weight matrix, can…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…

In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases…

This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs…

Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…

Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras, connections to random matrix theory and a discussion of open problems.

We introduce an algorithm for estimating the entropy of pairwise, probabilistic graph models by leveraging bridges between social communities and an accurate entropy estimator on sparse samples. We propose using a measure of investment from…

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…

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…

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…

This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…

Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of…

Prompt isolated leptons are essential in many analyses in high-energy particle physics but are subject to fake-lepton background, i.e. objects that mimic the lepton signature. The fake-lepton background is difficult to estimate from…