Related papers: On Classical Analogues of Free Entropy Dimension
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…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that…
For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to…
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…
We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension along Wasserstein geodesics, as well as study their topological…
We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
We give a pedagogical introduction to quantum discord. We the discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy…
Beckner's inequality is a family of inequalities that interpolates the two fundamental functional inequalities, the logarithmic Sobolev and Poincar\'e's inequalities. It is parametrized by exponent $p\in (1,2]$ and it implies the…
We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
We investigate double-interval entanglement measures, specifically reflected entropy, mutual information, and logarithmic negativity, in quasiparticle excited states for classical, bosonic, and fermionic systems. We develop an algorithm…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…