Related papers: Entropic independence via sparse localization
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as…
The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…
Standard probabilistic sparse coding assumes a Laplace prior, a linear mapping from latents to observables, and Gaussian observable distributions. We here derive a solely entropy-based learning objective for the parameters of standard…
The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendleyet al. that for some rectangular grids, with…
We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…
We show that for any invariant measure $\mu$ on a free group shift system, there are two numbers $h^\flat \leq h^\sharp$ which in some sense are the typical upper and lower sofic entropy values. We also give a condition under which $h^\flat…
This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
Randomized measurements access nonlinear functionals without full tomography, yet turning third-order local single-copy data into a strong entanglement test remains difficult. We convert the reduction criterion into an experimentally…
We develop an entropy based framework for analyzing symmetry breaking in dynamical systems. Information transfer, which measures the directional exchange of entropy between observables, provides a quantitative early indicator of symmetry…
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the…
We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
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,…
The classical Maximum-Entropy Principle (MEP) based on Shannon entropy is widely used to construct least-biased probability distributions from partial information. However, the Shore-Johnson axioms that single out the Shannon functional…