Related papers: A Third Information-Theoretic Approach to Finite d…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival…
In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a…
We study conditional mutual information (cMI) between a pair of variables $X,Y$ given a third one $Z$ and derived quantities including transfer entropy (TE) and causation entropy (CE) in the dynamically relevant context where $X=T(Y,Z)$ is…
The unknown amplitude law q(x) defining an observed effect may be found using the principle of Extreme Physical Information. EPI is derived as follows. The observations follow an information flow J --> I, with J the information intrinsic to…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting,…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on $\mathbb{R}^n$, two operations can be induced by considering the quotient of the space by…
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry,…
We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fr\'echet means) of independent non-identically distributed random variables taking values in Riemannian manifolds. In…