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Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…
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…
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
A probabilistic source is defined as the set of infinite words (over a given denumerable alphabet) endowed with a probability $\mu$. The paper deals with general binary sources where the distribution of any symbol (0 or 1) may depend on an…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…
The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out…
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
This research paper delves into the innovative integration of Shannon entropy and rough set theory, presenting a novel approach to generalize the evaluation approach in machine learning. The conventional application of entropy, primarily…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…