相关论文: Shannon Shakes Hands with Chernoff: Big Data Viewp…

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

In the setting where information cannot be verified, we propose a simple yet powerful information theoretical framework---the Mutual Information Paradigm---for information elicitation mechanisms. Our framework pays every agent a measure of…

We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…

Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…

Shannon based his information theory on the notion of probability measures as it we developed by Kolmogorov. In this paper we study some fundamental problems in information theory based on expectation measures. In the theory of expectation…

An information measure inspired by Onicescu's information energy and Uffink's information measure (recently discussed by Brukner and Zeilinger) are calculated as functions of the number of particles $N$ for fermionic systems (nuclei and…

The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…

Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…

Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…

We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information theory, introduced by Shannon, has been extremely successful and influential as a mathematical theory of communication. Shannon's notion of information does not consider the meaning of the messages being communicated but only…

This paper derives bounds for two omnipresent information theoretic measures, the Shannon entropy and its complementary dual, the extropy. Based on a large size data set from a logconcave model, the said bounds are obtained for the entropy…

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of…

A Massey-like inequality is any useful lower bound on guessing entropy in terms of the computationally scalable Shannon entropy. The asymptotically optimal Massey-like inequality is determined and further refined for finite-support…

Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…

Shannon information was defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two…

We reformulate and reframe a series of increasingly complex parametric statistical topics into a framework of response-vs-covariate (Re-Co) dynamics that is described without any explicit functional structures. Then we resolve these topics'…

Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…