Related papers: Towards a Semantic Information Theory (Introducing…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
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…
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…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…
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…
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 Shannon's seminal paper, entropy of printed English, treated as a stationary stochastic process, was estimated to be roughly 1 bit per character. However, considered as a means of communication, language differs considerably from its…
A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of…
The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of…
The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…
Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of…
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory.…
Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and…
Rough speaking, information theory deals with data transmitted over a channel such as the internet. Modern information theory is generally considered to have been founded in 1948 by Shannon in his seminal paper, "A mathematical theory of…
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…
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…