Related papers: Towards a Semantic Information Theory (Introducing…
Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
We propose a system of information-theoretic axioms from which we derive the formalism of quantum theory. Part I is devoted to the conceptual foundations of the information-theoretic approach. We argue that this approach belongs to the…
Logical probability theory was developed as a quantitative measure based on Boole's logic of subsets. But information theory was developed into a mature theory by Claude Shannon with no such connection to logic. A recent development in…
We provide an historical perspective of how the notion of correlations has evolved within quantum physics. We begin by reviewing Shannon's information theory and its first application in quantum physics, due to Everett, in explaining the…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information.…
Since Claude Shannon founded Information Theory, information theory has widely fostered other scientific fields, such as statistics, artificial intelligence, biology, behavioral science, neuroscience, economics, and finance. Unfortunately,…
We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined."…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theory of quantum information that embraces both classical and…
Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces a semantic…