Related papers: New Logical Foundations for Quantum Information Th…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
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."…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
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…
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u')…
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…
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…
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…
The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as…
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.…
According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and…
We review of the interface between (theoretical) physics and information for non-experts. The origin of information as related to the notion of entropy is described, first in the context of thermodynamics then in the context of statistical…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
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…
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…
Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very…
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…