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In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003);…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its…
In this presentation are discussed some problems, relevant with application of information technologies in nano-scale systems and devices. Some methods already developed in quantum information technologies may be very useful here. Here are…
Based on a synthesis of three main ingredients: (i) the Shannon information in nonequilibrium systems, (ii) the semiclassical energy-time quantization rule, and (iii) the quasistatic information-energy correspondence, a new general rule for…
We introduce Ideograph, a language for expressing and manipulating structured data. Its types describe kinds of structures, such as natural numbers, lists, multisets, binary trees, syntax trees with variable binding, directed multigraphs,…
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…
To formulate a universal framework of information theory is beneficial. This study proves that the sextuple model of the objective information theory (OIT) is a sufficient and necessary condition for discussing information with four basic…
In order to have the most safe way of dealing with unanalysable quantum whole the Copenhagen interpretation takes as a "frame of reference" the preparation parameters and outcomes of the measurements. It represents {\it passive}…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory.…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
A remarkable theorem by Clifton, Bub and Halvorson (2003)(CBH) characterizes quantum theory in terms of information--theoretic principles. According to Bub (2004, 2005) the philosophical significance of the theorem is that quantum theory…
What kind of object is a quantum state? Is it an object that encodes an exponentially growing amount of information (in the size of the system) or more akin to a probability distribution? It turns out that these questions are sensitive to…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
We describe a new approach to data modeling, called the concept-oriented model (COM), and a novel concept-oriented query language (COQL). The model is based on three principles: duality principle postulates that any element is a couple…