Author: Aleksandr I?Akovlevich Khinchin Publisher: Courier Corporation ISBN: 0486604349 Category : Mathematics Languages : en Pages : 130
Book Description
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author: A. Ya. Khinchin Publisher: Courier Corporation ISBN: 0486318443 Category : Mathematics Languages : en Pages : 130
Book Description
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author: Marco Tomamichel Publisher: Springer ISBN: 3319218913 Category : Science Languages : en Pages : 146
Book Description
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
Author: Mark M. Wilde Publisher: Cambridge University Press ISBN: 1316813304 Category : Computers Languages : en Pages : 1020
Book Description
Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.
Author: Masanori Ohya Publisher: Springer Science & Business Media ISBN: 9400701713 Category : Science Languages : en Pages : 768
Book Description
This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Author: S. Dominich Publisher: Springer Science & Business Media ISBN: 9401007527 Category : Computers Languages : en Pages : 300
Book Description
This book offers a comprehensive and consistent mathematical approach to information retrieval (IR) without which no implementation is possible, and sheds an entirely new light upon the structure of IR models. It contains the descriptions of all IR models in a unified formal style and language, along with examples for each, thus offering a comprehensive overview of them. The book also creates mathematical foundations and a consistent mathematical theory (including all mathematical results achieved so far) of IR as a stand-alone mathematical discipline, which thus can be read and taught independently. Also, the book contains all necessary mathematical knowledge on which IR relies, to help the reader avoid searching different sources. Audience: The book will be of interest to computer or information scientists, librarians, mathematicians, undergraduate students and researchers whose work involves information retrieval.
Author: David Ellerman Publisher: Springer Nature ISBN: 3030865525 Category : Philosophy Languages : en Pages : 121
Book Description
This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.
Author: Erchin Serpedin Publisher: CRC Press ISBN: 1439855145 Category : Computers Languages : en Pages : 852
Book Description
Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.
Author: Aleksandr I?Akovlevich Khinchin Publisher: Courier Corporation ISBN: 9780486601472 Category : Mathematics Languages : en Pages : 212
Book Description
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
Author: Herbert S. Green Publisher: Springer Science & Business Media ISBN: 364257162X Category : Science Languages : en Pages : 248
Book Description
In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.
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Author: Aleksandr I?Akovlevich Khinchin
Author: A. Ya. Khinchin
Author: Marco Tomamichel
Author: Mark M. Wilde
Author: Masanori Ohya
Author: S. Dominich
Author: David Ellerman
Author: Erchin Serpedin
Author: Aleksandr I?Akovlevich Khinchin
Author: Herbert S. Green