Mathematical Foundations Of Information Theory
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Mathematical Foundations Of Information Theory
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Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1957-01-01
Mathematical Foundations Of Information Theory written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957-01-01 with Mathematics categories.
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.
Mathematical Foundations Of Information Theory
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Author : A. Y. Khintchine
language : en
Publisher:
Release Date : 1957
Mathematical Foundations Of Information Theory written by A. Y. Khintchine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Information theory categories.
Mathematical Foundations Of Information Theory
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Author : A. Ya. Khinchin
language : en
Publisher: Courier Corporation
Release Date : 2013-04-09
Mathematical Foundations Of Information Theory written by A. Ya. Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
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.
Mathematical Foundations Of Information Theory
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Author : Aleksandr Jakovlevič Hinčin
language : en
Publisher:
Release Date : 1957
Mathematical Foundations Of Information Theory written by Aleksandr Jakovlevič Hinčin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Information theory categories.
Quantum Information Processing With Finite Resources
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Author : Marco Tomamichel
language : en
Publisher: Springer
Release Date : 2015-10-14
Quantum Information Processing With Finite Resources written by Marco Tomamichel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Science categories.
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.
Mathematical Foundations Of Information Retrieval
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Author : S. Dominich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Foundations Of Information Retrieval written by S. Dominich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Quantum Information Theory
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Author : Masahito Hayashi
language : en
Publisher: Springer
Release Date : 2016-11-03
Quantum Information Theory written by Masahito Hayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-03 with Computers categories.
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
Mathematical Foundations Of Quantum Information And Computation And Its Applications To Nano And Bio Systems
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Author : Masanori Ohya
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-15
Mathematical Foundations Of Quantum Information And Computation And Its Applications To Nano And Bio Systems written by Masanori Ohya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-15 with Science categories.
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.
New Foundations For Information Theory
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Author : David Ellerman
language : en
Publisher: Springer Nature
Release Date : 2021-10-30
New Foundations For Information Theory written by David Ellerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-30 with Philosophy categories.
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.
Stochastic Models Information Theory And Lie Groups Volume 1
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Author : Gregory S. Chirikjian
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-02
Stochastic Models Information Theory And Lie Groups Volume 1 written by Gregory S. Chirikjian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.