A Quantum Leap In Information Theory

by Stefano Mancini, Andreas Winter

Overview

This is an introductory textbook at graduate or advanced undergraduate level. Students with diverse backgrounds, in mathematics, physics and computer science, can use it to become acquainted with the quantum theory of information. Its scope is deliberately chosen to be not too broad, while being self-consistent and usable for a semester-long course for beginners. The subject is presented using a balanced mix of intuitive arguments and rigorous formalism. The emphasis is not on the physical information but rather in the formal and mathematical features of quantum information theory. Only a basic knowledge of algebra is required to understand the contents of this book. In particular, a background in quantum mechanics is not needed, since quantum theory is used as a mere mathematical framework without entering into physical interpretations.The book introduces all necessary concepts from quantum theory and classical information theory, to cover the elements of quantum Shannon theory: quantum states and channels, data compression and entropy, error correcting codes and channel capacities, as well as the basics of entanglement theory and quantum cryptography.Examples are provided to help the reader in understanding the different concepts, together with exercises at the end of each chapter.

Product Details

ISBN-13:	9789811201547
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/04/2020
Pages:	248
Product dimensions:	6.00(w) x 9.00(h) x 0.63(d)

Table of Contents

Preface; Acknowledgement; List of Abbreviations; Elements of Probability Theory; Introduction, Definition, and Interpretations of Shannon's Measure of Information; Properties of Shannon's Measure of Information; Conditional and Mutual Information; Multivariate Mutual Information; Entropy and the Second Law of Thermodynamics; Appendices: Proof of an Equivalent Markovian Property; Proof of the Uniqueness of the Function H; The SMI for the Continuous Random Variable; Functional Derivatives and Functional Taylor Expansion; Some Inequalities for Convex Functions; Distribution Functions in 1D Models; Entropy Change in an Expansion Process in a Gravitational Field; Notes; References and Suggested Reading; Index