Classical Zero-Error Information Theory
This chapter aims to introduce the main concepts of the classical zero-error information theory. We begin by defining the zero-error capacity of a discrete memoryless channel and presenting some basic concepts, like adjacency and adjacency-reducing mappin
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tum Zero-Error Information Theory
Quantum Zero-Error Information Theory
Elloá B. Guedes • Francisco Marcos de Assis Rex A.C. Medeiros
Quantum Zero-Error Information Theory
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Elloá B. Guedes Superior School of Technology Amazonas State University Manaus, AM, Brazil
Francisco Marcos de Assis Center of Electric Engineering and Informatics Campina Grande Federal University Campina Grande, PB, Brazil
Rex A.C. Medeiros School of Science and Technology Rio Grande do Norte Federal University Natal, RN, Brazil
ISBN 978-3-319-42793-5 ISBN 978-3-319-42794-2 (eBook) DOI 10.1007/978-3-319-42794-2 Library of Congress Control Number: 2016947428 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
“From error to error, one discovers the entire truth.” – Sigmund Freud (1856–1939)
Foreword
The field of Quantum Information Science (QIS) has the potential to lead to revolutionary advances in our capability to communicate and process information. It has grown and diversified with a spectacular dynamism since the 1980s, following the work of pioneers such as Charles Bennett, Richard Feynman, or Artur Ekert. Those progresses were rooted in a vision that has proved to be extremely fertile: asking—and answering—questions about information processing by combining quantum physics and computer science approaches. QIS is entering a new and exciting stage of its development, with the emergence of a focused effort on quantum engineering, stimulated by our ability to fabricate increasingly efficient and reliable devices for quantum information processing. This fact may soon allow to experimentally observe the so-called quantum supremacy, i.e., the ability of quantum processing machines to solve information processing tasks that are beyond the reach of existing classical computing devices. M
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