Quantum Information

It must be first noted that, despite the title, quantum information theory is not the main topic of this chapter. Instead, we will merely concentrate on descriptional differences between presenting information by using classical and quantum systems. In fa

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Advisory Board: S. Amari G. Brassard M. Conrad K.A. De Jong C.C.A.M. Gielen T. Head L. Kari L. Landweber T. Martinetz Z. Michalewicz M.C. Mozer E.Oja G. Paun J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel C. Torras D. Whitley E. Winfree J.M. Zurada

Springer-Verlag Berlin Heidelberg GmbH

Mika Hirvensalo

Quantum Computing Second Edition

Springer

Mika Hirvensalo University of Turku Department of Mathematics 20014 Thrku Finland [email protected]

Series Editors G. Rozenberg (Managing Editor) [email protected] Th. Bäck,}. N. Kok, H. P. Spaink Leiden Center for Natural Computing, Leiden University Niels Bohrweg 1, 2333 CA Leiden, The Netherlands A.E.Eiben Vrije Universiteit Amsterdam

Library of Congress Cataloging-in-Publication Data Hirvensalo, Mika, 1972Quantum computing / M. Hirvensalo. p. cm. - (Natural computing series) Includes bibliographical references and index. ISBN 978-3-642-07383-0 ISBN 978-3-662-09636-9 (eBook) DOI 10.1007/978-3-662-09636-9 1. Quantum

computers. I. Tide. 11. Series. QA76.889.H57 2003 004.1-dc22 2003066405

ACM Computing Classification (1998): F.1-2, G.1.2, G3, H.l.l, 1.1.2, J.2

ISBN 978-3-642-07383-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 2nd edition 2004 The use of general descriptive names, registered names, trademarks, 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. Cover design: KünkelLopka, Heidelberg Typesetting: Computer to film from author's data Printed on acid-free paper 45/3142PS - 543210

Preface to the Second Edition

After the first edition of this book was published, I received much positive feedback from the readers. It was very helpful to have all those comments suggesting improvements and corrections. In many cases, it was suggested that more aspects on quantum information would be welcome. Unfortunately, I am afraid that an attempt to cover such a broad area as quantum information theory would make this book too scattered to be helpful for educational purposes. On the other hand, ladmit that some aspects of quantum information should be discussed. The first edition already contained the so-called NoCloning Theorem. In this edition, I have added a stronger version of the afo