2 Quantum Theory and Discreteness
Total Page：16
File Type：pdf, Size：1020Kb
The New Quantum Age This page intentionally left blank The New Quantum Age From Bell’s Theorem to Quantum Computation and Teleportation Andrew Whitaker Department of Physics Queen’s University Belfast 1 3 Great Clarendon Street, Oxford ox2 6dp Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offi ces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Andrew Whitaker 2012 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2012 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by SPI Publisher Services, Pondicherry, India Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY ISBN 978–0–19–958913–5 1 3 5 7 9 10 8 6 4 2 For John and Peter This page intentionally left blank Preface Over the past half-century, the approach of the community of physicists to quantum theory has changed quite markedly. At the beginning of the 1960s, the theory was regarded as a superlative tool for the study of physical systems—atoms, molecules, nuclei, radiation, and those prop- erties of solids where their atomic nature was central to the behaviour. However, it was considered totally inappropriate even to think with any novelty about the fundamental nature of quantum theory and its rather surprising properties. That, it was practically universally believed, had been sorted out once and for all by Niels Bohr thirty years before. Fifty years or so later, it has been fairly generally realized that Bohr’s ideas were not necessarily the fi nal word on the topic, that the theory itself certainly merited and still merits much further analysis, and that the theory may inform us, not just of the behaviour of physical systems, but also of fundamental and important aspects of the Universe itself. Also, and perhaps even more surprisingly, this deeper analysis of the theory has led to the development of the new topic of study of quantum information theory, which may revolutionize several aspects of com- munication and computation. This book describes the changes that have taken place, and discusses some of the new ideas current in both quantum theory and quantum information theory. I have also taken the opportunity to give an account of some of those scientists mostly responsible for the change in attitude over this period. I hope that the book will be accessible to anybody interested in the topic; to paraphrase Einstein, it might be said that I have tried to make things as simple as possible, but no simpler, given that I do not wish to avoid even some of the more complex aspects of the topic. I should state that the initial idea of the book was that it should be written jointly by Dipankar Home and myself. However, after initial planning, Dipankar had unfortunately to drop out because of other com- mitments. I acknowledge his contribution to the planning of the book. I would also particularly thank Reinhold Bertlmann and Anton Zeilinger for a particular contribution to this book. About ten years ago I was privileged to speak at Quantum [Un]Speakables , a conference they organized in Vienna to celebrate the work of John Bell and his viii Preface followers. Among those attending this conference were virtually all those who contributed to the rise of the study of quantum foundations, and the early days of quantum information theory. Renate Bertlmann took a unique set of photographs of the participants, and I would thank Renate, Reinhold, and Anton for permission to use many of these in this book. I would also like to thank Gerlinde Fritz who arranged for me to receive these pictures. In the caption they are referred to as [ © Zentralbibliothek für Physik, Renate Bertlmann]. I would also like to thank Queen’s University Belfast for my appoint- ments as Emeritus Professor and Visiting Senior Research Fellow that have enabled me to complete this book. At Queen’s, I would like to thank Joan Whitaker, Subject Librarian in Mathematics and Physics, for considerable help in tracing books, papers, and pictures. I would also thank all the publishers and authors who have given permission for the reproduction in this book of copyright fi gures and pictures. Every effort has been made to contact the holders of copyright in materials reproduced in this book. I apologize for any omissions, which will be rectifi ed in future printings if notice is given to the publisher. At Oxford University Press, I would thank Sonke Adlung, April Warman, and Clare Charles for their courtesy and helpfulness in various aspects of the writing of this book. I would also like to thank Charles Lauder Jr for highly effi cient and helpful copyediting, and Marionne Cronin, Emma Lonie, and Vijayasankar Natesan at Oxford University Press and SPi for all their hard work in the production of this volume. Lastly I would thank my wife, Joan, and children, John and Peter, for their support and tolerance while I have been writing the book. Contents Introduction: The First Quantum Age and the New Quantum Age 1 Part I The First Quantum Age 3 1 Quantum theory—basic ideas 5 albert einstein 8 2 Quantum theory and discreteness 11 max planck 12 3 The Schrödinger equation 19 The time-independent Schrödinger equation, eigenfunctions, and eigenvalues 19 erwin schrödinger 20 niels bohr 22 The time-dependent Schrödinger equation and wave-functions 24 4 Superposition 27 Superposition 27 The Born probability rule or interpretation 28 max born 29 The conceptual challenges posed by superposition 31 The measurement problem of quantum theory 33 john von neumann 34 Hidden variables 36 louis de broglie 38 wolfgang pauli 39 5 Further complications 41 Measurement of other observables 41 Wave and particle, and the Heisenberg principle 44 werner heisenberg 45 pascual jordan 46 paul dirac 47 1 States of a spin- – 2 particle; photon polarization states 50 x Contents 6 Orthodox and non-orthodox interpretations of quantum theory 53 david bohm 54 hugh everett 56 Part II The foundations of quantum theory 5 9 7 Entanglement 61 Bohr, Einstein, and complementarity 61 Locality 68 Entanglement 73 Einstein, Podolsky, Rosen 76 Einstein and the EPR argument 80 Bohr and EPR 81 Schrödinger’s response to EPR 83 8 The achievement of John Bell 87 John Bell 87 John Bell and quantum theory—the early years and the Bohm interpretation 91 John Bell—von Neumann and the fi rst great paper 98 Bell and measurement—1966 109 Bell’s second great paper—realism and locality 114 Einstein and Bell 124 Bell and relativity 127 9 Experimental philosophy: the fi rst decade 145 Clauser and Shimony 145 Preliminaries and planning 152 CHSH—Clauser, Horne, Shimony, and Holt 165 The experiments of the fi rst decade 171 Putting the theory on fi rmer foundations 180 Conclusions towards the end of the decade 183 10 Alain Aspect: ruling out signalling 191 Aspect and Bell 191 The Aspect experiments 193 The aftermath 196 11 Recent developments on Bell’s inequalities 203 Zeilinger, Greenberger, and Gisin 203 The neutron interferometer 211 Parametric down-conversion 216 Closing the locality loophole 219 Gisin and the experiments at Lake Geneva 221 Other experiments on Bell’s theorem and the detector loophole (with a detour on Bell and Bertlmann) 223 Contents xi 12 Bell’s theorem without inequalities 236 GHZ: Greenberger, Horne, and Zeilinger 236 GHZ—experimental proof 241 Interaction-free measurement 244 Hardy’s experiment 246 13 The new age 251 Times have changed 251 Novel quantum interpretations 252 Environmental decoherence 263 The quantum Zeno effect 268 Macroscopic quantum theory 271 14 Bell’s last thoughts 277 Bell’s six possible worlds of quantum mechanics 277 Against ‘measurement’ 278 Part III An introduction to quantum information theory 283 15 Knowledge, information, and (a little about) quantum information 285 Peierls, knowledge, and information 285 Information, information, information 288 An introduction to classical information and computation 292 Some elements of classical computers 299 16 Feynman and the prehistory of quantum computation 303 Feynman and miniaturization 303 Feynman and quantum simulators 306 Reversibility in physics and in computation 308 Feynman and reversible computation 315 17 Quantum computation 321 Moore’s law 321 David Deutsch and quantum computation 322 The Deutsch algorithm 326 Shor’s algorithm 332 Grover’s algorithm 339 Decoherence and quantum error correction 341 18 Constructing a quantum computer 349 Requirements for a quantum computer 349 The NMR quantum computer 352 The ion trap quantum computer 357 Computing with quantum dots 359 Quantum computing with superconductors 361 xii Contents 19 More techniques in quantum information theory 365 Quantum cryptography 365 Quantum teleportation 370 Entanglement swapping 375 Super-dense coding 376 Conclusions 381 Index 383 Introduction The First Quantum Age and the New Quantum Age The First Quantum Age began with the pioneering work of the founders of quantum theory, in particular Max Planck, Albert Einstein, and Niels Bohr, in the fi rst quarter of the twentieth century.