Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information QUANTUM MEASUREMENT AND CONTROL The control of individual quantum systems promises a new technology for the twenty-first century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology. Readers are introduced to key experiments and technologies through dozens of recent experiments in cavity QED, quantum optics, mesoscopic electronics and trapped particles, several of which are analysed in detail. Nearly 300 exercises help build understanding, and prepare readers for research in these exciting areas. This important book will interest graduate students and researchers in quantum informa- tion, quantum metrology, quantum control and related fields. Novel topics covered include adaptive measurement; realistic detector models; mesoscopic current detection; Markovian, state-based and optimal feedback; and applications to quantum information processing. howard m. wiseman is Director of the Centre for Quantum Dynamics at Griffith University, Australia. He has worked in quantum measurement and control theory since 1992, and is a Fellow of the Australian Academy of Science (AAS). He has received the Bragg Medal of the Australian Institute of Physics, the Pawsey Medal of the AAS and the Malcolm Macintosh Medal of the Federal Science Ministry. gerard j. milburn is an Australian Research Council Federation Fellow at the Uni- versity of Queensland, Australia. He has written three previous books, on quantum optics, quantum technology and quantum computing. He has been awarded the Boas Medal of the Australian Institute of Physics and is a Fellow of the Australian Academy of Science and the American Physical Society. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information An outstanding introduction, at the advanced graduate level, to the mathematical description of quantum measurements, parameter estimation in quantum mechanics, and open quantum systems, with attention to how the theory applies in a variety of physical settings. Once assembled, these mathematical tools are used to formulate the theory of quantum feedback control. Highly recommended for the physicist who wants to understand the application of control theory to quantum systems and for the control theorist who is curious about how to use control theory in a quantum context. Carlton Caves, University of New Mexico A comprehensive and elegant presentation at the interface of quantum optics and quantum measurement theory. Essential reading for students and practitioners, both, in the growing quantum technologies revolution. Howard Carmichael, The University of Auckland Quantum Measurement and Control provides a comprehensive and pedagogical introduction to critical new engineering methodology for emerging applications in quantum and nano-scale technology. By presenting fundamental topics first in a classical setting and then with quantum generalizations, Wiseman and Milburn manage not only to provide a lucid guide to the contemporary toolbox of quantum measurement and control but also to clarify important underlying connections between quantum and classical probability theory. The level of presentation is suitable for a broad audience, including both physicists and engineers, and recommendations for further reading are provided in each chapter. It would make a fine textbook for graduate-level coursework. Hideo Mabuchi, Stanford University This book present a unique summary of the theory of quantum measurements and control by pioneers in the field. The clarity of presentation and the varied selection of examples and exercises guide the reader through the exciting development from the earliest foundation of measurements in quantum mechanics to the most recent fundamental and practical developments within the theory of quantum measurements and control. The ideal blend of precise mathematical arguments and physical explanations and examples reflects the authors’ affection for the topic to which they have themselves made pioneering contributions. Klaus Mølmer, University of Aarhus © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information QUANTUM MEASUREMENT AND CONTROL HOWARD M. WISEMAN Griffith University GERARD J. MILBURN University of Queensland © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521804424 C H. Wiseman and G. Milburn 2010 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2010 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Wiseman, H. M. (Howard M.) Quantum measurement and control / Howard M. Wiseman, Gerard J. Milburn. p. cm. Includes bibliographical references and index. ISBN 978-0-521-80442-4 (hardback) 1. Quantum measure theory. I. Milburn, G. J. (Gerard J.) II. Title. QC174.17.M4W57 2009 530.120151542 – dc22 2009034266 ISBN 978 0 521 80442 4 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information To our boys: Tom & Andy, Finlay & Bailey, who were much smaller when we began. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information Contents Preface page xi 1 Quantum measurement theory 1 1.1 Classical measurement theory 1 1.2 Quantum measurement theory 8 1.3 Representing outcomes as operators 27 1.4 Most general formulation of quantum measurements 32 1.5 Measuring a single photon 42 1.6 Further reading 49 2 Quantum parameter estimation 51 2.1 Quantum limits to parameter estimation 51 2.2 Optimality using Fisher information 54 2.3 Examples of BC-optimal parameter estimation 62 2.4 Interferometry – other optimality conditions 68 2.5 Interferometry – adaptive parameter estimation 76 2.6 Experimental results for adaptive phase estimation 83 2.7 Quantum state discrimination 85 2.8 Further reading 94 3 Open quantum systems 97 3.1 Introduction 97 3.2 The Born–Markov master equation 99 3.3 The radiative-damping master equation 102 3.4 Irreversibility without the rotating-wave approximation 109 3.5 Fermionic reservoirs 113 3.6 The Lindblad form and positivity 119 3.7 Decoherence and the pointer basis 121 3.8 Preferred ensembles 124 3.9 Decoherence in a quantum optical system 130 3.10 Other examples of decoherence 136 vii © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-80442-4 - Quantum Measurement and Control Howard M. Wiseman and Gerard J. Milburn Frontmatter More information viii Contents 3.11 Heisenberg-picture dynamics 141 3.12 Further reading 146 4 Quantum trajectories 148 4.1 Introduction 148 4.2 Quantum jumps 149 4.3 Photodetection 154 4.4 Homodyne detection 157 4.5 Heterodyne detection and beyond 166 4.6 Illustration on the Bloch sphere 172 4.7 Monitoring in the Heisenberg picture 181 4.8 Imperfect detection 190 4.9 Continuous measurement in mesoscopic electronics 201 4.10 Further reading 215 5 Quantum feedback control 216 5.1 Introduction 216 5.2 Feedback with optical beams using linear optics 217 5.3 Feedback with optical beams using nonlinear optics 231 5.4 Feedback control of a monitored system 237 5.5 Homodyne-mediated feedback control 246 5.6 Markovian feedback in a linear system 251 5.7 Deterministic spin-squeezing 259 5.8 Further reading 265 6 State-based quantum feedback control 269 6.1 Introduction 269 6.2 Freezing a conditional state 270 6.3 General classical systems 278 6.4 Linear classical systems 283 6.5 General quantum systems 308 6.6 Linear quantum systems 312 6.7 Further reading 337 7 Applications to quantum information processing 341 7.1 Introduction 341 7.2 Quantum teleportation of a qubit 343 7.3 Quantum teleportation for continuous variables 347 7.4 Errors and error correction 353 7.5 Feedback to correct continuously detected errors 362 7.6 QEC using continuous feedback 368 7.7 Continuous