Quantum Measurement and Control - Wiseman & Milburn

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    The control of individual quantum systems promises a new technology for the twenty-firstcentury quantum technology. This book is the first comprehensive treatment of modernquantum measurement and measurement-based quantum control, which are vital elementsfor realizing quantum technology.

    Readers are introduced to key experiments and technologies through dozens of recentexperiments in cavity QED, quantum optics, mesoscopic electronics and trapped particles,several of which are analysed in detail. Nearly 300 exercises help build understanding, andprepare 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 includeadaptive 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 GriffithUniversity, Australia. He has worked in quantum measurement and control theory since1992, and is a Fellow of the Australian Academy of Science (AAS). He has received theBragg Medal of the Australian Institute of Physics, the Pawsey Medal of the AAS and theMalcolm 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 theAustralian Institute of Physics and is a Fellow of the Australian Academy of Science andthe American Physical Society.

  • An outstanding introduction, at the advanced graduate level, to the mathematical description of quantummeasurements, parameter estimation in quantum mechanics, and open quantum systems, with attention tohow the theory applies in a variety of physical settings. Once assembled, these mathematical tools areused to formulate the theory of quantum feedback control. Highly recommended for the physicist whowants to understand the application of control theory to quantum systems and for the control theorist whois 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 measurementtheory. Essential reading for students and practitioners, both, in the growing quantum technologiesrevolution.

    Howard Carmichael, The University of Auckland

    Quantum Measurement and Control provides a comprehensive and pedagogical introduction to criticalnew engineering methodology for emerging applications in quantum and nano-scale technology. Bypresenting fundamental topics first in a classical setting and then with quantum generalizations, Wisemanand Milburn manage not only to provide a lucid guide to the contemporary toolbox of quantummeasurement and control but also to clarify important underlying connections between quantum andclassical probability theory. The level of presentation is suitable for a broad audience, including bothphysicists and engineers, and recommendations for further reading are provided in each chapter. It wouldmake 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 inthe field. The clarity of presentation and the varied selection of examples and exercises guide the readerthrough the exciting development from the earliest foundation of measurements in quantum mechanics tothe most recent fundamental and practical developments within the theory of quantum measurements andcontrol. The ideal blend of precise mathematical arguments and physical explanations and examplesreflects the authors affection for the topic to which they have themselves made pioneering contributions.

    Klaus Mlmer, University of Aarhus


    HOWARD M. WISEMANGriffith University

    GERARD J. MILBURNUniversity of Queensland


    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,

    So Paulo, Delhi, Dubai, Tokyo

    Cambridge University Press

    The Edinburgh Building, Cambridge CB2 8RU, UK

    First published in print format

    ISBN-13 978-0-521-80442-4

    ISBN-13 978-0-511-65841-9

    H. Wiseman and G. Milburn 2010


    Information on this title: www.cambridge.org/9780521804424

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    Published in the United States of America by Cambridge University Press, New York


    eBook (NetLibrary)


  • To our boys: Tom & Andy, Finlay & Bailey,who were much smaller when we began.

  • Contents

    Preface page xi1 Quantum measurement theory 1

    1.1 Classical measurement theory 11.2 Quantum measurement theory 81.3 Representing outcomes as operators 271.4 Most general formulation of quantum measurements 321.5 Measuring a single photon 421.6 Further reading 49

    2 Quantum parameter estimation 512.1 Quantum limits to parameter estimation 512.2 Optimality using Fisher information 542.3 Examples of BC-optimal parameter estimation 622.4 Interferometry other optimality conditions 682.5 Interferometry adaptive parameter estimation 762.6 Experimental results for adaptive phase estimation 832.7 Quantum state discrimination 852.8 Further reading 94

    3 Open quantum systems 973.1 Introduction 973.2 The BornMarkov master equation 993.3 The radiative-damping master equation 1023.4 Irreversibility without the rotating-wave approximation 1093.5 Fermionic reservoirs 1133.6 The Lindblad form and positivity 1193.7 Decoherence and the pointer basis 1213.8 Preferred ensembles 1243.9 Decoherence in a quantum optical system 1303.10 Other examples of decoherence 136


  • viii Contents

    3.11 Heisenberg-picture dynamics 1413.12 Further reading 146

    4 Quantum trajectories 1484.1 Introduction 1484.2 Quantum jumps 1494.3 Photodetection 1544.4 Homodyne detection 1574.5 Heterodyne detection and beyond 1664.6 Illustration on the Bloch sphere 1724.7 Monitoring in the Heisenberg picture 1814.8 Imperfect detection 1904.9 Continuous measurement in mesoscopic electronics 2014.10 Further reading 215

    5 Quantum feedback control 2165.1 Introduction 2165.2 Feedback with optical beams using linear optics 2175.3 Feedback with optical beams using nonlinear optics 2315.4 Feedback control of a monitored system 2375.5 Homodyne-mediated feedback control 2465.6 Markovian feedback in a linear system 2515.7 Deterministic spin-squeezing 2595.8 Further reading 265

    6 State-based quantum feedback control 2696.1 Introduction 2696.2 Freezing a conditional state 2706.3 General classical systems 2786.4 Linear classical systems 2836.5 General quantum systems 3086.6 Linear quantum systems 3126.7 Further reading 337

    7 Applications to quantum information processing 3417.1 Introduction 3417.2 Quantum teleportation of a qubit 3437.3 Quantum teleportation for continuous variables 3477.4 Errors and error correction 3537.5 Feedback to correct continuously detected errors 3627.6 QEC using continuous feedback 3687.7 Continuous QEC without measurement 3757.8 Linear optical quantum computation 379

  • Contents ix

    7.9 Adaptive phase measurement and single-rail LOQC 3907.10 Further reading 395Appendix A: Quantum mechanics and phase-space 398A.1 Fundamentals of quantum mechanics 398A.2 Multipartite systems and entanglement 404A.3 Position and momentum 407A.4 The harmonic oscillator 410A.5 Quasiprobability distributions 414Appendix B: Stochastic differential equations 418B.1 Gaussian white noise 418B.2 Ito stochastic differential calculus 420B.3 The ItoStratonovich relation 422B.4 Solutions to SDEs 423B.5 The connection to the FokkerPlanck equation 424B.6 More general noise 425References 430Index 449

  • Preface

    The twenty-first century is seeing the emergence of the first truly quantum technologies;that is, technologies that rely on the counter-intuitive properties of individual quantum sys-tems and can often outperform any conventional technology. Examples include quantumcomputing, which promises to be much faster than conventional computing for certain prob-lems, and quantum metrology, which promises much more sensitive parameter estimationthan that offered by conventional techniques. To realize these promises, it is necessary tounderstand the measurement and control of quantum systems. This book serves as an intro-duction to quantum measurement and control, including some of the latest developmentsin both theory and experiment.

    Scope and aims

    To begin, we should make clear that the title of this book is best taken as short-handfor Quantum measurements with applications, principally to quantum control. That is,the reader should be aware that (i) a considerable part of the book concerns quantummeasurement theory, and applications other than quantum control; and (ii) the sort ofquantum control with which we are concerned is that in which measurement plays anessential r