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Quantum Measurement and Control

Book Description

The control of individual quantum systems promises a new technology for the 21st 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 information, 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.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. 1. Quantum measurement theory
    1. 1.1 Classical measurement theory
    2. 1.2 Quantum measurement theory
    3. 1.3 Representing outcomes as operators
    4. 1.4 Most general formulation of quantum measurements
    5. 1.5 Measuring a single photon
    6. 1.6 Further reading
  9. 2. Quantum parameter estimation
    1. 2.1 Quantum limits to parameter estimation
    2. 2.2 Optimality using Fisher information
    3. 2.3 Examples of BC-optimal parameter estimation
    4. 2.4 Interferometry – other optimality conditions
    5. 2.5 Interferometry – adaptive parameter estimation
    6. 2.6 Experimental results for adaptive phase estimation
    7. 2.7 Quantum state discrimination
    8. 2.8 Further reading
  10. 3. Open quantum systems
    1. 3.1 Introduction
    2. 3.2 The Born–Markov master equation
    3. 3.3 The radiative-damping master equation
    4. 3.4 Irreversibility without the rotating-wave approximation
    5. 3.5 Fermionic reservoirs
    6. 3.6 The Lindblad form and positivity
    7. 3.7 Decoherence and the pointer basis
    8. 3.8 Preferred ensembles
    9. 3.9 Decoherence in a quantum optical system
    10. 3.10 Other examples of decoherence
    11. 3.11 Heisenberg-picture dynamics
    12. 3.12 Further reading
  11. 4. Quantum trajectories
    1. 4.1 Introduction
    2. 4.2 Quantum jumps
    3. 4.3 Photodetection
    4. 4.4 Homodyne detection
    5. 4.5 Heterodyne detection and beyond
    6. 4.6 Illustration on the Bloch sphere
    7. 4.7 Monitoring in the Heisenberg picture
    8. 4.8 Imperfect detection
    9. 4.9 Continuous measurement in mesoscopic electronics
    10. 4.10 Further reading
  12. 5. Quantum feedback control
    1. 5.1 Introduction
    2. 5.2 Feedback with optical beams using linear optics
    3. 5.3 Feedback with optical beams using nonlinear optics
    4. 5.4 Feedback control of a monitored system
    5. 5.5 Homodyne-mediated feedback control
    6. 5.6 Markovian feedback in a linear system
    7. 5.7 Deterministic spin-squeezing
    8. 5.8 Further reading
  13. 6. State-based quantum feedback control
    1. 6.1 Introduction
    2. 6.2 Freezing a conditional state
    3. 6.3 General classical systems
    4. 6.4 Linear classical systems
    5. 6.5 General quantum systems
    6. 6.6 Linear quantum systems
    7. 6.7 Further reading
  14. 7. Applications to quantum information processing
    1. 7.1 Introduction
    2. 7.2 Quantum teleportation of a qubit
    3. 7.3 Quantum teleportation for continuous variables
    4. 7.4 Errors and error correction
    5. 7.5 Feedback to correct continuously detected errors
    6. 7.6 QEC using continuous feedback
    7. 7.7 Continuous QEC without measurement
    8. 7.8 Linear optical quantum computation
    9. 7.9 Adaptive phase measurement and single-rail LOQC
    10. 7.10 Further reading
  15. Appendix A: Quantum mechanics and phase-space
    1. A.1 Fundamentals of quantum mechanics
    2. A.2 Multipartite systems and entanglement
    3. A.3 Position and momentum
    4. A.4 The harmonic oscillator
    5. A.5 Quasiprobability distributions
  16. Appendix B: Stochastic differential equations
    1. B.1 Gaussian white noise
    2. B.2 Itô stochastic differential calculus
    3. B.3 The Itô–Stratonovich relation
    4. B.4 Solutions to SDEs
    5. B.5 The connection to the Fokker–Planck equation
    6. B.6 More general noise
  17. References
  18. Index