Quantum Measurement: Theory and Practice

✍ Scribed by Andrew N. Jordan, Irfan A. Siddiqi

• Publisher: Independently Published
• Year: 2024
• Tongue: English
• Leaves: 283
• Category: Library

✦ Synopsis

This book adopts a novel, physics-first approach to quantum measurement, using physical experiments as the basis to describe the underlying mathematical formalism. Topics covered include weak measurements, quantum measurement reversal, quantum trajectories and the stochastic path integral formalism. The theory of quantum measurement is also covered in detail, including discussion of how it can be tested and demonstrated in a laboratory: how to build quantum-limited amplifiers, fundamental noise limits imposed on measurement by quantum mechanics, and the design of superconducting circuits. This text is an excellent introduction for students with a basic understanding of quantum mechanics wanting to learn more about measurement theory, and the inclusion of a wide selection of end-of-chapter exercises make this book ideal for emerging courses on the topic. Key chapters introducing the foundations of quantum computing and the history of measurement theory are equally accessible to a broader, less specialised audience.

✦ Table of Contents

1 Introduction to Quantum Physics and Measurement
1.1 Prologue
1.2 The Era of the Founders: 1920s–1950s
1.3 The Era of Bell: 1960–1970s
1.4 Classic Experiments: 1970–1980s
1.5 The Quantum Information Era: 1990s–Present
1.6 Generalized Measurements
1.7 What You Will Learn in This Book
2 Projective Measurement
2.1 The Stern–Gerlach Experiment
2.2 Measurements on Multiple Systems
2.3 Mathematics of Projective Measurement
2.4 Continuous Variables
2.5 Discussion of the Cardinal Properties of Projective Measurement
3 Generalized Measurement
3.1 Measuring the Polarization of a Single Photon
3.2 Measuring Polarization with Position
3.3 Polarization State Update
3.4 Mathematics of Generalized Measurement
3.5 von Neumann's Model: An Example with a Qubit and Free Particle Meter
3.6 Generalization to Mixed States
3.7 Quantum Bayesian Point of View
4 Weak Measurement
4.1 The Limit of a Very Weak Stern–Gerlach Magnet
4.2 Information–Disturbance Trade-off
4.3 Weak Value
4.4 Weak Value Amplification
4.5 Generalized Eigenvalues for Any Measurement Type
5 Continuous Measurement: Diffusive Case
5.1 Measuring the Location of an Electron on a Double Quantum Dot with a Quantum Point Contact
5.2 Measuring the State of a Superconducting Quantum Circuit with Electromagnetic Radiation
5.3 Stochastic Schrodinger and Master Equations
5.4 Continuous Measurement
5.5 Stochastic Path Integral
5.6 Diffusive Measurement with Continuous Variables
6 Continuous Measurement: Quantum Jump Case
6.1 Blinking Atoms and Their Emitted Photons
6.2 Quantum Jumps in Superconducting Qubits
6.3 Continuous Nature of Quantum Jumps
6.4 Modified Stochastic Quantum Equations of Motion
7 Linear Detectors
7.1 Quantum Noise and Measurement Limits
7.2 Linear Response Theory
7.3 Quantum Limited Pointer States
8 Quantum Amplification
8.1 Quantum-Noise-Limited Operation
8.2 Superconducting Josephson Tunnel Junction Circuits
8.3 Degenerate Parametric Amplifier
8.4 Standing-Wave Amplifier Circuits
8.5 Traveling-Wave Amplifier Circuits
9 Measurement-Related Phenomena and Applications
9.1 Measurement Reversal
9.2 Most Likely Path
9.3 Joint Measurement of Noncommuting Observables
9.4 Entanglement by Measurement: Direct and Indirect
10 Feedback and Control
10.1 General Theory of Feedback
10.2 Continuous Quantum State Analog Stabilization
10.3 Canonical Phase Measurement
10.4 Continuous Error Correction
11 Epilogue: What Does It All Mean?
11.1 What Quantum Mechanics Is and Is Not
11.2 Charting the Quantum Technological Frontier
11.3 What We Have Learned and the Road Ahead
11.4 Beyond Quantum
Appendix A Review of Classical Probability Theory
Appendix B Mixed Quantum States
References
Index