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Wiley eBooks

Quantum Measurement of a Single System

Orly Alter, Y. Yamamoto

Published Jul 5, 2001• 30 citations
Publisher

Abstract

Preface List of Illustrations Open Fundamental Questions of Limits to Information in the Quantum Measurement of a Single System Impossibility of Determining the Unknown Quantum Wavefunction of a Single System Quantum Nondemolition (QND) Measurements of a Single System Measurements without Entanglement of a Single Quantum System Adiabatic Measurements of a Single Quantum System Quantum Zeno Effect of a Single System Fundamental Quantum Limit to External Force Detection via Monitoring a Single Harmonic Oscillator (or Free Mass) Established Limits to Information in the Quantum Measurement of a Single System Bibliography Index.

DOI
10.1002/9783527617128

Related papers

Fundamental quantum limit to external force detection via monitoring a single harmonic oscillator or free mass

Orly Alter, Y. Yamamoto

We show that there is a fundamental quantum limit to external force detection via monitoring a single harmonic oscillator, which was neglected so far. This limit is equivalent to the impossibility of determining the quantum state of a single oscillator, and the quantum Zeno effect of the oscillator, and requires an exchange of at least a quantum of energy between the oscillator and the force. q 1999 Elsevier Science B.V. All rights reserved.

Physics Letters A•Dec 1, 1999•3 citations

Continuous quantum measurements and path integrals

Михаил Борисович Менский

Preface INTRODUCTION TO CONTINUOUS QUANTUM MEASUREMENTS Quantum and Classical Systems Amplitudes and Alternatives Paths and Continuous Measurements The Action Uncertainty Principle INSTANTANEOUS AND SEQUENTIAL MEASUREMENTS Measurement of a Quantum System Quantum Zeno Paradox Approximate and Sequential Measurements TECHNIQUE OF PATH INTEGRALS Propagators and Path Integrals Definition of a Path Integral The Path Integral for an Oscillator Gaussian Path Integrals CONTINUOUS MEASUREMENT AND EVOLUTION OF THE MEASURED SYSTEM The Measurement Amplitude Effective Lagrangian Evolution of a Quantum System Subject to Continuous Measurement Scattering by the Measuring Medium CONTINUOUS MEASUREMENTS OF OSCILLATORS Position Monitoring (Path measurement) Estimation of Force Acting on an Oscillator Spectral Measurements of an Oscillator Evolution of a Harmonic Oscillator Subject to Spectral Measurement Measurement of a Path of a Nonlinear Oscillator CONTINUOUS QUANTUM NONDEMOLITION MEASUREMENTS Quantum Nondemolition Measurements Monitoring of Linear Momentum Velocity versus Momentum QND Measurements of Oscillators MEASUREMENT OF AN ELECTROMAGNETIC FIELD Exposition of the Method Measurement Amplitude Analysis of the Results Another Definition of the Field Strength Explicit Model of a Meter TIME IN QUANTUM COSMOLOGY Statement of the Problem Measurements in Quantum Cosmology Minisuperspace without Measurement Minisuperspace under Measurement Analysis of the results Concluding Remarks THE ACTION UNCERTAINTY PRINCIPLE Uncertainties in Continuous Measurements Classical Regime of Measurements Quantum Regime and AUP AUP and Equations of Motion Examples from Quantum Mechanics Quantum Nondemolition Measurements AUP in Quantum Gravity Concluding Remarks GROUP-THEORETICAL STRUCTURE OF QUANTUM CONTINUOUS MEASUREMENTS Evolution under Measurement Transverse Group for Alternatives Longitudinal Semigroup for Evolution Unification of Transverse and Longitudinal Structures Concluding Remarks PATHS AND MEASUREMENTS: FURTHER DEVELOPMENT Quantum and Classical Features in Continuous Measurement The Two-Slit Experiment Wave-Particle Dualism Conceptual Problems References Index

•Jan 1, 1993•101 citations

Quantum Measurements and Decoherence: Models and Phenomenology

Михаил Борисович Менский

List of Figures. Preface. 1. Introduction. I: The Nature of Quantum Measurements. 2. The Physics Behind Quantum Measurements. 3. Measurement induced uncertainties. II: Continuous Quantum Measurements: Theory. 4. Continuous Quantum Measurements: The General Notion. 5. Fuzzy Continuous Measurements: Phenomenology. 6. Restricted Path Integrals: General Features. III: Continuous Quantum Measurements: Applications. 7. The Monitoring of Energy. 8. Monitoring by a series of observations. 9. The Quantum Zeno effect in a passive setup. IV: Conceptual Problems and Prospects. 10. RPI and the Philosophy of Quantum Mechanics. 11. Conclusion: New Prospects. A. The Formalism of Quantum Mechanics. References. Index.

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Quantum nondemolition measurements: the route from toys to tools

Vladimir B. Braginsky, Farid Ya Khalili

The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed. The definition and main principles of QND measurements are outlined. Achievements in the experimental realization of QND measurements and several new promising schemes of QND measurements are described. A list of the most important problems (from the authors' point of view) in the area of QND measurements is presented. The problem of measurement of a quantum oscillator phase is considered. A new method of phase measurement is proposed. Examples of possible solutions of fundamental physical problems using QND methods are given.

Reviews of Modern Physics•Jan 1, 1996•377 citations

Quantum Measurement

Giacomo Mauro D’Ariano

In recent years advances in technology, especially in the field of quantum optics, have made possible repetitive quantum measurements on a single quantum object, an issue that remained an academic curiosity until 25 years ago. This book, first published in 1992, provides a tutorial introduction to this field. The book is coauthored by an experimentalist and a theorist: the former - Braginsky - was the first experimentalist after Weber to develop techniques for gravitational-wave detection; the latter - Khalili - contributed with Braginsky to develop the formal apparatus to describe the experimental devices for measurement schemes. After the first part, intended as a pedagogical appendix of a standard textbook, and devoted to the modern approach to quantum measurement, the second part is a review of some new methods of quantum measurements for macroscopic objects. The central problem is the detection of a small time-dependent classical force that acts on a quantum probe. This is the typical situation that occurs in gravitational-wave detection, where the probe is a macroscopic moving mass weakly coupled to a classical wave. The problem of gravitational-wave detection and the limitation to accuracy of measurement of position of a moving mass - the so-called standard quantum limit (SQL), which is a consequence of the random back-action of the measuring device on the mass - triggered the development of new quantum nondemolition (QND) measurements, i.e. measurements where the measured quantity is left unperturbed after the measurement. SQL and QND measurements (both Braginsky inventions) permeate the whole book as a transversal chapter. The aim is to give simple criteria and recipes to design a measuring device in order to optimize the accuracy of the measurement, and, at the same time, to minimize the perturbation that the device exerts on the measured object, so that it will not interfere with successive measurements on the same object. The continuous measurements are regarded as the limiting case of a sequence of repeated discrete measurements, when the interval between the measurements is much smaller than the characteristic time-scale on which the measured quantity changes. The analysis of continuous measurements give to the authors the opportunity to illustrate the watchdog effect and the quantum Zeno paradox (real effect), while deriving the master equation for the evolution of the object state. Then, an entire chapter is devoted to the analysis of devices for continuous measurement of small mechanical displacements. The book is easy to understand, and can serve as a complementary reading for graduate level courses in quantum mechanics. The material of the book can be useful for all scientists and engineers involved in researches related to high-sensitive quantum measurements, quantum information theory and quantum computation. The reader, however, should be aware that this book presents a very particular point of view, with no room left to very relevant concepts in quantum measurement theory, as, for example, squeezing, quantum amplification, joint-measurements of non-commuting observables and phase-measurements. More regrettably, the list of references is unsatisfactorily incomplete, with no mention of alternative developments, for example, regarding the SQL for measuring the position of a free mass. Here, schemes to breach the SQL have been proposed in the literature (Yuen H P 1983 Phys. Rev. Lett. 51 719, Ozawa M 1988 Phys. Rev. Lett. 60 385), whereas from the book one could conclude that such SQL would be unsurpassable. Also, a criticism is in order of the way of deriving some SQL's, based solely on the Heisenberg relation, even in consideration that the aim of such derivations is mostly pedagogical.

Measurement Science and Technology•Jul 1, 1997•0 citations

Impossibility of Determining the Unknown Quantum Wavefunction of a Single System: Quantum Non-Demolition Measurements, Measurements without Entanglement and Adiabatic Measurements

Orly Alter, Yoshihisa Xamamoto

We establish that the information which can be obtained in the measurement of a single system about the unknown quantum wavefunction of the system is limited to estimates of the expectation values of the measured observables, with the estimate errors satisfying the uncertainty principle. Only the fully a-priori known wavefunction could be determined exactly. We consider specifically measurement schemes which may induce minimal change in the measured system, such as quantum non-demolition measurements, measurements without entanglement and adiabatic measurements.

Fortschritte der Physik•Nov 1, 1998•3 citations
Preface List of Illustrations Open Fundamental Questions of Limits to Information in the Quantum Measurement of a Single System Impossibility of Determining the Unknown Quantum Wavefunction of a Single System Quantum Nondemolition (QND) Measurements of a Single System Measurements without Entanglement of a Single Quantum System Adiabatic Measurements of a Single Quantum System Quantum Zeno Effect of a Single System Fundamental Quantum Limit to External Force Detection via Monitoring a Single Harmonic Oscillator (or Free Mass) Established Limits to Information in the Quantum Measurement of a Single System Bibliography Index.
Preface INTRODUCTION TO CONTINUOUS QUANTUM MEASUREMENTS Quantum and Classical Systems Amplitudes and Alternatives Paths and Continuous Measurements The Action Uncertainty Principle INSTANTANEOUS AND SEQUENTIAL MEASUREMENTS Measurement of a Quantum System Quantum Zeno Paradox Approximate and Sequential Measurements TECHNIQUE OF PATH INTEGRALS Propagators and Path Integrals Definition of a Path Integral The Path Integral for an Oscillator Gaussian Path Integrals CONTINUOUS MEASUREMENT AND EVOLUTION OF THE MEASURED SYSTEM The Measurement Amplitude Effective Lagrangian Evolution of a Quantum System Subject to Continuous Measurement Scattering by the Measuring Medium CONTINUOUS MEASUREMENTS OF OSCILLATORS Position Monitoring (Path measurement) Estimation of Force Acting on an Oscillator Spectral Measurements of an Oscillator Evolution of a Harmonic Oscillator Subject to Spectral Measurement Measurement of a Path of a Nonlinear Oscillator CONTINUOUS QUANTUM NONDEMOLITION MEASUREMENTS Quantum Nondemolition Measurements Monitoring of Linear Momentum Velocity versus Momentum QND Measurements of Oscillators MEASUREMENT OF AN ELECTROMAGNETIC FIELD Exposition of the Method Measurement Amplitude Analysis of the Results Another Definition of the Field Strength Explicit Model of a Meter TIME IN QUANTUM COSMOLOGY Statement of the Problem Measurements in Quantum Cosmology Minisuperspace without Measurement Minisuperspace under Measurement Analysis of the results Concluding Remarks THE ACTION UNCERTAINTY PRINCIPLE Uncertainties in Continuous Measurements Classical Regime of Measurements Quantum Regime and AUP AUP and Equations of Motion Examples from Quantum Mechanics Quantum Nondemolition Measurements AUP in Quantum Gravity Concluding Remarks GROUP-THEORETICAL STRUCTURE OF QUANTUM CONTINUOUS MEASUREMENTS Evolution under Measurement Transverse Group for Alternatives Longitudinal Semigroup for Evolution Unification of Transverse and Longitudinal Structures Concluding Remarks PATHS AND MEASUREMENTS: FURTHER DEVELOPMENT Quantum and Classical Features in Continuous Measurement The Two-Slit Experiment Wave-Particle Dualism Conceptual Problems References Index
List of Figures. Preface. 1. Introduction. I: The Nature of Quantum Measurements. 2. The Physics Behind Quantum Measurements. 3. Measurement induced uncertainties. II: Continuous Quantum Measurements: Theory. 4. Continuous Quantum Measurements: The General Notion. 5. Fuzzy Continuous Measurements: Phenomenology. 6. Restricted Path Integrals: General Features. III: Continuous Quantum Measurements: Applications. 7. The Monitoring of Energy. 8. Monitoring by a series of observations. 9. The Quantum Zeno effect in a passive setup. IV: Conceptual Problems and Prospects. 10. RPI and the Philosophy of Quantum Mechanics. 11. Conclusion: New Prospects. A. The Formalism of Quantum Mechanics. References. Index.
The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed. The definition and main principles of QND measurements are outlined. Achievements in the experimental realization of QND measurements and several new promising schemes of QND measurements are described. A list of the most important problems (from the authors' point of view) in the area of QND measurements is presented. The problem of measurement of a quantum oscillator phase is considered. A new method of phase measurement is proposed. Examples of possible solutions of fundamental physical problems using QND methods are given.
In recent years advances in technology, especially in the field of quantum optics, have made possible repetitive quantum measurements on a single quantum object, an issue that remained an academic curiosity until 25 years ago. This book, first published in 1992, provides a tutorial introduction to this field. The book is coauthored by an experimentalist and a theorist: the former - Braginsky - was the first experimentalist after Weber to develop techniques for gravitational-wave detection; the latter - Khalili - contributed with Braginsky to develop the formal apparatus to describe the experimental devices for measurement schemes. After the first part, intended as a pedagogical appendix of a standard textbook, and devoted to the modern approach to quantum measurement, the second part is a review of some new methods of quantum measurements for macroscopic objects. The central problem is the detection of a small time-dependent classical force that acts on a quantum probe. This is the typical situation that occurs in gravitational-wave detection, where the probe is a macroscopic moving mass weakly coupled to a classical wave. The problem of gravitational-wave detection and the limitation to accuracy of measurement of position of a moving mass - the so-called standard quantum limit (SQL), which is a consequence of the random back-action of the measuring device on the mass - triggered the development of new quantum nondemolition (QND) measurements, i.e. measurements where the measured quantity is left unperturbed after the measurement. SQL and QND measurements (both Braginsky inventions) permeate the whole book as a transversal chapter. The aim is to give simple criteria and recipes to design a measuring device in order to optimize the accuracy of the measurement, and, at the same time, to minimize the perturbation that the device exerts on the measured object, so that it will not interfere with successive measurements on the same object. The continuous measurements are regarded as the limiting case of a sequence of repeated discrete measurements, when the interval between the measurements is much smaller than the characteristic time-scale on which the measured quantity changes. The analysis of continuous measurements give to the authors the opportunity to illustrate the watchdog effect and the quantum Zeno paradox (real effect), while deriving the master equation for the evolution of the object state. Then, an entire chapter is devoted to the analysis of devices for continuous measurement of small mechanical displacements. The book is easy to understand, and can serve as a complementary reading for graduate level courses in quantum mechanics. The material of the book can be useful for all scientists and engineers involved in researches related to high-sensitive quantum measurements, quantum information theory and quantum computation. The reader, however, should be aware that this book presents a very particular point of view, with no room left to very relevant concepts in quantum measurement theory, as, for example, squeezing, quantum amplification, joint-measurements of non-commuting observables and phase-measurements. More regrettably, the list of references is unsatisfactorily incomplete, with no mention of alternative developments, for example, regarding the SQL for measuring the position of a free mass. Here, schemes to breach the SQL have been proposed in the literature (Yuen H P 1983 Phys. Rev. Lett. 51 719, Ozawa M 1988 Phys. Rev. Lett. 60 385), whereas from the book one could conclude that such SQL would be unsurpassable. Also, a criticism is in order of the way of deriving some SQL's, based solely on the Heisenberg relation, even in consideration that the aim of such derivations is mostly pedagogical.
We establish that the information which can be obtained in the measurement of a single system about the unknown quantum wavefunction of the system is limited to estimates of the expectation values of the measured observables, with the estimate errors satisfying the uncertainty principle. Only the fully a-priori known wavefunction could be determined exactly. We consider specifically measurement schemes which may induce minimal change in the measured system, such as quantum non-demolition measurements, measurements without entanglement and adiabatic measurements.