Book contents
- Frontmatter
- Contents
- Introduction
- 1 Experiment: Detecting Single Quantum Objects
- 2 Description of Quantum Systems in Terms of the Density Matrix
- 3 Experiment: Quantum Processes
- 4 Evolution
- 5 Measurement
- 6 Experiment: Bipartite Systems
- 7 Entanglement
- 8 Experiment: Continuous Quantum Fluctuations
- 9 Continuous Variable Systems
- 10 Experiment: Parameter Estimation
- 11 Theory: Parameter Estimation
- A Basic Postulates of QuantumMechanics: a Reminder
- B Generalized Postulates of Quantum Mechanics
- C Description of Composite Systems
- D Qubits
- E Quantum Particle
- F Quantum Electromagnetic Field
- G Interaction between Light and Atoms
- H Interaction between Light Beams and Linear OpticalMedia
- I Interaction between Light Beams and Nonlinear OpticalMedia
- J Optomechanics
- K Basics of Circuit Quantum Electrodynamics
- References
- Index
5 - Measurement
Published online by Cambridge University Press: 27 July 2023
- Frontmatter
- Contents
- Introduction
- 1 Experiment: Detecting Single Quantum Objects
- 2 Description of Quantum Systems in Terms of the Density Matrix
- 3 Experiment: Quantum Processes
- 4 Evolution
- 5 Measurement
- 6 Experiment: Bipartite Systems
- 7 Entanglement
- 8 Experiment: Continuous Quantum Fluctuations
- 9 Continuous Variable Systems
- 10 Experiment: Parameter Estimation
- 11 Theory: Parameter Estimation
- A Basic Postulates of QuantumMechanics: a Reminder
- B Generalized Postulates of Quantum Mechanics
- C Description of Composite Systems
- D Qubits
- E Quantum Particle
- F Quantum Electromagnetic Field
- G Interaction between Light and Atoms
- H Interaction between Light Beams and Linear OpticalMedia
- I Interaction between Light Beams and Nonlinear OpticalMedia
- J Optomechanics
- K Basics of Circuit Quantum Electrodynamics
- References
- Index
Summary
This chapter presents the theoretical framework, based on Gleason’s theorem, allowing to describegeneralized measurements, in addition to von Neumann measurements, in terms of POVMs, probability operators and post-measurement operators. It mentions the Naimark theorem according to which a generalized measurement is a von Neumann measurement if one describes it in a Hilbert space of higher dimension. Examples of generalized measurements are given: imperfect measurements, simultaneous measurements of noncommuting operators. It presents the Zurek model that accounts for the decoherence process occurring in a measurement and shows that the quantum measurement process, including state collapse, is not a physical evolution. Finally, it studies the case of successive measurements using Bayes statistics in which the state collapse appears as an updating of the information about a system, and the fundamental property of repeatability of quantum mechanics.
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- Quantum Processes and MeasurementTheory and Experiment, pp. 66 - 103Publisher: Cambridge University PressPrint publication year: 2023