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
11 - Theory: Parameter Estimation
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
Theoretical chapter devoted to the domain of parameter estimation by quantum measurements. It first details the implications of the Heisenberg inequality and gives the expression of the quantum Cramér–Rao bound, a limit that is optimized over all data processing strategies and measurements on a given parameter-dependent quantum state. Measurement optimization over different quantum states and different optical modes in which the quantum state is defined is also discussed in various situations. The chapter then focusses on the measurement-induced perturbation bydiscussing the Heisenberg microscope and the Ozawa inequality, then on different implementations of quantum nondemolition (QND) measurements using the crossed-Kerr effect in quantum optics and opto-mechanics.
Keywords
- Type
- Chapter
- Information
- Quantum Processes and MeasurementTheory and Experiment, pp. 186 - 209Publisher: Cambridge University PressPrint publication year: 2023