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11 - Theory: Parameter Estimation

Published online by Cambridge University Press:  27 July 2023

Claude Fabre
With contributions by
Rodrigo G. Cortiñas
Claude Fabre
Affiliation:
Sorbonne Université, Paris
Rodrigo G. Cortiñas
Affiliation:
Yale University, Connecticut
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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

generalized Heisenberg inequalityquantum Cramér–Rao boundquantum Fisher informationsqueezed stateNOON stateHeisenberg limitstandard quantum noise limitHeisenberg microscopeHeisenberg–Osaqa inequalityQND measurement
Type
Chapter
Information
Quantum Processes and Measurement
Theory and Experiment
 , pp. 186 - 209
Publisher: Cambridge University Press
Print publication year: 2023

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