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5 - Measurement

Published online by Cambridge University Press:  27 July 2023

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

Type
Chapter
Information
Quantum Processes and Measurement
Theory and Experiment
, pp. 66 - 103
Publisher: Cambridge University Press
Print publication year: 2023

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  • Measurement
  • Claude Fabre, Sorbonne Université, Paris
  • With contributions by Rodrigo G. Cortiñas
  • Book: Quantum Processes and Measurement
  • Online publication: 27 July 2023
  • Chapter DOI: https://doi.org/10.1017/9781108774918.006
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  • Measurement
  • Claude Fabre, Sorbonne Université, Paris
  • With contributions by Rodrigo G. Cortiñas
  • Book: Quantum Processes and Measurement
  • Online publication: 27 July 2023
  • Chapter DOI: https://doi.org/10.1017/9781108774918.006
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Measurement
  • Claude Fabre, Sorbonne Université, Paris
  • With contributions by Rodrigo G. Cortiñas
  • Book: Quantum Processes and Measurement
  • Online publication: 27 July 2023
  • Chapter DOI: https://doi.org/10.1017/9781108774918.006
Available formats
×