Cambridge University Press eBooks

Measurement

Claude Fabre, Rodrigo G. Cortiñas

Published Jul 27, 2023• 0 citations

Abstract

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.

DOI: 10.1017/9781108774918.006

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