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Mathematics 2015, 3(1), 92-118;

Quantum Measurements of Scattered Particles

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada
Current Address: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
Author to whom correspondence should be addressed.
Academic Editor: Palle Jorgensen
Received: 18 January 2015 / Accepted: 11 March 2015 / Published: 19 March 2015
(This article belongs to the Special Issue Mathematical physics)
Full-Text   |   PDF [373 KB, uploaded 19 March 2015]


We investigate the process of quantum measurements on scattered probes. Before scattering, the probes are independent, but they become entangled afterwards, due to the interaction with the scatterer. The collection of measurement results (the history) is a stochastic process of dependent random variables. We link the asymptotic properties of this process to spectral characteristics of the dynamics. We show that the process has decaying time correlations and that a zero-one law holds. We deduce that if the incoming probes are not sharply localized with respect to the spectrum of the measurement operator, then the process does not converge. Nevertheless, the scattering modifies the measurement outcome frequencies, which are shown to be the average of the measurement projection operator, evolved for one interaction period, in an asymptotic state. We illustrate the results on a truncated Jaynes–Cummings model. View Full-Text
Keywords: repeated interactions; quantum measurement; quantum scattering repeated interactions; quantum measurement; quantum scattering
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Merkli, M.; Penney, M. Quantum Measurements of Scattered Particles. Mathematics 2015, 3, 92-118.

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