Quantum Measurements of Scattered Particles

Mathematics

Marco Merkli¹  Mark Penney¹ 

[1] Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

关键词: repeated interactions;    quantum measurement;    quantum scattering;   

DOI  :  10.3390/math3010092

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland