Abstract
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.
Highlights
Introduction and Main ResultsWe consider a scattering experiment in which a beam of probes is directed at a scatterer
The present work can be viewed as the continuation of recently developed techniques for the mathematical analysis of repeated interaction quantum systems [1,2,3,4]
As explained in the references above, in absence of quantum measurements on probes and under a generic ergodicity assumption, one shows that the scatterer approaches a so-called repeated interaction asymptotic state after many interactions
Summary
We consider a scattering experiment in which a beam of probes is directed at a scatterer. The present work can be viewed as the continuation of recently developed techniques for the mathematical analysis of repeated interaction quantum systems [1,2,3,4] In these references, asymptotic properties of the scatterer have been investigated, without considering the fate of the outcoming probes and without quantum measurements. As explained in the references above, in absence of quantum measurements on probes and under a generic ergodicity assumption, one shows that the scatterer approaches a so-called repeated interaction asymptotic state after many interactions. We keep this assumption in the present work.
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