Quantum Measurements of Scattered Particles

TL;DR

This paper studies quantum measurements on scattered particles, revealing how entanglement and spectral properties influence measurement outcomes and correlations over time.

Contribution

It establishes a link between the asymptotic behavior of measurement histories and spectral characteristics of the scattering process, including decay of correlations and conditions for convergence.

Findings

Measurement outcomes are affected by scattering and spectral properties.

The process exhibits decaying time correlations and obeys a zero-one law.

Scattering modifies measurement frequencies, which converge under certain conditions.

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.