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Quantum Measurements of Scattered Particles

Author

Listed:
  • Marco Merkli

    (Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada)

  • Mark Penney

    (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)

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.

Suggested Citation

  • Marco Merkli & Mark Penney, 2015. "Quantum Measurements of Scattered Particles," Mathematics, MDPI, vol. 3(1), pages 1-27, March.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:1:p:92-118:d:47061
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    References listed on IDEAS

    as
    1. Andrews, Donald W. K., 1985. "A Zero-One Result for the Least Squares Estimator," Econometric Theory, Cambridge University Press, vol. 1(1), pages 85-96, April.
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