Quantum probability rule: a generalization of the theorems of Gleason and Busch

Barnett, S. M. , Cresser, J. D., Jeffers, J. and Pegg, D. T. (2014) Quantum probability rule: a generalization of the theorems of Gleason and Busch. New Journal of Physics, 16(4), 043025. (doi: 10.1088/1367-2630/16/4/043025)

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Publisher's URL: http://dx.doi.org/10.1088/1367-2630/16/4/043025

Abstract

Buschʼs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasonʼs theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction–retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Barnett, Professor Stephen
Authors: Barnett, S. M., Cresser, J. D., Jeffers, J., and Pegg, D. T.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:New Journal of Physics
Publisher:Institute of Physics Publishing Ltd.
ISSN:1367-2630
ISSN (Online):1367-2630
Copyright Holders:Copyright © 2014 The Authors
First Published:First published in New Journal of Physics 16(4):043025
Publisher Policy:Reproduced under a Creative Commons License

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