Quantum probability rule

A generalization of the theorems of Gleason and Busch

Stephen M. Barnett, James D. Cresser, John Jeffers, David T. Pegg

Research output: Contribution to journalArticle

5 Citations (Scopus)
5 Downloads (Pure)

Abstract

Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons 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.

Original languageEnglish
Article number043025
Pages (from-to)1-12
Number of pages12
JournalNew Journal of Physics
Volume16
DOIs
Publication statusPublished - 29 Apr 2014

Bibliographical note

Copyright 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. First published in New J. Phys. 16, 043025. The original publication is available at http://www.doi.org/10.1088/1367-2630/16/4/043025, published by IOP Publishing. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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