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)

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.

LanguageEnglish
Article number043025
Number of pages13
JournalNew Journal of Physics
Volume16
DOIs
Publication statusPublished - 29 Apr 2014

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theorems
axioms
operators
quantum communication
quantum theory
symmetry
predictions

Keywords

  • quantum information
  • quantum probability
  • quantum theory

Cite this

Barnett, Stephen M. ; Cresser, James D. ; Jeffers, John ; Pegg, David T. / Quantum probability rule : a generalization of the theorems of Gleason and Busch. In: New Journal of Physics. 2014 ; Vol. 16.
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Quantum probability rule : a generalization of the theorems of Gleason and Busch. / Barnett, Stephen M.; Cresser, James D.; Jeffers, John; Pegg, David T.

In: New Journal of Physics, Vol. 16, 043025, 29.04.2014.

Research output: Contribution to journalArticle

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