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Article overview
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Gleason-Busch theorem and Bayesian quantum theory | Stephen M. Barnett
; James D. Cresser
; John Jeffers
; David T. Pegg
; | Date: |
5 Aug 2013 | Abstract: | We show that Gleason’s theorem, in the form recently generalised by Busch,
may be further simplified by dropping one of the three properties from which it
was derived. The result is a more general probability than that usually
employed in quantum theory in that it shows that any set of positive operators
can represent the probabilities for a set of possible events. Remarkably, our
more general form seems to contain Bayes’s rule for conditional probabilities
so there is no need to add it as an additional element. There is no need,
moreover, to postulate that the measurement operators sum to the identity;
rather this condition follows from our more general rule when there is no prior
measurement outcome information available. We show how the new and general
probability law may be applied in quantum communications and in retrodictive
quantum theory. | Source: | arXiv, 1308.0946 | Services: | Forum | Review | PDF | Favorites |
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