The structure of classical extensions of quantum probability theory

Paul Busch, Werner Stulpe

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On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.
Original languageEnglish
Article number032104
Pages (from-to)1-22
Number of pages22
JournalJournal of Mathematical Physics
Issue number3
Publication statusPublished - 7 Mar 2008

Bibliographical note

© 2008 American Institute of Physics. This is an author produced version of a paper published in Journal of Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy.


  • quantum probability
  • statistical model
  • hidden variables
  • projective Hilbert space

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