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The structure of classical extensions of quantum probability theory

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Publication details

JournalJournal of Mathematical Physics
DatePublished - 7 Mar 2008
Issue number3
Number of pages22
Pages (from-to)1-22
Original languageEnglish


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.

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.

    Research areas

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

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