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The structure of classical extensions of quantum probability theory

Busch, Paul (orcid.org/0000-0002-2559-9721) and Stulpe, Werner (2008) The structure of classical extensions of quantum probability theory. Journal of Mathematical Physics. 032104. pp. 1-22. ISSN 0022-2488

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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.

Item Type: Article
Copyright, Publisher and Additional Information: © 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.
Keywords: quantum probability,statistical model,hidden variables,projective Hilbert space,Mathematical Physics,Physics and Astronomy,Statistical and Nonlinear Physics
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Prof Paul Busch
Date Deposited: 22 Apr 2008 17:51
Last Modified: 22 Mar 2016 00:33
Published Version: http://dx.doi.org/10.1063/1.2884581
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/3754

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