Busch, Paul (orcid.org/0000000225599721) and Stulpe, Werner (2008) The structure of classical extensions of quantum probability theory. Journal of Mathematical Physics. 032104. pp. 122. ISSN 00222488

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Abstract
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 socalled 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 hiddenvariable 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 selfarchiving 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:  10 Jan 2016 01:03 
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 