The Structure of Classical Extensions of Quantum Probability Theory

Details The Structure of Classical Extensions of Quantum Probability Theory The Structure of Classical Extensions of Quantum Probability Theory

2007-08-11

arxiv.org/abs/0708.1539v1

J. Math. Phys. 49 (2008) 032104/1-22

Physics

Quantum Physics

Scientific paper

10.1063/1.2884581

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-variables model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.

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