The Structure of Classical Extensions of Quantum Probability Theory

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 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.

References in corpus (2)

• Contextuality for preparations, transformations, and unsharp measurements
• Geometric Quantum Mechanics

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• The Transition from Quantum to Classical in weak measurements and reconstruction of Quantum Correlation
• From the Attempt of Certain Classical Reformulations of Quantum Mechanics to Quasi-Probability Representations
• Quantum Mechanics as a Framework for Dealing with Uncertainty
• Topologies and Measurable Structures on the Projective Hilbert Space