The structure of classical extensions of quantum probability theory

TY - JOUR

T1 - The structure of classical extensions of quantum probability theory

AU - Busch, Paul

AU - Stulpe, Werner

N1 - © 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.

PY - 2008/3/7

Y1 - 2008/3/7

N2 - 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.

AB - 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.

KW - quantum probability

KW - statistical model

KW - hidden variables

KW - projective Hilbert space

UR - http://www.scopus.com/inward/record.url?scp=41549155119&partnerID=8YFLogxK

U2 - 10.1063/1.2884581

DO - 10.1063/1.2884581

M3 - Article

SN - 0022-2488

VL - 49

SP - 1

EP - 22

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

M1 - 032104

ER -