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Axioms 2014, 3(2), 244-259; doi:10.3390/axioms3020244
Article

Classical Probability and Quantum Outcomes

Center for Information Technology, National Institutes of Health (NIH), Bethesda, MD 20892, USA
Received: 2 April 2014 / Revised: 20 May 2014 / Accepted: 20 May 2014 / Published: 26 May 2014
(This article belongs to the Special Issue Quantum Statistical Inference)
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Abstract

There is a contact problem between classical probability and quantum outcomes. Thus, a standard result from classical probability on the existence of joint distributions ultimately implies that all quantum observables must commute. An essential task here is a closer identification of this conflict based on deriving commutativity from the weakest possible assumptions, and showing that stronger assumptions in some of the existing no-go proofs are unnecessary. An example of an unnecessary assumption in such proofs is an entangled system involving nonlocal observables. Another example involves the Kochen-Specker hidden variable model, features of which are also not needed to derive commutativity. A diagram is provided by which user-selected projectors can be easily assembled into many new, graphical no-go proofs.
Keywords: Kochen-Specker; quantum hidden variables; noncontextuality; joint distributions; quantum conditional probability Kochen-Specker; quantum hidden variables; noncontextuality; joint distributions; quantum conditional probability
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Malley, J.D. Classical Probability and Quantum Outcomes. Axioms 2014, 3, 244-259.

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