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Joint Distributions and Quantum Nonlocal Models
Axioms 2014, 3(2), 244-259; doi:10.3390/axioms3020244

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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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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Malley, J.D. Classical Probability and Quantum Outcomes. Axioms 2014, 3, 244-259.

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