Kitajima, Yuichiro and Rédei, Miklós ORCID: 0000000152981443 (2015) Characterizing common cause closedness of quantum probability theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52 (B). pp. 234241. ISSN 13552198

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Abstract
We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a noncommutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common cause of the correlation. The main result we prove is that a quantum probability space is common cause closed if and only if it has at most one measure theoretic atom. This result improves earlier ones published in [1]. The result is discussed from the perspective of status of the Common Cause Principle. Open problems on common cause closedness of general probability spaces (L, ϕ) are formulated, where L is an orthomodular bounded lattice and ϕ is a probability measure on L.
Item Type:  Article 

Official URL:  http://www.journals.elsevier.com/studiesinhistor... 
Additional Information:  © 2015 Elsevier Ltd. 
Divisions:  Philosophy, Logic and Scientific Method 
Subjects:  B Philosophy. Psychology. Religion > B Philosophy (General) Q Science > QC Physics 
Sets:  Departments > Philosophy, Logic and Scientific Method 
Date Deposited:  25 Aug 2015 09:23 
Last Modified:  20 Jan 2020 05:45 
URI:  http://eprints.lse.ac.uk/id/eprint/63301 
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