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Characterizing common cause closedness of quantum probability theories

Kitajima, Yuichiro and Rédei, Miklós (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. 234-241. ISSN 1355-2198

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Identification Number: 10.1016/j.shpsb.2015.08.003

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 non-commutative 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/studies-in-histor...
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 Mar 2019 02:43
URI: http://eprints.lse.ac.uk/id/eprint/63301

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