Kitajima, Yuichiro and Rédei, Miklós 
ORCID: 0000-0001-5298-1443
(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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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 |
| Date Deposited: | 25 Aug 2015 09:23 |
| Last Modified: | 01 Apr 2024 08:23 |
| URI: | http://eprints.lse.ac.uk/id/eprint/63301 |
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