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):234-241 (2015)
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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.

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Miklós Rédei
London School of Economics

References found in this work

The logic of scientific discovery.Karl Raimund Popper - 1934 - New York: Routledge. Edited by Hutchinson Publishing Group.
Venetian sea levels, british bread prices, and the principle of the common cause.Elliott Sober - 2001 - British Journal for the Philosophy of Science 52 (2):331-346.
On Reichenbach's common cause principle and Reichenbach's notion of common cause.G. Hofer-Szabo - 1999 - British Journal for the Philosophy of Science 50 (3):377-399.

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