Common cause completability of classical and quantum probability spaces

It is shown that for a given set of correlations either in a classical or in a quantumprobability space both the classical and the quantum probability spaces areextendable in such a way that the extension contains common causes of thegiven correlations, where common cause is taken in the sense of Reichenbach'sdefinition. These results strongly restrict the possible ways of disprovingReichenbach's common cause principle and indicate that EPR-type quantumcorrelations might very well have a common cause explanation.