Reichenbach's common cause principle and quantum field theory

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V₁) andA(V₂) pertaining to spacelike separated spacetime regions V₁ and V₂ can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events inA(V₁) andA(V₂) have a genuinely probabilistic common cause, then the local algebrasA(V₁) andA(V₂) must be statistically independent in the sense of C^*-independence.