 The quantum probability spaces describing relativistic quantum field theory are based on type III von Neumann algebras (Haag 1992; Horuzhy 1986 [1990]; Araki 1993 [1999]; entry on  quantum field theory;  consequently, these quantum probability spaces are measure theoretically purely non-atomic. It follows then from the common cause completeness of such quantum probability spaces that there exists common causes of the correlations between spacelike separated observables. Yet, one cannot conclude from this that quantum field theory satisfies the Common Cause Principle, for the following reason: observables in quantum field theory are explicitly associated with specific spacetime regions. So the common causes also should be required to belong to specific spacetime regions. Given a correlation between observable A localized in spacetime region \(V_1\) and observable B localized in spacetime region \(V_2\) spacelike separated from \(V_1\), the common cause for this correlation should be localized in a region V that is in the intersection of the backward light cones of the spacelike separated spacetime regions \(V_1\) and \(V_2\). But the mere pure non-atomicity of the quantum probability space of quantum field theory does not entail any such locality of the common causes that exist as a consequence of the non-atomicity of the quantum probability space describing quantum fields. When one imposes this additional localizability constraint on the common causes in quantum field theory, the question of whether such properly localized common causes exist according to the theory, becomes a highly non-trivial problem (Rédei 1997). So non-trivial that the answer to it is still not known—the problem of status of causal completeness of quantum field theory is an open question.