A probabilistic theory is called causally complete if it provides a causal explanation of all the correlations it predicts. The causal explanation can be of two sorts: in terms of a causal connection between the correlated entities, or in terms of a so-called common cause of the correlation. The talk defines first the notion of common cause and causal completeness in classical probability spaces and reviews some results on the problem of causal completeness of classical probability theories. This is followed by recalling results showing that Algebraic Quantum Field Theory (AQFT) predicts correlations between projections in algebras localized in spacelike separated spacetime regions. Since a causal link between spacelike separated entities is prohibited, an explanation of these correlations should be given in terms of suitably localized common causes. The talk defines three notions of localized common causes in AQFT and raises the question of whether the axioms of AQFT entail the existence of such localized common causes. It is shown that weakly localized common causes exist under certain assumptions but it remains open whether more strongly localized common causes exist.
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