A Stronger Bell Argument for Quantum Non-Locality
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It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a stronger Bell argument which even forbids certain non-local theories. Among these excluded non-local theories are those whose only non-local connection is a probabilistic (or functional) dependence between the space-like separated measurement outcomes of EPR/B experiments (a subset of outcome dependent theories). In this way, the new argument shows that the result of the received Bell argument, which requires just any kind of non-locality, is inappropriately weak. Positively, the remaining non-local theories, which can violate Bell inequalities (among them quantum theory), are characterized by the fact that at least one of the measurement outcomes in some sense probabilistically depends both on its local as well as on its distant measurement setting (probabilistic Bell contextuality). Whether an additional dependence between the outcomes holds, is irrelevant for the question whether a certain theory can violate Bell inequalities. This new concept of quantum non-locality is considerably tighter and more informative than the one following from the usual Bell argument. We prove that (given usual background assumptions) the result of the stronger Bell argument presented here is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level.