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 argu- ment which even forbids certain non-local theories. The remaining non-local theories, which can violate Bell inequalities, are characterised by the fact that at least one of the outcomes in some sense probabilistically depends both on its distant as well as on its local setting. While this is not to say that parameter dependence in the usual sense necessarily holds, it shows that some kind of parameter dependence cannot be avoided, even if the outcomes depend on another. Our results are the strongest possible consequences from the violation of Bell inequalities on a qualitative probabilistic level.