Probabilistic Structure of Bell's Argument

Andrei Yu. Khrennikov

Paul M. Näger

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.

Enrico G. Beltrametti, Slawomir Bugajski

Marian Kupczyński

The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality . In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, consistent with quantum predictions, is possible and it depends explicitly on the context of each experiment. It is also deterministic in the sense that the outcome is determined by supplementary local parameters describing both physical signals and measuring instruments. The existence of such description gives additional arguments that quantum theory is emergent from some more detailed theory respecting causality and local determinism. If quantum theory is emergent then there exist perhaps some fine structures in time-series of experimental data which were not predicted by quantum theory. In this paper we explain how a systematic search for such fine structures can be done. If such reproducible fine structures were found it would show that quantum theory is not predictably complete, which would be a major discovery.

Gordon Watson

Paul M. Näger

We examine possible causal structures of experiments with entangled quantum objects. Previously, these structures have been obscured (i) by assuming a misleading probabilistic analysis of quantum non locality as 'Outcome Dependence or Parameter Dependence' and (ii) by directly associating these correlations with influences. Here we try to overcome these shortcomings: (i) we proceed from a recent stronger Bell argument (Näger 2012), which provides an appropriate probabilistic description, and (ii) apply the rigorous methods of causal graph theory. Against the standard view that there is only an influence between the measurement outcomes, we show that there must be an influence from one setting (parameter) to its distant outcome: EPR correlations can only come about if one of the outcomes is a common effect of both settings. Our discussion makes explicit under which assumptions similar conclusions from information theoretic considerations (Maudlin 2002, ch. 6; Pawlowski et al. 2010) can be interpreted causally.