Causal Networks and Freedom of Choice in Bell's Theorem
This work addresses foundational issues in quantum mechanics and causality, offering incremental advances in understanding classical models and Bell inequalities.
The paper tackles the problem of quantifying measurement dependence in Bell tests by arranging them within networks, showing that such dependence can be upper bounded and deriving nonlinear Bell inequalities for various causal networks, with quantum correlations violating these inequalities.
Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured. Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network. Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.