Exploring non-classical correlations in causal scenarios

Quantum Mechanics has been one of our most successful theory. However its foundations are shrouded with various conceptual and interpretational challenges. One of them has been Quantum Non-Locality. Bell’s eponymous theorem implies that Quantum Mechanics is incompatible with Local Causality. Here we study causality in the context of Quantum Mechanics by resorting to Classical Causal Models. The classical causal relations between a set of variables, some observed and some latent, can be studied using the formalism of Directed Acyclic Graphs (DAGs) and Bayesian Networks. In quantum foundations the challenging task of ascertaining when correlations are non-classical within a directed acyclic graph (or causal scenario) remains a significant area of research. In this work we study how to distinguish between correlations that are classically explainable from those that are non-classical and potentially realizable by Quantum Mechanics in various causal scenarios. We provide various sufficient conditions to check which causal scenarios can support non-classical correlations, meanwhile providing evidence towards a conjecture. We characterize all but three causal scenarios of up to four visible nodes into those which can sustain non-classical correlations and those which cannot. For specific scenarios, we also focus on understanding when a set of probability distributions can be explained by quantum mechanics but not by any classical theory. It is also shown here that there exist a range of causal scenarios beyond just the Bell scenario which can support non-classical correlations but their causal explanation requires fine-tuning. The multi-partite Bell scenario is conjectured to be an example of such a scenario. On the other hand, for a number of
causal scenarios, which exhibit non-classically explainable quantum-correlations, we show
that we can always explain such non-classical quantum-correlations by resorting instead to
another causal scenario perfectly classically. Digressing into the subject of elimination of variables from system of linear inequalities, we also provide some conditions to accelerate the algorithm to do so, the Fourier-Motzkin elimination algorithm.