Quantum non-classicality in the simplest causal network

Abstract

Bell's theorem prompts us with a fundamental inquiry: what is the simplest scenario leading to the incompatibility between quantum correlations and the classical theory of causality? Here we demonstrate that quantum non-classicality is possible in a network consisting of only three dichotomic variables, without the need of the locality assumption neither external measurement choices. We also show that the use of interventions, a central tool in the field of causal inference, significantly improves the noise robustness of this new kind of non-classical behaviour, making it feasible for experimental tests with current technology.