Minimal Example of Quantum Nonclassicality without Freedom of Choice

Bell's theorem is often considered the most stringent notion of nonclassicality. The generalization of Bell's theorem to causal networks offers interesting new perspectives on the phenomenon of quantum nonclassicality and 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 nonclassicality is possible in an entanglement swapping network consisting of only three dichotomic variables, without the need for the locality assumption or external measurement choices. We also show that interventions, a central tool in the field of causal inference, significantly improve the noise robustness of this new kind of nonclassical behavior, making it feasible for experimental tests with current technology.