A minimal example of quantum non-classicality without freedom of choice

Abstract

Bell's theorem is often considered the most stringent notion of non-classicality. The generalization of Bell's theorem to causal networks offers interesting new perspectives on the phenomenon of quantum non-classicality 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 non-classicality 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 non-classical behavior, making it feasible for experimental tests with current technology.

Corrected the classical bound of the general observational witness and the dependent robustness figures; conclusions unchanged

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