Experimental nonclassicality in a causal network without assuming freedom of choice

The triangle causal structure represents a departure from the usual Bell scenario, as it should allow to violate classical predictions without the need for external inputs setting the measurement bases. Here the authors realise this scenario using a photonic setup with three independent photon sources. In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.

Automated summary

The authors realize a photonic experiment to demonstrate a triangle causal structure, which violates classical predictions without external inputs. The violation of Bell inequalities can only be explained by modeling causal dependencies as intrinsically quantum. There are also other causal structures beyond Bell that can witness nonclassicality, some of which do not require external inputs.