Detecting Nonclassicality in Quantum Networks via a Novel Intervention Framework

Causal interventions have emerged as an effective tool for certifying nonclassicality, offering improved detection efficiency and robustness to noise compared to purely observational approaches. However, standard node interventions (Pearl interventions) become uninformative in space-like separated networks such as the Triangle Network.

 

To address this limitation, we introduce Latent Splitting, a framework that generalizes the notion of intervention from observable variables to the latent quantum sources themselves. Latent Splitting subsumes standard interventions as a special case and provides an effective causal probe for the Triangle Network. Using this framework, we derive robust witnesses for the RGB4 family and establish nonclassicality in the minimal binary-outcome triangle scenario, a regime previously thought to admit a classical model.