Latent splitting as a causal probe

Abstract: Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such interventions, however, become uninformative when all observable variables are space-like separated. To address this limitation, we introduce the latent splitting procedure, a generalization of interventions to quantum networks in which controlled manipulations are applied to latent quantum systems. We show that latent splitting enables the detection of nonclassicality by combining observational and interventional data even when conventional interventions fail. Focusing on the triangle network, we derive new analytical witnesses that robustly certify nonclassicality, including nonlinear inequalities for minimal binary-variable scenarios and extensions of the nonclassical region of previously proposed experiments.