Causal Data Fusion with Quantum Confounders

Abstract: From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization of Bell's theorem to quantum networks has led to several breakthrough results and novel applications. Here, we consider the problem of causal data fusion, where we piece together multiple datasets collected under heterogeneous conditions. In particular, we show quantum experiments can generate observational and interventional data with a non-classical signature when pieced together that cannot be reproduced classically. We prove this quantum non-classicality emerges from the fusion of the datasets and is present in a plethora of scenarios, even where standard Bell non-classicality is impossible. Furthermore, we show that non-classicality genuine to the fusion of multiple data tables is achievable with quantum resources. Our work shows incorporating interventions -- a central tool in causal inference -- can be a powerful tool to detect non-classicality beyond the violation of a standard Bell inequality. In a companion article "Quantum Non-classicality from Causal Data Fusion", we extend our investigation considering all latent exogenous causal structures with 3 observable variables.