Quantum latents: distinguishing causal scenarios with indistinguishable classical

The field of causal inference examines the relationship between statistical correlations and causal connections among a set of variables. Recently, the quantum information community has shown interest in this field, recognizing it as a highly precise framework for understanding and studying Bell nonlocality. Physicists have innovated by allowing latent nodes to represent quantum systems. Since causal inference techniques were initially developed for causal structures with only classical latent nodes, causal scenarios where some latent nodes have other latent nodes as parents are overlooked. This omission is due to the existence of an exogenization procedure that relies on the ability to clone classical information, enabling the construction of a DAG that is observationally equivalent (i.e., produces the same set of possible observed correlations) but includes only exogenous latent nodes, meaning no latent node has latent parents. However, this procedure fails when quantum resources are introduced, as quantum information cannot be cloned. In this work, we explore when the presence of multiple layers of latent nodes (i.e., latent nodes with latent parents) in a DAG affects the set of probability distributions compared to the set of distributions derived from the exogenous version of the DAG. We also study whether different scenarios with two layers of latent nodes, originating from the same one-layer DAG, are observationally equivalent. Finally, we investigate the significance of the classicality or non-classicality of intermediate latent nodes for the probabilities that can be observed. Additionally, we obtain some entropic monogamy relations.