Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes

The area of Causal Inference was born as a sub-area of statistics to answer questions about the underlying causal explanations for the observed statistical data. This area was brought to the attention of Quantum physicists by the realization that the famous Bell's Theorem can be seen as a statement about causality. In fact, Bell's theorem poses a challenge to the classical notions of causality, and begs for a modification that has lead to the development of the area of Quantum Causal Models.

There are open questions in classical Causal Inference that could be of interest for understanding causality in the quantum world. This work tackles one of those questions: the indistinguishability of causal structures under interventions. In general, one can obtain more information about the causal structure by intervening on the experiment. For example, if we force one group of people to take a drug and other to take the placebo, any remaining correlation between the drug and recovery must be due to direct causation. Sometimes, however, even interventions cannot distinguish between two causal structures. In this work, we find a necessary and sufficient condition for this to happen.

Knowing about such indistinguishabilities is important to adjudicate between different causal explanations for a set of data. Such a classification can also help us filter which causal structures might present quantum-classical gaps, that is, nonclassical features like the one witnessed by the causal structure related to Bell's theorem.