Fig. 1: Quantum causal inference problem.

The observer gains data from observing two quantum systems A (white ball) and B (red ball) which is correlated. In line with Reichenbach’s principle, we allow for five possible causal structures: (1) A has direct influence on B; (2) B has a direct influence on A; (3) there is a common cause (dashed ball) acting on A and B, meaning correlations in the initial state; (4) a combination of cases 1 and 3; 5) a combination of cases 2 and 3. The observer wants to determine which of those possible causal structures is the case.