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Causal models with unobserved variables impose nontrivial constraints on thedistributions over the observed variables. When a common cause of two variablesis unobserved, it is impossible to uncover the causal relation between themwithout making additional assumptions about the model. In this work, weconsider causal models with a promise that unobserved variables have knowncardinalities. We derive inequality constraints implied by d-separation in suchmodels. Moreover, we explore the possibility of leveraging this result to studycausal influence in models that involve quantum systems.

Restricted Hidden Cardinality Constraints in Causal Models