Quantum Causal Networks

Intervention theories of causality define a relationship as causal if appropriately specified interventions to manipulate a putative cause tend to produce changes in the putative effect. Interventionist causal theories are commonly formalized by using directed graphs to represent causal relationships, local probability models to quantify the relationship between cause and effect, and a special kind of conditioning operator to represent the effects of interventions. Such a formal model represents a family of joint probability distributions, one for each allowable intervention policy. This paper interprets the von Neumann formalization of quantum theory as an interventionist theory of causality, describes its relationship to interventionist theories popular in the artificial intelligence literature, and presents a new family of graphical models that extends causal Bayesian networks to quantum systems.