  We introduce a formalism for the evaluation of counterfactual queries in the
framework of quantum causal models, by generalising the three-step procedure of
abduction, action, and prediction in Pearl's classical formalism of
counterfactuals. To this end, we define a suitable extension of Pearl's notion
of a "classical structural causal model", which we denote analogously by
"quantum structural causal model". We show that every classical (probabilistic)
structural causal model can be extended to a quantum structural causal model,
and prove that counterfactual queries that can be formulated within a classical
structural causal model agree with their corresponding queries in the quantum
extension - but the latter is more expressive. Counterfactuals in quantum
causal models come in different forms: we distinguish between active and
passive counterfactual queries, depending on whether or not an intervention is
to be performed in the action step. This is in contrast to the classical case,
where counterfactuals are always interpreted in the active sense. As a
consequence of this distinction, we observe that quantum causal models break
the connection between causal and counterfactual dependence that exists in the
classical case: (passive) quantum counterfactuals allow counterfactual
dependence without causal dependence. This illuminates an important distinction
between classical and quantum causal models, which underlies the fact that the
latter can reproduce quantum correlations that violate Bell inequalities while
being faithful to the relativistic causal structure.
