Identification of causal influences in quantum processes

Recent years have seen great interest in extending causal inference concepts developed in the context of classical statistical models to quantum theory. So far, this program has only barely addressed causal identification, a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal relationships generating the data, and hence the effects of hypothetical interventions. A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of “observational data,” as any means of extracting data at a locus will almost certainly disturb the system. One might think a priori that quantum measurements are already too much like interventions, so that the problem of causal identification is trivialized. This is not the case: when we fix a limited class of quantum measurement instruments (namely, the class of all projective measurements) to play the role of “observations,” there exist scenarios for which causal identification is impossible. In this paper, we present a framework, based on process theories (also known as strict symmetric monoidal categories), for studying quantum causal identification scenarios on the same footing as their classical counterparts. Within this framework, we present sufficient conditions for quantum causal identification in networks with unobserved confounding systems, including quantum analogs of the well-known “back-door” and “front-door” criteria. These results arise from a type of causal model designed to facilitate the transfer of inference techniques from the classical to the quantum setting.