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Though the topic of causal inference is typically considered in the contextof classical statistical models, recent years have seen great interest inextending causal inference techniques to quantum and generalized theories.Causal identification is a type of causal inference problem concerned withrecovering from observational data and qualitative assumptions the causalmechanisms generating the data, and hence the effects of hypotheticalinterventions. A major obstacle to a theory of causal identification in thequantum setting is the question of what should play the role of "observationaldata," as any means of extracting data at a certain locus will almost certainlydisturb the system. Hence, one might think a priori that quantum measurementsare already too much like interventions, so that the problem of causalidentification trivializes. This is not the case. Fixing a limited class ofquantum instruments (namely the class of all projective measurements) to playthe role of "observations," we note that as in the classical setting, thereexist scenarios for which causal identification is not possible. We thenpresent sufficient conditions for quantum causal identification, starting witha quantum analogue of the well-known "front-door criterion" and finishing witha broader class of scenarios for which the effect of a single intervention isidentifiable. These results emerge from generalizing the process-theoreticaccount of classical causal inference due to Jacobs, Kissinger, and Zanasibeyond the setting of Markov categories, and thereby treating the classical andquantum problems uniformly.

Identification of Causal Influences in Quantum Processes