Though the topic of causal inference is typically considered in the context of classical statistical models, recent years have seen great interest in extending causal inference techniques to quantum and generalized theories. Causal identification is a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal mechanisms 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 certain locus will almost certainly disturb the system. Hence, one might think a priori that quantum measurements are already too much like interventions, so that the problem of causal identification trivializes. This is not the case. Fixing a limited class of quantum instruments (namely the class of all projective measurements) to play the role of "observations," we note that as in the classical setting, there exist scenarios for which causal identification is not possible. We then present sufficient conditions for quantum causal identification, starting with a quantum analogue of the well-known "front-door criterion" and finishing with a broader class of scenarios for which the effect of a single intervention is identifiable. These results emerge from generalizing the process-theoretic account of classical causal inference due to Jacobs, Kissinger, and Zanasi beyond the setting of Markov categories, and thereby treating the classical and quantum problems uniformly.

翻译：尽管因果推断的主题通常是在经典统计模型的背景下讨论的，但近年来，将因果推断技术扩展到量子及广义理论领域引起了极大兴趣。因果识别是一类因果推断问题，旨在从观测数据和定性假设中恢复生成数据的因果机制，从而推断假设性干预的效果。量子背景下因果识别理论的一个主要障碍在于，应当将什么视为“观测数据”——因为任何在特定位置提取数据的方法几乎必然会对系统产生扰动。因此，人们可能先验地认为量子测量已过于接近干预，导致因果识别问题变得微不足道。然而事实并非如此。通过限定一类特定的量子仪器（即所有投影测量的类别）来扮演“观测”的角色，我们注意到，与经典设定类似，也存在无法实现因果识别的场景。随后，我们提出量子因果识别的充分条件：从著名的“前门准则”的量子类似物出发，最终覆盖更广泛的可识别单一干预效应的场景。这些结果源于将Jacobs、Kissinger和Zanasi提出的基于过程论的经典因果推断描述推广至马尔可夫范畴之外，从而实现了经典与量子问题的统一处理。