  The class of problems in causal inference which seeks to isolate causal
correlations solely from observational data even without interventions has come
to the forefront of machine learning, neuroscience and social sciences. As new
large scale quantum systems go online, it opens interesting questions of
whether a quantum framework exists on isolating causal correlations without any
interventions on a quantum system. We put forth a theoretical framework for
merging quantum information science and causal inference by exploiting entropic
principles. At the root of our approach is the proposition that the true causal
direction minimizes the entropy of exogenous variables in a non-local hidden
variable theory. The proposed framework uses a quantum causal structural
equation model to build the connection between two fields: entropic causal
inference and the quantum marginal problem. First, inspired by the definition
of geometric quantum discord, we fill the gap between classical and quantum
conditional density matrices to define quantum causal models. Subsequently,
using a greedy approach, we develop a scalable algorithm for quantum entropic
causal inference unifying classical and quantum causality in a principled way.
We apply our proposed algorithm to an experimentally relevant scenario of
identifying the subsystem impacted by noise starting from an entangled state.
This successful inference on a synthetic quantum dataset can have practical
applications in identifying originators of malicious activity on future
multi-node quantum networks as well as quantum error correction. As quantum
datasets and systems grow in complexity, our framework can play a foundational
role in bringing observational causal inference from the classical to the
quantum domain.
