  As quantum computing and networking nodes scale-up, important open questions
arise on the causal influence of various sub-systems on the total system
performance. These questions are related to the tomographic reconstruction of
the macroscopic wavefunction and optimizing connectivity of large engineered
qubit systems, the reliable broadcasting of information across quantum networks
as well as speed-up of classical causal inference algorithms on quantum
computers. A direct generalization of the existing causal inference techniques
to the quantum domain is not possible due to superposition and entanglement. We
put forth a new theoretical framework for merging quantum information science
and causal inference by exploiting entropic principles. First, we build the
fundamental connection between the celebrated quantum marginal problem and
entropic causal inference. Second, inspired by the definition of geometric
quantum discord, we fill the gap between classical conditional probabilities
and quantum conditional density matrices. These fundamental theoretical
advances are exploited to develop a scalable algorithmic approach for quantum
entropic causal inference. We apply our proposed framework to an experimentally
relevant scenario of identifying message senders on quantum noisy links. This
successful inference on a synthetic quantum dataset can lay the foundations of
identifying originators of malicious activity on future multi-node quantum
networks. We unify classical and quantum causal inference in a principled way
paving the way for future applications in quantum computing and networking.
