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.
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