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Large-scale multisource networks have been employed to overcome the practicalconstraints that entangled systems are difficult to faithfully transmit overlarge distance or store in long time. However, a full characterization of themultipartite nonlocality of these networks remains out of reach, mainly due tothe complexity of multipartite causal models. In this paper, we propose ageneral framework of Bayesian networks to reveal connections among differentcausal structures. The present model implies a special star-convex set ofnon-signaling correlations from multisource networks that allows constructingpolynomial-time algorithm for solving the compatibility problem of a givencorrelation distribution and a fixed causal network. It is then used toclassify the nonlocality originated from the standard entanglement swapping oftripartite networks. Our model provides a unified device-independentinformation processing method for exploring the practical security againstnon-signaling eavesdroppers on multisource quantum networks.

Non-signaling Causal Hierarchy of General Multisource Networks