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Register a new userNon-signaling Causal Hierarchy of General Multisource Networks
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Ming-Xing Luo
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Large-scale multisource networks have been employed to overcome the practical constraints that entangled systems are difficult to faithfully transmit over large distance or store in long time. However, a full characterization of the multipartite nonlocality of these networks remains out of reach, mainly due to the complexity of multipartite causal models. In this paper, we propose a general framework of Bayesian networks to reveal connections among different causal structures. The present model implies a special star-convex set of non-signaling correlations from multisource networks that allows constructing polynomial-time algorithm for solving the compatibility problem of a given correlation distribution and a fixed causal network. It is then used to classify the nonlocality originated from the standard entanglement swapping of tripartite networks. Our model provides a unified device-independent information processing method for exploring the practical security against non-signaling eavesdroppers on multisource quantum networks.
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As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.
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