Linear Programming Approach for Demonstrating Network Nonlocality for Arbitrary Networks

Device-independent protocols will play a crucial role in the future of quantum networks. The properties of network settings lend themselves to the novel concept of network non-locality. Detecting it is a challenging task due to the independence of multiple, causally separated sources, which renders the set of network local behaviors non-convex and forces the use of nonlinear inequalities or semi-definite programs. We propose a linear programming framework for demonstrating network nonlocality using linear optics and single-photon sources for an arbitrary network. Furthermore, we investigate natural network topologies where the number of sources is smaller than the number of parties, allowing a more efficient use of resources. The resulting linear program depends only on observed probabilities and a tunable experimental parameter, and can be solved more efficiently than current semi-definite program approaches. Our method provides a systematic, device-independent witness for network nonlocality, allowing us to explore the range of networks which demonstrate network nonlocality and work towards scalable certification in complex quantum networks.