Bäumer, E., Gitton, V., Kriváchy, T., Gisin, N., & Renner, R. (2025). Exploring the local landscape in the triangle network. Physical Review A, 111(5), Article 052453. https://doi.org/10.1103/PhysRevA.111.052453
Characterizing the set of distributions that can be realized in the triangle network is a notoriously difficult problem. In this work, we investigate inner approximations of the set of local (classical) distributions of the triangle network. A quantum distribution that appears to be nonlocal is the elegant joint measurement (EJM) [Entropy 21, 325 (2019)1099-430010.3390/e21030325], which motivates us to study distributions having the same symmetries as the EJM. We compare analytical and neural-network-based inner approximations and find a remarkable agreement between the two methods. Using neural network tools, we also conjecture network Bell inequalities that give a trade-off between the levels of correlation and symmetry that a local distribution may feature. Our results considerably strengthen the conjecture that the EJM is nonlocal.
