Quantum nonlocality can be demonstrated without inputs (i.e. each party using a fixed measurement setting) in a network with independent sources. Here we consider this effect on ring networks, and show that the underlying quantum strategy can be partially characterized, or self-tested, from observed correlations. Applying these results to the triangle network allows us to show that the nonlocal distribution of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)] requires that (i) all sources produce a minimal amount of entanglement, (ii) all local measurements are entangled, and (iii) each local outcome features a minimal entropy. Hence we show that the triangle network allows for genuine network quantum nonlocality and certifiable randomness.
@article{arxiv.2209.09921,
title = {Partial self-testing and randomness certification in the triangle network},
author = {Pavel Sekatski and Sadra Boreiri and Nicolas Brunner},
journal= {arXiv preprint arXiv:2209.09921},
year = {2025}
}