Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities

Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.