ABSTRACT Full quantum network nonlocality (FQNN) is an innovative perspective which signifies that all sources within the network exhibit quantum characteristics. So far, FQNN has been certified by violating a single Bell‐like inequality, but only for star networks. No such test exists for general topologies. (Luo et al., Phys. Rev. A 110, 022617 (2024)) suggested iterating the FQNN criteria of star networks to cover general networks, since any general network can be decomposed into a collection of star subnetworks. However, this method requires a large number of inequalities for large networks. This paper aims to clarify how a smaller set of Bell‐like inequalities can be employed to detect FQNN in general networks. By exploiting the structural features of the network, we derive a new class of inequalities. Violations of these inequalities reveal the locations of several quantum sources, enabling the detection of overall FQNN with fewer tests. We demonstrate the advantage of our approach explicitly for two types of networks, ‐layer ‐forked tree‐shaped and Bethe lattice networks. We demonstrate an exponential reduction in the number of Bell‐like inequalities required to witness FQNNs on these two types of networks.
Yang et al. (Sun,) studied this question.