  In practical quantum networks, a variety of multi-qubit stabilized states
emitted from independent sources are distributed among the agents, and the
correlations across the entire network can be derived from each agent's local
measurements on the shared composite quantum systems. To reveal the Bell
non-locality in such cases as a quantum feature, minimal knowledge of the
emitted stabilizer state is required. Here, we demonstrate that knowing the
stabilizing and logical operators indeed provides a new way of exploring Bell
non-locality in quantum networks. For the qubit distribution in quantum
networks, the associated nonlinear Bell inequalities are derived. On the other
hand, to violate these inequalities, one can design local incompatible
observables using minimal knowledge of the emitted states. The tilted nonlinear
Bell inequalities tailored for specific non-maximal entangled stabilizer states
and a way of achieving the maximal violation are also explored.
