Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

In practical quantum networks, a variety of multiqubit 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 nonlocality 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 way of exploring Bell nonlocality 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 nonmaximal entangled stabilizer states and a way of achieving the maximal violation are also explored.