Device-independently verifying full network nonlocality of quantum networks

Quantum networks consisting of multipartite sources are flexible and scalable for large-scale quantum applications. The device-independent verification of these sources is the main problem of the Bell theory in quantum network scenarios. Our goal in this paper is to verify the full network nonlocality that witnesses the strongest nonlocality of quantum networks beyond all hybrid networks consisting of local hidden variables and non-signaling sources. We verify the full network nonlocality of general networks by constructing Bell inequalities with two different methods. These results provide the strongest nonlocality of quantum networks which is important for the security of cryptographical applications on quantum networks.