Necessary and sufficient conditions for Bell violations in one-sided device-independent scenarios

We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also obtained. For two users, and two inputs and two outputs per user, our criterion becomes necessary and sufficient for Bell nonlocality. Furthermore, in that setting, its form generalizes recently obtained steering inequalities, which allows us to provide useful feedback from nonlocality to the detection of steering. Our findings constitute a practical tool for the study of the interplay between EPR steering and Bell nonlocality, with potential applications in multipartite information processing.