Quantum steering in networks: Measurement-device-independent detection, continuous variables, and practical Gaussian schemes

arXiv:2606.25690v1 Announce Type: new Abstract: We consider quantum steering certification in multipartite networks, with a focus on minimal trust scenarios: all-except-one parties are untrusted and treated device-independently. We show that it is always possible to lift steering certification to the measurement-device-independent regime, in which even the (last) trusted party can treat their local hardware as a black-box, except for a set of fiduciary quantum states used as the inputs to the experiment. This holds both for finite-dimensional systems as well as for bosonic continuous-variable systems, for which we provide a full characterization in the bipartite case. Additionally, we introduce measurement-device-independent network steering protocols based entirely on Gaussian operations – which cannot be used for fully device-independent protocols, and thus become instead a viable option for minimal trust certification as soon as a single trusted input is inserted in the network. Our results present a basis for steering-based applications (such as randomness generation) with minimal trust beyond full nonlocality and with feasible experimental requirements.