  The future of quantum communication relies on quantum networks composed by
observers sharing multipartite quantum states. The certification of
multipartite entanglement will be crucial to the usefulness of these networks.
In many real situations it is natural to assume that some observers are more
trusted than others in the sense that they have more knowledge of their
measurement apparatuses. Here we propose a general method to certify all kinds
of multipartite entanglement in this asymmetric scenario and experimentally
demonstrate it in an optical experiment. Our results, which can be seen as a
definition of genuine multipartite quantum steering, give a method to detect
entanglement in a scenario in between the standard entanglement and fully
device-independent scenarios, and provide a basis for semi-device-independent
cryptographic applications in quantum networks.
