Self-Testing with Dishonest Parties and Device-Independent Entanglement Certification in Quantum Communication Networks.

We consider the task of device-independent quantum state certification in a network where some of the nodes may collude and act dishonestly. We introduce the paradigm of self-testing with dishonest parties and provide a certification protocol for the Greenberger-Horne-Zeilinger state in this framework, together with robust statements about the fidelity of the shared state. We extend our results to the cluster scenario, where many subgroups of parties may collude. Our findings provide a new operational motivation for the strong definition of genuine multipartite nonlocality originally introduced by Svetlichny.