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Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario. [ABSTRACT FROM AUTHOR]

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way. [ABSTRACT FROM AUTHOR]

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.

In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party XOR game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games that have no quantum advantage for arbitrary input probability distributions, up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum nonlocal correlations.