Continuous-variable quantum cryptography with untrusted relays

We extend the field of continuous-variable quantum cryptography to a more robust formulation which can be applied to untrusted networks. We consider two remote parties connected to an untrusted relay by insecure quantum links. To generate correlations, they transmit coherent states to the relay where a continuous-variable Bell detection is performed. Despite the possibility that the working mechanism of the relay could be fully corrupted and the links subject to optimal coherent attacks, the parties are still able to extract a secret key. Furthermore, our analysis shows that very long distances and high rates can be reached when the relay is proximal to one of the parties, configuration typical of a mobile device connecting to a public access point. Thus, using the cheapest possible quantum resources, we show the possibility of long-distance high-rate quantum key distribution in network topologies where direct links are missing between two end-users and intermediate relays cannot be trusted.