On the QKD relaying models
  We investigate Quantum Key Distribution (QKD) relaying models. Firstly, we propose a novel quasi-trusted QKD relaying model. The quasi-trusted relays are defined as follows: (i) being honest enough to correctly follow a given multi-party finite-time communication protocol; (ii) however, being under the monitoring of eavesdroppers. We develop a simple 3-party quasi-trusted model, called Quantum Quasi-Trusted Bridge (QQTB) model, to show that we could securely extend up to two times the limited range of single-photon based QKD schemes. We also develop the Quantum Quasi-Trusted Relay (QQTR) model to show that we could securely distribute QKD keys over arbitrarily long distances. The QQTR model requires EPR pair sources, but does not use entanglement swapping and entanglement purification schemes. Secondly, we show that our quasi-trusted models could be improved to become untrusted models in which the security is not compromised even though attackers have full controls over some relaying nodes. We call our two improved models the Quantum Untrusted Bridge (QUB) and Quantum Untrusted Relay (QUR) ones. The QUB model works on single photons and allows securely extend up to two times the limited QKD range. The QUR model works on entangled photons but does not use entanglement swapping and entanglement purification operations. This model allows securely transmit shared keys over arbitrarily long distances without dramatically decreasing the key rate of the original QKD schemes. 
Quoc-Cuong Le and Patrick Bellot