Long-Distance Measurement-Device-Independent QKD

Quantum key distribution (QKD) promises unconditional security for sharing secret keys by relying on the laws of quantum physics. Its practical implementation, however, faces some challenges. For instance, that we need to trust some of the equipment used by our legitimate users poses a threat that has partly been remedied by recently proposed measurement-device-independent QKD (MDI-QKD) schemes [1]. In such schemes, the end users encode (decoy) BB84 signals and transmit them to a middle station at which entanglement swapping operation is performed; see Fig. 1(a)-(b). Channel loss will also impose an exponential decay of the key rate with distance. This can in principle be avoided by using (probabilistic) quantum repeater (QR) setups, which also rely on entanglement swapping. The combination of the two systems, MDI-QKD and QRs, will then provide us with a system that while offers easy affordable access to the end users, will enable them to exchange secret keys over long distances. Here, we present such a hybrid system as in Fig. 1(c), and find the secret key generation rate, RQKD, for such a system. While MDI-QKD systems can be run using weak laser pulses, quantum repeaters often rely on quantum memories, e.g., (quasi-) atomic systems. Once two quantum memories are entangled, one need to read them out, i.e., convert their internal states to photonic states, and interfere the resulting photons with those sent by QKD users. The photons obtained from quantum memories is typically an imperfect single photon. In our analysis, we then first consider the scheme proposed in [2], see Fig. 1(a), where one (or both) of the sources could be an imperfect single-photon source, representing the memory, and the other is a coherent state. The scheme works as follows. Two parties randomly choose between x and z basis by using diagonal or rectangular polarized beams, respectively, at the source. A partial Bell state measurement (BSM) is performed by an untrusted party in the middle station. A successful partial BSM occurs when one, and only one, of r0 and r1, and one, and only one, of s0 and s1, click. All other detection events are discarded.