Security of round-robin differential-phase-shift quantum-key-distribution protocol with correlated light sources

Among various quantum-key-distribution (QKD) protocols, the round-robin differential-phase- shift (RRDPS) protocol has a unique feature where its security is guaranteed without monitoring the signal disturbance. Moreover, this protocol has the remarkable property of being robust against source imperfections, assuming that the emitted pulses are independent. Unfortunately, some experiments with high-speed QKD systems confirmed the violation of the independence due to pulse correlations, and therefore the lack of a security proof, without taking into account this effect is an obstacle for guaranteeing the implementation security. In this paper, we show that the RRDPS protocol is secure against any source imperfections by establishing a security proof with the pulse correlations. The proof is simple in the sense that we make only three experimentally simple assumptions on the source. Our numerical simulation based on the proof shows that the long-range pulse correlation does not cause a significant impact on the key rate, which reveals another striking feature of the RRDPS protocol. Our security proof is thus effective and applicable to a wide range of practical sources and paves the way to realizing truly secure QKD in high-speed systems.