Abstract
By introducing four-phase modulations into round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol, the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol is proposed. According to the security proof of RRDQPS protocol, it is able to tolerate a higher error rate of key bits. However, its performance with a practical weak coherent source is still unknown since that security proof only applies to a single photon source. In this article, we give the security proof for the general $n$-photon RRDQPS protocol, by which RRDQPS with a practical weak coherent source becomes feasible in the experiment. Through numerical simulation, it is verified that RRDQPS protocol has an advantage over RRDPS protocol on transmission distance, especially when the pulse number is small.
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