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The differential-phase-shift (DPS) quantum key distribution (QKD) protocolwas proposed aiming at simple implementation, but it can tolerate only a smalldisturbance in a quantum channel. The round-robin DPS (RRDPS) protocol could bea good solution for this problem, which in fact can tolerate even up to $50\%$of a bit error rate. Unfortunately, however, such a high tolerance can beachieved only when we compromise the simplicity, i.e., Bob's measurement mustinvolve a large number of random delays ($|\mathcal{R}|$ denotes its number),and in a practical regime of $|\mathcal{R}|$ being small, the tolerance is low.In this paper, we propose a new DPS protocol to achieve a higher tolerance thanthe one in the original DPS protocol, in which the measurement setup is lessdemanding than the one of the RRDPS protocol for the high tolerance regime. Wecall the new protocol the small-number-random DPS (SNRDPS) protocol, and inthis protocol, we add only a small amount of randomness to the original DPSprotocol, i.e., $2\leq|\mathcal{R}|\leq10$. In fact, we found that theperformance of the SNRDPS protocol is significantly enhanced over the originalDPS protocol only by employing a few additional delays such as$|\mathcal{R}|=2$. Also, we found that the key generation rate of the SNRDPSprotocol outperforms the RRDPS protocol without monitoring the bit error ratewhen it is less than $5\%$ and $|\mathcal{R}|\leq10$. Our protocol is anintermediate protocol between the original DPS protocol and the RRDPS protocol,and it increases the variety of the DPS-type protocols with quantifiedsecurity.

Differential-phase-shift quantum key distribution protocol with small number of random delays