  The differential-phase-shift (DPS) quantum key distribution (QKD) protocol
was proposed aiming at simple implementation, but it can tolerate only a small
disturbance in a quantum channel. The round-robin DPS (RRDPS) protocol could be
a 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 be
achieved only when we compromise the simplicity, i.e., Bob's measurement must
involve 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 than
the one in the original DPS protocol, in which the measurement setup is less
demanding than the one of the RRDPS protocol for the high tolerance regime. We
call the new protocol the small-number-random DPS (SNRDPS) protocol, and in
this protocol, we add only a small amount of randomness to the original DPS
protocol, i.e., $2\leq|\mathcal{R}|\leq10$. In fact, we found that the
performance of the SNRDPS protocol is significantly enhanced over the original
DPS protocol only by employing a few additional delays such as
$|\mathcal{R}|=2$. Also, we found that the key generation rate of the SNRDPS
protocol outperforms the RRDPS protocol without monitoring the bit error rate
when it is less than $5\%$ and $|\mathcal{R}|\leq10$. Our protocol is an
intermediate protocol between the original DPS protocol and the RRDPS protocol,
and it increases the variety of the DPS-type protocols with quantified
security.

Quantum Physics