Round robin differential phase shift quantum key distribution with yes-no detectors only

In the original round-robin differential-phase-shift (RRDPS) quantum key distribution and its improved method, the photon-number-resolving detectors are must for the security. We present a RRDPS protocol with yes-no detectors only. We get the upper bounds of mutual information of Alice and Eve, and Bob and Eve, and the formula of key rate. Our main idea is to divide all counts into two classes, the counts due to the odd number photons of incident detectors and the counts due to the even number photons of incident detectors. The fact that the bit-flip error rate of the later class is certainly $50\%$ makes it possible for us to perform a tightened estimation of the upper bound of the leakage information. The robustness of original RRDPS against source flaws such as side-channel attacks still holds for the RRDPS with yes-no detectors. The simulation results show that the key rate of RRDPS with yes-no detectors is close to that of RRDPS with photon-number-resolving detectors. Our results make the RRDPS protocol much more practical.