Finite-key analysis for round-robin-differential-phase-shift quantum key distribution

Since the round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol was proposed, it has attracted much attention due to its unique characteristic i.e., it can bind the amount of information leakage without monitoring signal disturbance. Recently, Yin et al. have developed a novel theory to estimate its information leakage tightly. However, the finite-sized key effects are not taken into account. Here, we fill this gap and extend the security proof of the RRDPS protocol to the finite-sized regime using post-selection technique. As a consequence, it's predicted that the key rate of RRDPS in a finite-sized key scenario can be comparable to the asymptotic one, which is meaningful for the real-life applications.