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Among many quantum key distribution (QKD) protocols, the round-robindifferential phase shift (RRDPS) protocol is unique in that it can upper-boundthe amount of the information leakage without monitoring the signaldisturbance. To expedite implementation of the protocol, however, the number ofpulses forming a single block should be kept small, which significantlydecreases the key rates in the original security proof. In the present paper,we refine the security proof of the RRDPS protocol in the finite-sized regimeand achieve a tighter estimation for the information leakage without changingthe original experimental setups. As a consequence, we obtain better key ratesin both asymptotic and finite-sized cases while keeping the preferable featuresof the protocol, such as omission of phase randomization.

Refined security proof of the round-robin differential phase shift quantum key distribution and its improved performance in the finite-sized case