Security proof for round-robin differential phase shift QKD

Abstract

We give a security proof of the 'round-robin differential phase shift' (RRDPS) quantum key distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We show that the RRDPS protocol is equivalent to RRDPS with basis permutation and phase flips performed by Alice and Bob; this causes a symmetrization of Eve's state. We identify Eve's optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value β. As a function of β, we derive, for non-asymptotic key size, the trace distance between the real state and a state in which no leakage exists. We invoke postselection in order to go from qudit-wise attacks to general attacks. For asymptotic key size, we obtain a bound on the trace distance based on the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds. At low qudit dimension, even our non-asymptotic result is sharper than existing asymptotic bounds.

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

“…The key rate gets even worse when we decrease L to simplify the implementation. Therefore, it is desired to improve the key rate of the RRDPS protocol especially for relatively small L. There have been intensive researches to mitigate or to get over these problems both in theory [11][12][13][14][15][16][17][18] and experiment [7,19].…”