Security of differential quadrature phase shift quantum key distribution

The differential phase shift (DPS) protocol is one of the simplest quantum key distribution protocols for implementation. Despite its practical advantage, current security proofs for the DPS protocol lead to much lower key generation rates compared to the BB84 protocol. We prove the security of a variant of the DPS protocol, called differential quadrature phase shift (DQPS) protocol. In addition to the fact that the DQPS protocol can be implemented with essentially the same hardware as the BB84 protocol with phase encoding (PE-BB84), our results show that the key generation rate of the DQPS protocol is eight thirds as high as that of the PE-BB84 protocol in the asymptotic key-size limit, and that the advantage still holds when the effect of finite-sized key is taken into account.