Unconditional Security of Single-Photon Differential Phase Shift Quantum Key Distribution

In this Letter, we prove the unconditional security of the single-photon differential phase shift quantum key distribution (DPS-QKD) protocol, based on the conversion to an equivalent entanglement-based protocol. We estimate the upper bound of the phase error rate from the bit error rate, and show that the DPS-QKD protocol can generate an unconditionally secure key when the bit error rate is not greater than 4.12%. This proof is the first step to the unconditional security proof of a coherent state DPS-QKD.