Security of the Decoy State Two-Way Quantum Key Distribution with Finite Resources

The quantum key distribution (QKD) allows two parties to share a secret key by typically making use of a one-way quantum channel. However, the two-way QKD has its own unique advantages, which means the two-way QKD has become a focus recently. To improve the practical performance of the two-way QKD, we present a security analysis of a two-way QKD protocol based on the decoy method with heralded single-photon sources (HSPSs). We make use of two approaches to calculate the yield and the quantum bit error rate of single-photon and two-photon pulses. Then we present the secret key generation rate based on the GLLP formula. The numerical simulation shows that the protocol with HSPSs has an advantage in the secure distance compared with weak coherent state sources. In addition, we present the final secret key generation rate of the LM05 protocol with finite resources by considering the statistical fluctuation of the yield and the error rate.