Fully measurement-device-independent two-way quantum key distribution with finite single-photon sources

Despite the proven security in theory and its potential to achieve high secret key rates, eavesdroppers may crack two-way quantum key distribution (TWQKD) systems by exploiting imperfections of the detection devices that most loopholes exist in, in actual implementations. Lu et al. (Phys. Rev. A 88(4):0443021–044302, 2013) have proved that TWQKD is measurement-device-independent (MDI) security on Bob’s side while assuming ideal detectors on Alice’s side. However, the MDI security proof on Alice’s side is still missing. In this paper, we focus on proving that the TWQKD protocol, secure deterministic communication without entanglement, proposed by Lucamarini and Mancini in 2005 (LM05), is MDI security on both sides of Alice and Bob (fully MDI scenario). First, using a relatively simple method, we give a qubit-based analytical proof that the LM05 is fully MDI security in a depolarizing quantum channel. Then, based on the analytical proof, we derive the expected lower bound of the security formula for it with the reasonable model of finite single-photon sources based on recent experiment progress. Moreover, with the parameters of the current technology, simulation results of the lower bound are presented. It shows that TWQKD can achieve good performances in the fully MDI scenario.