In practical quantum key distribution systems, there inevitably exists errors during the quantum state preparation process due to imperfections in realistic equipments and devices. Those errors would lead to some security loopholes in the quantum key distribution systems. Based on the work of Kiyoshi Tamaki et al. (Physical Review A, 90, 052314 (2014)), here in this paper, we proposes a state preparation error tolerant quantum key distribution protocol based on heralded single-photon sources.
In this protocol, we characterize the size of the errors in the preparation state of Alice and bring it into the security analysis, avoiding possible security loopholes, and improving the security of the system. Moreover, we take the three-intensity decoy-state method as an example to introduce the method of model construction and parameter estimation, and carry out corresponding numerical simulations.
We do comparisons between the loss tolerant protocol with WCS and our present protocol using HSPS. Simulation results shows that under the same state preparation errors, the key generation rate of the protocol based on WCS is higher than the key generation rate of protocol based on HSPS at short transmission distances (e.g., less than 150km). The main reason is that the detection efficiency of the local detector used in the latter scheme is low. However, In the case of long transmission distances (e.g., greater than 200km), the key generation rate of scheme with WCS drops deeply, while the decline of the key generation rate of the present scheme is much more flat. As a result, the former can no longer generate keys after 211 kilometers, while the maximum transmission distance of the latter can reach 228km.
Moreover, we also do comparisons between the present cheme and the GLLP protocol with HSPS. Simulation results show that the GLLP protocol with HSPS is very sensitive to the state preparation error and its key generation rate will rapidly decrease with the increase of the state preparation error. On the contrary, our present protocol shows almost no performance degradation under practical state preparation errors. It thus verify the robustness aganist state preparation errors of our present work.
In addition, in principle, the method can also be combined with the measurement-device-independent quantum key distribution protocol and the twin-field quantum key distribution protocol to further increase the secure communication transmission distance that the present system can support. Therefore, this work may provide important reference value for the practical application of long-distance quantum secure communication in the near future.