Measurement-device-independent quantum key distribution with multiple crystal heralded source with post-selection

The multiple crystal heralded source with post-selection (MHPS), originally introduced to improve the single-photon character of the heralded source, has specific applications for quantum information protocols. In this paper, by combining decoy-state measurement-device-independent quantum key distribution (MDI-QKD) with spontaneous parametric downconversion process, we present a modified MDI-QKD scheme with MHPS where two architectures are proposed corresponding to symmetric scheme and asymmetric scheme. The symmetric scheme, which linked by photon switches in a log-tree structure, is adopted to overcome the limitation of the current low efficiency of m-to-1 optical switches. The asymmetric scheme, which shows a chained structure, is used to cope with the scalability issue with increase in the number of crystals suffered in symmetric scheme. The numerical simulations show that our modified scheme has apparent advances both in transmission distance and key generation rate compared to the original MDI-QKD with weak coherent source and traditional heralded source with post-selection. Furthermore, the recent advances in integrated photonics suggest that if built into a single chip, the MHPS might be a practical alternative source in quantum key distribution tasks requiring single photons to work.