Memory-assisted measurement-device-independent quantum secret sharing

Measurement-device-independent quantum secret sharing (MDI-QSS) can eliminate all the security loopholes associated with imperfect measurement devices and greatly enhance QS's security under practical experimental condition. MDI-QSS requires each communication user to send single photon to the measurement party for the coincident measurement. However, the unsynchronization of the transmitted photons greatly limits MDI-QSS's practical performance.In the paper, we propose a high-efficient quantum memory (QM)-assisted MDI-QSS protocol, which employs the QM-assisted synchronization of three heralded single-photon sources to efficiently generate three simultaneous single-photon states. The QM constructed with all-optical, polarization-insensitive storage loop has superior performance in terms of bandwidth, storage efficiency, and noise resistance, and is feasible under current experiment conditions. Combining with the decoy-state method, we perform the numerical simulation of the secure key rate in the symmetric model without considering the finite-size effect. The simulation results show that our QM-assisted MDI-QSS protocol exhibit largely improved secure key rate and maximal photon transmission distance compared with all existing MDI-QSS protocols without QM. Our protocol provides a promising way for implementing the high-efficient long-distance MDI-QSS in the near future.