Measurement-device-independent quantum secret sharing with hyper-encoding

Quantum secret sharing(QSS) is a typical multi-party quantum communication mode, in which the key sender splits a key into several parts and the participants can obtain the key by cooperation. Measurement-device-independent quantum secret sharing(MDI-QSS) is immune to all possible attacks from measurement devices and can greatly enhance QSS's security in practical applications. However, previous MDI-QSS's key generation rate is relatively low. Here, we adopt the polarization-spatial-mode hyper-encoding technology in the MDI-QSS, which can increase single photon's channel capacity. Meanwhile, we use the cross-Kerr nonlinearity to realize the complete hyper-entangled Greenberger-Horne-Zeilinger state analysis. Both above factors can increase MDI-QSS's key generation rate by about 10^(3). The proposed hyper-encoded MDI-QSS protocol may be useful for future multiparity quantum communication applications.