High-capacity dual degrees of freedom quantum secret sharing protocol beyond the linear rate-distance bound

Quantum secret sharing (QSS) is a multipartite cryptographic primitive. Most existing QSS protocols are limited by the linear rate-distance bound and cannot realize long-distance and high-capacity multipartite key distribution. This paper proposes a polarization (Pol) and phase dual degrees of freedom QSS protocol based on weak coherent pulse (WCP) sources. Our protocol combines single-photon interference, two-photon interference, and non-interference principles and can resist internal attacks from dishonest players. We develop a simulation method to estimate its performance under a beam splitting attack. The simulation results show that our protocol can surpass the linear bound. Compared with the differential-phase-shift twin-field QSS and WCP-Ph-QSS protocols, our protocol has stronger resistance against the beam splitting attack, and thus has a longer maximal communication distance and a higher key rate. By using the WCPs with high average photon number (μ=1.5), our protocol achieves a key rate of about 5.4 times that of the WCP-Ph-QSS protocol. Its maximal communication distance (441.7 km) is about 7.9% longer than that of the WCP-Ph-QSS. Our protocol is feasible with current experimental technology and offers a promising approach for long-distance and high-capacity quantum networks.