Device-independent quantum secret sharing with noise preprocessing and postselection

Device-independent (DI) quantum secret sharing (QSS) can relax the security assumptions about the devices' internal workings and provide QSS the highest level of security in theory. The original DI QSS protocol proved its correctness and completeness under a causal independence assumption regarding measurement devices. However, there has been a lack of DI QSS's performance characterization in practical communication situations, which impedes its experimental demonstration and application in the future. Here we propose a three-partite DI QSS protocol with noise preprocessing and postselection strategies and develop the numerical methods to implement its performance characterization in practical communication situations. The adoption of the noise preprocessing and postselection can reduce DI QSS's global detection efficiency threshold from 96.32% to 94.30% and increase the noise threshold from 7.148% to 8.072%. Our DI QSS protocol has two advantages. First, it is a DI QSS protocol with performance characterization in practical communication situations. Second, the adoption of noise preprocessing and postselection can effectively relax its experimental requirement and enhance the noise resistance. Our DI QSS protocol has potential for future experimental demonstration and application.