Currently most progresses on quantum secret sharing suffer from rate-distance bound, and thus the key rates are limited. In addition to the limited key rate, the technical difficulty and the corresponding cost together prevent large-scale deployment. Furthermore, the performance of most existing protocols is analyzed in the asymptotic regime without considering participant attacks. Here we report a measurement-device-independent quantum secret sharing protocol with improved key rate and transmission distance. Based on spatial multiplexing, our protocol shows it can break rate-distance bounds over network under at least ten communication parties. Compared with other protocols, our work improves the secret key rate by more than two orders of magnitude and has a longer transmission distance. We analyze the security of our protocol in the composable framework considering participant attacks and evaluate its performance in the finite-size regime. In addition, we investigate applying our protocol to digital signatures where the signature rate is improved more than $10^7$ times compared with existing protocols. We anticipate that our quantum secret sharing protocol will provide a solid future for multiparty applications on the quantum network.

翻译：目前大多数量子秘密共享的进展受到速率-距离界限的制约，因此密钥率受限。除密钥率受限外，技术难度及相应成本共同阻碍了其大规模部署。此外，现有多数协议的性能仅基于渐近区域分析，未考虑参与者攻击。本文提出一种测量设备无关的量子秘密共享协议，在密钥率和传输距离方面均有改进。基于空间复用的特性，我们的协议表明，在至少十个通信方参与的量子网络中，它能够打破速率-距离界限。与其他协议相比，本工作在密钥率上提升了两个数量级以上，并实现了更长的传输距离。我们在可组合框架下分析了考虑参与者攻击的协议安全性，并在有限长区域评估了其性能。此外，我们还将协议应用于数字签名场景，与现有协议相比，签名率提升了超过10^7倍。我们预期该量子秘密共享协议将为量子网络上多方应用奠定坚实基础。