Device-independent quantum secret sharing (DI-QSS) provides security against untrusted quantum devices. While device-independent quantum key distribution (DI-QKD) using Mermin-Peres magic square game [Zhen et al., Phys. Rev. Lett, 2023] has been proposed, we present the first DI-QSS protocol based on a pseudo-telepathy parity game without requiring dedicated rounds and specific basis configuration, unlike CHSH-based DI-QSS schemes [Zhang et al., Phys. Rev. A, 2024]. Our scheme simultaneously certifies device-independence and key generation using a single test, achieving optimal performance for a seven-qubit GHZ state configuration. Security against collective attacks is analyzed, and a positive key rate is obtained under white noise and photon loss. Moreover, we show a bitwise advantage over the previous protocol for producing the same raw key length.

翻译：设备无关量子秘密共享（DI-QSS）提供了针对不可信量子设备的安全性保障。尽管已有基于Mermin-Peres幻方游戏的设备无关量子密钥分发（DI-QKD）方案被提出[Zhen等人，Phys. Rev. Lett, 2023]，本文首次提出了一种基于伪心灵感应奇偶校验游戏的DI-QSS协议。与基于CHSH不等式的DI-QSS方案[Zhang等人，Phys. Rev. A, 2024]不同，本方案无需专用轮次和特定基矢配置。我们的方案通过单次测试同时实现设备无关性认证与密钥生成，在七量子比特GHZ态配置下达到最优性能。分析了方案对集体攻击的安全性，并在白噪声和光子损耗条件下获得了正密钥率。此外，在生成相同原始密钥长度的情况下，本方案相比先前协议展现出比特级优势。