AI 中文总结
本文研究Shamir秘密共享中相关资源导致的量子泄漏，证明在足够份额和混合条件下泄漏态迹距离指数小，并给出独立设备-参考对的最优指数基数，从而提供安全保证。
AI 中文摘要
我们研究了当每个设备使用其份额从初始量子资源中产生一个量子比特时，Shamir秘密共享的泄漏问题，该量子资源独立于秘密和共享随机性。我们证明了，当重建需要足够大比例的份额时，对于满足上算子混合条件的固定平稳链，以及由具有原始转移信道的固定有限量子存储器生成的资源，任意两个秘密的泄漏态之间的迹距离呈指数级小。这些保证允许设备边际的任意扩展作为对手的侧信息，并且对大于份额数的素数域均匀成立。对于独立设备-参考对，这为论证提供了定量输入，我们确定了当重建需要所有份额时的最优指数基数：量子比特为$2\sqrt{2}/\pi$，经典比特为$2/\pi$，在两种情况下都允许任意有限参考。选定边际与乘积态的比较将独立设备-参考对的界转换为相关资源的安全保证。
英文摘要
We study leakage from Shamir secret sharing when each device uses its share to produce one qubit from an initial quantum resource independent of the secret and sharing randomness. We prove exponentially small trace distance between the leakage states of any two secrets, when reconstruction requires a sufficiently large fraction of the shares, for fixed stationary chains satisfying an upper operator mixing condition and for resources generated by fixed finite quantum memories with primitive transfer channels. These guarantees permit arbitrary extensions of the device marginal as adversary side information and hold uniformly over prime fields larger than the number of shares. For independent device--reference pairs, which provide the quantitative input to the argument, we determine the optimal exponential base when reconstruction requires all shares: $2\sqrt2/π$ for a qubit and $2/π$ for a classical bit, in both cases allowing arbitrary finite references. A comparison of selected marginals with product states converts the bounds for independent device--reference pairs into security guarantees for the correlated resources.
Comments25 pages
