我们引入量子计算时间锁（QCT）模型，将时间锁加密与定量噪声量子存储假设相结合。时间锁加密使鲍勃（Bob）可立即获取编码种子，而 Eve 仅在受保护间隔后才能获得与访问该种子相同的最终信息，Eve 可在无计算限制的情况下处理其保留的信息。我们明确提出此延迟访问加密假设，并基于维度 d 的一组完备相互无偏基（MUB）和仿射两两独立置换族构造 MUB-QCT。对于单副本编码，所有与种子无关的即时测量的迹距离优势最大为 1/(2√(d+1))，互信息最大为 1/(d+1)。在菱形距离与替换的有效残余存储最多为 δ 的情况下，个体攻击区分界最多增加 δ。在独立同分布（i.i.d.）个体攻击和熵保持接受的条件下，我们获得渐近密钥率界，并在可组合迹距离中表述最终密钥保密性。对于 m 个共享 1 比特和种子的独立随机信号，非自适应乘积测量下的最优泄漏为 min{1, m/(d+1)}，在该攻击模型中实现线性于 d 的检测增强。我们还构造与种子无关的联合测量，在披露后从 O(log d + log(1/ε)) 个信号中恢复比特时误差最多为 ε，测量后仅保留经典信息，这在乘积测量和联合测量之间形成定量分离。鲍勃使用两个与 d 无关的逻辑检测结果。
英文摘要：
We introduce the Quantum Computational Timelock (QCT) model, combining time-lock encryption with a quantitative noisy-quantum-storage assumption. Time-lock encryption gives Bob immediate access to the encoding seed and gives Eve the same final information as access to that seed only after a protected interval. Eve may then process her retained information without computational restriction. We state this delayed-access encryption assumption explicitly and construct MUB-QCT from a complete set of mutually unbiased bases in dimension $d$ and an affine pair-wise independent permutation family.
For single-copy encoding, every seed-independent immediate measurement has trace-distance advantage at most $1/(2\sqrt{d+1})$ and mutual information at most $1/(d+1)$. Effective residual storage at diamond distance at most $δ$ from replacement adds at most $δ$ to the individual-attack distinguishing bound. Under i.i.d. individual attacks and entropy-preserving acceptance, we obtain an asymptotic key-rate bound and formulate final-key secrecy in composable trace distance.
For $m$ independently randomized signals sharing one bit and seed, the optimal leakage under non-adaptive product measurements is $\min\{1,m/(d+1)\}$, allowing a linear-in-$d$ detection enhancement in that attack model. We also construct a seed-independent joint measurement that recovers the bit after disclosure with error at most $\varepsilon$ from $O(\log d+\log(1/\varepsilon))$ signals, retaining only classical information after measurement. This gives a quantitative separation between product and joint measurements. Bob uses two logical detection outcomes independently of $d$.
Computational Monogamy of Entanglement and Non-Interactive Quantum Key Distribution
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；LIP6（LIP6实验室）；Bocconi University（博科尼大学）；Faculty of Computer Science, Ruhr University Bochum（鲁尔大学波鸿分校计算机学院）；Korteweg-de Vries Institute for Mathematics and QuSoft, University of Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所与QuSoft）；Faculty of Physics, Ludwig Maximilian University of Munich（慕尼黑大学物理学院）；Max Planck Institute for Security and Privacy（马克斯·普朗克安全与隐私研究所）
