发表机构
Zhejiang Sci-Tech University; Graduate School of China Academy of Engineering Physics（浙江理工大学; 中国工程物理研究院研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对量子态认证问题，将其建模为复合量子假设检验，揭示了最小错误概率的普适标度律，发现标度行为转变为二级相变，无需完整态层析即可实现大系综量子态认证。
AI 中文摘要
量子态认证用于判断未知量子态属于哪两组量子态之一，这两组由两个不同的参数区域标记。我们将该问题建模为复合量子假设检验，并揭示了N个拷贝下最小错误概率的普适标度律。以偏振方向认证和纯度认证为例，我们证明N个拷贝的置换对称性及参数区域的几何对称性可确定最优测量和“最坏成对态”。对于不相交区域，最小错误概率按N^{-3/2}exp(-Nξ)标度；对于相邻区域，按(NF)^{-1/2}标度，其中ξ和F分别是与“最坏成对态”相关的量子Chernoff散度和量子Fisher信息。以最小错误概率作为序参量，当N→∞时，标度行为之间的转变为二级相变。我们的方法无需完整量子态层析即可判断量子态是否属于给定集合，从而能用有限样本实现大系综的认证。
英文摘要
Qualification of quantum states judges which of two sets of quantum states an unknown state lies in, where the two sets are labeled by two distinct parameter regions. We formulate this problem as a composite quantum hypothesis test and uncover universal scaling laws for the minimum error probability for $N$ copies. Taking polarization-direction qualification and purity qualification as examples, we show that the $N$-copy permutation symmetry and the geometric symmetries of the parameter regions identify the optimal measurements and the "worst pairwise states". The minimum error probability scales as $N^{-3/2}\exp(-Nξ)$ for disjoint regions and as $(NF)^{-1/2}$ for adjacent regions, where $ξ$ and $F$ are the quantum Chernoff divergence and quantum Fisher information associated with the "worst pairwise states", respectively. With the minimum error probability serving as an order parameter, the transition between the scaling behaviors becomes a second-order phase transition as $N\to\infty$. Our approach determines whether a quantum state belongs to a given set without full state tomography, thereby enabling qualification of large ensembles using finite samples.
