均匀稳定子态识别的精确临界曲线
Exact Critical Curve for Uniform Stabilizer-State Identification
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中文总结 AI 辅助
本文通过Clifford张量幂对偶和缺陷过滤对角化稳定子Gram算子，精确求解了均匀纯稳定子态在集体测量下的临界交叉曲线，得到最优成功概率的显式级数及$n+O(1)$拷贝阈值。
中文摘要 AI 辅助
识别未知纯稳定子态的样本复杂度一直是量子信息中的一个长期问题。本文在无侧信息且允许任意集体测量的条件下，解决了纯$n$量子比特稳定子态均匀系综的整个精确临界交叉问题。对于$k=n+c$（其中$c$为固定整数），最优成功概率收敛于一个显式的正项级数$P_{\infty}(c)$。特别地，$P_{\infty}(0)=0.1760837896\ldots$，而其两个尾部分别遵循阈值以下的二次指数律和阈值以上的$1-P_{\infty}(c)\sim2^{-c}$。对于每个有限的$n$和$k$，pretty-good测量是精确最优的。证明通过Clifford张量幂对偶和缺陷过滤（包括异常二元扇区）对稳定子Gram算子进行对角化。由此得到的整数尺度律量化了$n+O(1)$份拷贝阈值。
英文摘要
The sample complexity of identifying an unknown pure stabilizer state has been a longstanding problem in quantum information. In this paper, we resolve the entire exact critical crossover for the uniform ensemble of pure $n$-qubit stabilizer states under arbitrary collective measurements and without side information. For $k=n+c$, with fixed integer $c$, the optimal success probability converges to an explicit positive series $P_{\infty}(c)$. In particular, $P_{\infty}(0)=0.1760837896\ldots$, while its two tails obey a quadratic-exponential law below threshold and $1-P_{\infty}(c)\sim2^{-c}$ above threshold. The pretty-good measurement is exactly optimal for every finite $n$ and $k$. The proof diagonalizes the stabilizer Gram operator through Clifford tensor-power duality and a defect filtration, including the exceptional binary sectors. The resulting integer-scale law quantifies the $n+O(1)$ copy threshold.
发表机构
- The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
- International Quantum Academy（国际量子科学院）
- Nagoya University（名古屋大学）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。
