量化量子态检测所需样本数，给出精确理论边界。
Sample Complexity of Composite Quantum Hypothesis Testing
- 通过上下界分析，刻画复合量子假设检验的样本复杂度
- 对有限与无限不确定性集均给出紧致样本数量界限
- 首次建立差分隐私下量子检测的样本需求理论
本文研究对称复合二元量子假设检验（QHT）问题，目标是判断未知量子态属于两个不确定性集中的哪一个。尽管该问题的渐近错误指数已有深入研究，但有限样本情形仍不明确。本文填补这一空白，刻画了样本复杂度——即达到指定误差水平所需的最少态副本数。具体而言，我们推导出推广自简单QHT的下界，并为多种不确定性集（包括有限与无限基数）提出新的上界。值得注意的是，我们的上下界仅相差一个绝对常数，实现了样本复杂度的紧致刻画。最后，我们将分析扩展至差分隐私场景，建立了隐私保护下复合量子假设检验的样本复杂度。
原文摘要 · Abstract (English)
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are well-studied, the finite-sample regime remains poorly understood. We bridge this gap by characterizing the sample complexity -- the minimum number of state copies required to achieve a target error level. Specifically, we derive lower bounds that generalize the sample complexity of simple QHT and introduce new upper bounds for various uncertainty sets, including of both finite and infinite cardinalities. Notably, our upper and lower bounds match up to universal constants, providing a tight characterization of the sample complexity. Finally, we extend our analysis to the differentially private setting, establishing the sample complexity for privacy-preserving composite QHT.
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