相干性产生功率偏差：超越平均相干性产生的涨落与输入选择性
Coherence-generating power deviation: Fluctuations and input selectivity beyond average coherence generation
- Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出相干性产生功率偏差（CGPD）以刻画量子过程相干性产生的涨落与输入选择性，证明非平凡酉生成器必有涨落，并揭示拓扑与局域化对CGPD的显著影响。
AI中文摘要：
相干性产生功率（CGP）衡量量子过程从非相干输入平均产生多少相干性，但平均值可能掩盖相干性的来源。我们引入相干性产生功率偏差（CGPD），即非相干态均匀单纯形上生成的希尔伯特-施密特相干性的标准差。CGPD将相干性产生转化为一个景观：小值表示跨输入群体的稳健产生，而大值则揭示对特定群体不平衡的选择性转换。通过将酉相干性产生表示为群体空间上的二次响应，我们获得了任意有限维度下的精确一阶和二阶矩。我们证明每个非平凡的酉生成器必然存在涨落，并将这种不可避免的各向同性涨落与多余的各向异性分离。由此产生的平均强度与输入选择性之间的区分，对基准测试、可靠性保证、输入系综敏感性以及四副本测量协议具有直接影响；它也自然扩展到幺正量子信道。匹配的量子行走和准周期输运示例表明，拓扑和局域化可以保持CGP不变，同时显著改变CGPD，揭示了仅靠平均值无法看到的结构。
英文摘要：
Coherence-generating power (CGP) tells how much coherence a quantum process produces on average from incoherent inputs, but an average can hide where that coherence comes from. We introduce the coherence-generating power deviation (CGPD), the standard deviation of the generated Hilbert--Schmidt coherence over the uniform simplex of incoherent states. CGPD turns coherence generation into a landscape: a small value signals robust production across input populations, whereas a large value reveals selective conversion of particular population imbalances. By representing unitary coherence generation as a quadratic response on population space, we obtain exact first and second moments in arbitrary finite dimension. We prove that every nontrivial unitary generator must fluctuate, and we separate this unavoidable isotropic fluctuation from excess anisotropy. The resulting distinction between average strength and input selectivity has direct consequences for benchmarking, reliability guarantees, input-ensemble susceptibility, and four-copy measurement protocols; it also extends naturally to unital quantum channels. Matched quantum-walk and quasiperiodic-transport examples show that topology and localization can leave CGP unchanged while substantially changing CGPD, revealing structure invisible to the mean alone.
