AI 中文总结
研究非局域魔法，通过纠缠谱的沃尔什 - 哈达玛自相关导出其表示，明确潜在谐波结构，证明可由纠缠熵给出上界，为多种量子态得出解析结果，确定谱组织是关键因素并提供分析框架。
AI 中文摘要
非局域魔法最近已成为表征真正非局域非稳定器关联的基本资源。然而，除了小系统外，其直接计算是一个难以处理的数值问题，人们对它的理解仍然有限。我们根据纠缠谱的沃尔什 - 哈达玛自相关导出了非局域魔法的一种表示。这种表示使潜在的谐波结构明确，并能对各种情况下的行为进行系统分析。我们证明非局域魔法可以由纠缠熵给出上界，并为广泛的量子态类别得出了精确的解析结果，刻画了体积律态以及一维能隙和临界系统基态的非局域魔法标度。我们的结果确定了纠缠谱的谱组织是控制非局域魔法的关键因素，并为进一步的系统分析研究提供了框架。
英文摘要
Non-local magic has recently emerged as a fundamental resource for characterizing genuinely non-local non-stabilizer correlations. However, its direct calculation is an intractable numerical problem, except for small systems, and its understanding remains limited. We derive a representation of non-local magic in terms of the Walsh--Hadamard autocorrelations of the entanglement spectrum. Our representation makes the underlying harmonic structure explicit and enables a systematic analysis of its behaviors for various scenarios. We prove that non-local magic can be upper-bounded by an entanglement entropy and we derive exact analytical results for broad classes of quantum states, characterizing the scaling of non-local magic for volume-law states, as well as ground states of one-dimensional gapped and critical systems. Our results identify the spectral organization of the entanglement spectrum as the key ingredient governing non-local magic and provide a framework for further systematic analytical investigation.
