纠缠、反平坦性与非局域非稳定子性：来自纠缠谱的统一视角
Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum
- School of Physics, Beihang University（北京航空航天大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构建了非局域非稳定子性的统一谱框架，推导了非局域稳定子Rényi熵的普适上下界，提出二进壳层三明治构造，揭示了纠缠与非局域非稳定子性的关联，为量子多体系统纠缠谱分析提供了通用工具。
AI中文摘要：
纠缠与非稳定子性分别刻画了量子复杂性的不同方面，但二者通过纠缠谱的关联仍未被完全理解。本文针对二分非局域非稳定子性构建了统一的谱框架，引入广义反平坦性，并基于Rényi纠缠熵与谱非均匀性推导了非局域稳定子Rényi熵（SRE）的普适上下界。将这些界应用于指数衰减和代数衰减谱，揭示了纠缠与非局域非稳定子性的不同关联；针对边缘代数谱和Calabrese-Lefevre谱，进一步提出二进壳层三明治构造，通过上下壳层平坦谱约束有序纠缠谱，确定了非局域SRE的渐近标度。在一维共形临界点处，该构造给出了双对数标度律的普适层级。本文的谱界与二进壳层三明治构造为分析非局域SRE提供了通用工具，形成了可应用于量子多体系统各类纠缠谱的灵活框架。
英文摘要：
Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer $α\geq2$. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer $α\geq2$. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.
