轻微纠缠量子多体状态的非局域非稳定性
Nonlocal nonstabilizerness for slightly entangled quantum many-body states
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中文总结 AI 辅助
研究轻微纠缠量子多体状态的非局域非稳定性，提出施密特参考态框架，通过排序后的施密特谱直接构建取代局部酉变换上的高度非凸优化，支持非局域稳定器雷尼熵推测，表明该框架能有效获取弱纠缠多体状态的非局域非稳定性。
中文摘要 AI 辅助
非局域非稳定性量化了二分纠缠中编码的不可约魔术资源，但其评估通常受到局部酉变换上高度非凸优化的阻碍。在此，我们提出了一个施密特参考态框架，该框架通过从排序后的施密特谱直接构建来取代这种优化。我们推测非局域稳定器雷尼熵（SRE）由相应参考态的SRE给出，并通过解析和数值证据支持这一推测。只要纠缠谱可用，我们的框架就能有效地获取弱纠缠多体状态的非局域非稳定性。将其应用于哈尔随机态、临界自旋链和PXP动力学，我们表明非局域SRE捕获了纠缠谱中传统纠缠度量不可见的非稳定器结构。我们的结果将纠缠谱确立为洞察不可约非稳定器相关性的有力窗口，为研究平衡和非平衡量子多体系统的非局域魔术资源开辟了一条广泛适用的途径。
英文摘要
Nonlocal nonstabilizerness quantifies the irreducible magic resource encoded in bipartite entanglement, but its evaluation is generally hindered by a highly nonconvex optimization over local unitary transformations. Here we propose a Schmidt-reference-state framework that replaces this optimization by a direct construction from the sorted Schmidt spectrum. We conjecture that the nonlocal stabilizer Rényi entropy (SRE) is given by the SRE of the corresponding reference state, and support this conjecture through analytical and numerical evidences. Our framework makes nonlocal nonstabilizerness efficiently accessible for weakly entangled many-body states whenever the entanglement spectrum is available. Applying it to Haar-random states, critical spin chains, and PXP dynamics, we show that nonlocal SRE captures nonstabilizer structures in the entanglement spectrum that are invisible to conventional entanglement measures. Our results establish entanglement spectra as a powerful window into irreducible nonstabilizer correlations, opening a broadly applicable route to studying nonlocal magic resources of quantum many-body systems in and out of equilibrium.
