AI 中文总结
该研究证明混沌多体系统平衡纯态的魔性具有普适性，由热Scrooge系综捕获，仅为温度的函数，还给出稳定子Rényi熵的普适预测并通过分析与数值模拟验证，确立魔性为混沌多体系统的热力学性质。
AI 中文摘要
热化通常描述孤立多体系统在平衡态下的局域性质，而魔性（又称非稳定子性，是实现通用量子计算的资源）则相反，编码在多体波函数的全局结构中。我们证明，尽管魔性具有全局性质，混沌多体系统的平衡纯态（包括后期演化态和能量本征态）的魔性是普适的：它由热Scrooge系综捕获，该系综是与相同有效温度下吉布斯态一致的纯态的最小信息系综。因此，对于除总能量外无其他守恒量的系统，平衡魔性仅为温度的函数，与初始态及平衡态的其他微观特征无关。这对稳定子Rényi熵（SRE）给出了具体的普适预测：在无限温度下，SRE由Pauli谱的类Haar涨落决定；在有限温度下，能量守恒会诱导出由热Pauli谱控制的体积律热力学修正。我们通过分析论证和大量数值模拟支持这些预测，还证明高温下的混沌多体系统具有无法被有限深度局域量子电路移除的长程魔性和纠缠。我们的结果确立了魔性为混沌多体系统的一种热力学性质，并表明Scrooge系综可能为量子多体资源提供统一框架。
英文摘要
Thermalization conventionally describes local properties of isolated many-body systems at equilibrium. Magic, or nonstabilizerness $\unicode{x2013}$ the resource enabling universal quantum computation $\unicode{x2013}$ is by contrast encoded in the global structure of the many-body wavefunction. We show that, despite its global nature, the magic of equilibrium pure states of chaotic many-body systems, including late-time evolved states and energy eigenstates, is universal: it is captured by the thermal Scrooge ensemble, the minimally informative ensemble of pure states consistent with the Gibbs state at the same effective temperature. Therefore, for systems with no conserved quantities other than the total energy, equilibrium magic is a function of temperature alone, independent of the initial state and other microscopic features of the equilibrium state. This yields concrete universal predictions for the stabilizer Rényi entropies (SREs). At infinite temperature, the SRE is set by Haar-like fluctuations of the Pauli spectrum, while at finite temperature energy conservation induces a volume-law thermodynamic correction controlled by the thermal Pauli spectrum. We support these predictions with analytical arguments and extensive numerical simulations. We further show that chaotic many-body systems at high temperatures possess long-range magic and entanglement that cannot be removed by finite-depth local quantum circuits. Our results establish magic as a thermodynamic property of chaotic many-body systems and suggest that Scrooge ensembles may provide a unified framework for quantum many-body resources.
Comments9 pages + Appendices, 9 figures
