发表机构
Harvard University; MIT; Harvard Quantum Initiative（哈佛大学; 麻省理工学院; 哈佛量子倡议）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对长程泡利相互作用的量子吉布斯态，证明其经典特征随温度降低的层级转变，解决了两个开放问题，给出多项式时间经典算法并改进了可分温度的紧边界。
AI 中文摘要
在高温下，量子吉布斯态保留了最大混合态的若干经典特征：无纠缠、无魔性、配分函数解析性、关联衰减以及算法可处理性。我们证明了新的严格边界，表明这些特征会持续到与系统大小无关的有限温度，但在不同的逆温度尺度上失效，形成了经典到量子转变的层级结构。我们的结果适用于每个位点强度有界的长程泡利相互作用。尽管存在这种全对全相互作用，我们证明纠缠的消失发生在恒定温度下，解决了Rouze、Franca和Alhambra（STOC'25）提出的开放问题。我们给出了一个多项式时间经典算法，可在纠缠消失转变前制备吉布斯态。值得注意的是，该温度比已知量子吉布斯采样器快速混合的温度渐近更低，也比Bakshi等人（FOCS'24）提出的原始可分温度更低，我们将其改进为常数因子内的紧边界。在渐近更冷的温度下，我们证明吉布斯态仍处于热力学无限温度相，这为估计热期望值提供了多项式时间经典算法，尽管存在纠缠和魔性，同时解决了Harrow、Mehraban和Soleimanifar（STOC'20）提出的关联衰减猜想。
英文摘要
At high temperature, quantum Gibbs states retain several classical features of the maximally mixed state: the absence of entanglement, the absence of magic, analyticity of the partition function, correlation decay, and algorithmic tractability. We prove new and sharp bounds showing that these features persist down to finite temperatures independent of system size, but fail at distinct inverse-temperature scales, forming a hierarchy of classical-to-quantum transitions. Our results hold for long-range Pauli interactions with bounded strength at every site. Despite such all-to-all interactions, we show that the death of entanglement occurs at constant temperature, resolving an open question of Rouze, Franca and Alhambra (STOC'25). We give a polynomial-time classical algorithm that prepares Gibbs states up to the death of entanglement transition. Notably, this is asymptotically colder than temperatures at which quantum Gibbs samplers are known to mix quickly, as well as the original separability temperature of Bakshi et al. (FOCS'24), which we improve to be tight up to constants. At asymptotically even colder temperatures, we show that the Gibbs state remains in the thermodynamic infinite-temperature phase. We give polynomial-time classical algorithms for estimating thermal expectations up to the phase transition (despite both entanglement and magic), and as a corollary resolve a correlation decay conjecture of Harrow, Mehraban and Soleimanifar (STOC'20).
Comments102 pages, 3 figures; improved k dependence of zero-free radius to be tight
