发表机构
Massachusetts Institute of Technology; Max Planck Institute of Quantum Optics; New York University; University of Basel（麻省理工学院; 马克斯·普朗克量子光学研究所; 纽约大学; 巴塞尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明任意恒定温度下自旋链的吉布斯态可分解为有界块乘积态混合，从而可用恒定深度局域电路制备，并限制热纠缠结构，同时推广到费米子系统。
AI 中文摘要
我们证明了在任意恒定温度下，任何自旋链的吉布斯态都可以精确分解为长度有界的连续量子比特块上的乘积态的混合。因此，任何这样的吉布斯态都可以通过恒定深度的局域幺正电路制备，并伴随高效的经典预处理。我们对热纠缠的空间结构施加了强限制：纠缠深度和纠缠宽度（多粒子纠缠的度量）均受常数限制，而可局域化纠缠（通过局域测量和经典通信辅助生成的双粒子纠缠）在超过恒定阈值距离后精确消失。我们的结果对量子热化也有启示：对于任何具有非简并谱隙的平移不变自旋链哈密顿量，在任意恒定有效温度下，从最大熵系综中抽取的典型低复杂度纯态在幺正演化后，与吉布斯态在局域上不可区分。此外，我们获得了费米子系统的类似分解：任何一维局域费米子哈密顿量的吉布斯态精确地是作用于高斯态上的恒定深度局域费米子电路的混合。
英文摘要
We prove that the Gibbs state of any spin chain can be exactly decomposed into a mixture of product states over contiguous blocks of qubits with bounded length, at any constant temperature. As a consequence, any such Gibbs state can be prepared by local unitary circuits of constant depth, with efficient classical preprocessing. We place strong limits on the spatial structure of thermal entanglement: both the entanglement depth and entanglement width (measures of multiparticle entanglement) are bounded by constants, while the localizable entanglement (the bipartite entanglement that can be generated with the aid of local measurements and classical communication) vanishes exactly beyond a constant threshold distance. Our result also has implications for quantum thermalization: for any translation-invariant spin-chain Hamiltonian with nondegenerate spectral gaps, typical low-complexity pure states drawn from a maximally entropic ensemble at any constant effective temperature become locally indistinguishable from the Gibbs state upon unitary evolution. Additionally, we obtain an analogous decomposition for fermionic systems: the Gibbs state of any 1D local fermionic Hamiltonian is exactly a mixture of constant-depth local fermionic circuits acting on Gaussian states.
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