Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in the closed-system dynamics of quantum simulators remains a challenge in today’s era of intermediate-scale quantum devices. Here we discuss an efficient tomographic protocol for reconstructing reduced density matrices and entanglement spectra for spin systems. The key step is a parametrization of the reduced density matrix in terms of an entanglement Hamiltonian involving only quasilocal few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomized measurements. By analysing data from trapped-ion quantum simulators for quench dynamics of a one-dimensional long-range Ising model, we demonstrate the ability of the protocol to measure the time evolution of the entanglement spectrum, in agreement with theoretical expectations. Furthermore, we develop the protocol as a testbed for predictions of entanglement structure in quantum field theories, which we illustrate for conformal field theory in quench dynamics, as well as the Bisognano–Wichmann theorem for ground states. In theoretical simulations, we demonstrate favourable scaling of sampling efficiency with subsystem size. Although the post-processing might ultimately be exponential, our protocol addresses the bottleneck of exponential sampling complexity in the investigation of entanglement structure in quantum simulation, and brings subsystems of tens of spins into reach for present experiments

纠缠是量子多体物理学的关键成分，在量子模拟器的封闭系统动力学中表征和量化纠缠仍然是当今中等规模量子器件时代的挑战。在这里，我们讨论了一种有效的断层扫描协议，用于重建自旋系统的降低密度矩阵和纠缠光谱。关键步骤是根据仅涉及准局部少体项的纠缠哈密顿量对约化密度矩阵进行参数化。该 ansatz 适用于少量随机测量，并且可以独立验证。通过分析来自捕获离子量子模拟器的数据，用于一维长程 ​​Ising 模型的猝灭动力学，我们证明了该协议测量纠缠光谱的时间演化的能力，符合理论预期。此外，我们将该协议开发为预测量子场论中纠缠结构的试验台，我们说明了淬火动力学中的共形场论，以及基态的 Bisognano-Wichmann 定理。在理论模拟中，我们证明了采样效率随子系统大小的有利缩放。尽管后处理最终可能是指数的，但我们的协议解决了量子模拟中纠缠结构研究中指数采样复杂性的瓶颈，并为目前的实验带来了数十个自旋的子系统 我们说明了淬火动力学中的共形场论，以及基态的 Bisognano-Wichmann 定理。在理论模拟中，我们证明了采样效率随子系统大小的有利缩放。尽管后处理最终可能是指数的，但我们的协议解决了量子模拟中纠缠结构研究中指数采样复杂性的瓶颈，并为目前的实验带来了数十个自旋的子系统 我们说明了淬火动力学中的共形场论，以及基态的 Bisognano-Wichmann 定理。在理论模拟中，我们证明了采样效率随子系统大小的有利缩放。尽管后处理最终可能是指数的，但我们的协议解决了量子模拟中纠缠结构研究中指数采样复杂性的瓶颈，并为目前的实验带来了数十个自旋的子系统