AI 中文总结
研究针对具有U(1)粒子数对称性的置换不变费米子多体态，开发层析成像协议。通过总粒子数分布等确定状态，所需可观测量与系统规模线性相关，在相关模型中演示该协议，为强关联巡游量子物质表征开辟途径。
AI 中文摘要
量子态层析成像可提供量子态的完整信息，但其测量成本通常随系统规模呈指数增长。在多粒子量子模拟器中，局部测量和控制的有限可达性使这一挑战更复杂。本文针对具有U(1)粒子数对称性的置换不变费米子多体态开发了一种层析成像协议。我们表明，任何此类状态都完全由总粒子数分布和每个粒子数扇区内单个集体模式的占据情况决定，这两者在当前超冷原子实验中均可获取。所需可观测量的数量仅与系统规模呈线性比例。更一般地，该协议可重构任意U(1)对称费米子态的置换对称分量，其仍可编码超越传统少体可观测量的非平凡多体和态级结构。我们在复Sachdev-Ye-Kitaev模型的相互作用非高斯态和跨越Lifshitz转变的自由费米子链中演示了该协议。此框架为在实验上可行的费米子量子模拟器中对强关联巡游量子物质进行信息理论表征开辟了一条途径。
英文摘要
Quantum state tomography provides complete information about a quantum state, but its measurement cost generally grows exponentially with system size. In many-particle quantum simulators, this challenge is further compounded by the limited accessibility of local measurements and controls. Here we develop a tomography protocol for permutation-invariant fermionic many-body states with U(1) particle-number symmetry. We show that any such state is completely determined by the distribution of the total particle number and the occupation of a single collective mode within each particle-number sector, both of which are accessible in current ultracold-atom experiments. The number of required observables scales only linearly with the system size. More generally, the protocol reconstructs the permutation-symmetrized component of arbitrary U(1)-symmetric fermionic states, which can still encode nontrivial many-body and state-level structure beyond conventional few-body observables. We demonstrate this protocol in interacting non-Gaussian states of the complex Sachdev-Ye-Kitaev model and in free-fermion chains across a Lifshitz transition. This framework opens a route toward information-theoretic characterization of strongly correlated itinerant quantum matter in experimentally realistic fermionic quantum simulators.
Comments7+4 pages, 2 figures
