对称投影兼容多参数量子传感
Symmetry-Projected Weakly Compatible Multiparameter Quantum Sensing
AI总结：
该研究提出对称投影框架用于多参数量子传感，揭示奇偶性保护自旋系统的 QFIM 特性，发现耗散单轴扭转系统瞬态态的 QFIM 海森堡标度及稳态的奇偶性依赖，实现多参数量子克拉美罗界的渐近饱和。
AI中文摘要：
我们建立了一种通用的多参数量子传感对称投影框架。将编码生成元相对于对称扇区分解为子空间保持和子空间变化分量，可完全消除量子费舍尔信息矩阵（QFIM）和对称对数导数（SLD） commutator 矩阵的所有跨扇区元素。当投影后的子空间变化生成元在占据子空间内表现为标量时，无论探针态纯度如何，对应的 QFIM 块都会简化为四倍的对称协方差矩阵。对于奇偶性保护的集体 SU(2) 自旋系统，这使得横向 QFIM 可通过自旋涨落直接验证，最优轴与反压缩 quadrature 对齐。将该框架应用于耗散单轴扭转系统，研究发现，在较宽的时间窗口内，高度混合的瞬态态对横向-纵向参数对（θ_y,θ_z）可呈现近乎平衡的海森堡标度 QFIM 分量；稳态则保留各向同性的横向 QFIM，标度为 N²/3，而横向参数对（θ_x,θ_y）的弱兼容性呈现明显的奇偶性依赖——N 为奇数时失效，N 为偶数时恢复。由此产生的对称性保护消除了横向-纵向参数对的乌尔曼曲率，使渐近极限下多参数量子克拉美罗界可同时达到饱和。
英文摘要：
Achieving joint quantum-enhanced precision in multiparameter sensing requires both high sensitivity and measurement compatibility. These two aspects are characterized by the quantum Fisher information matrix (QFIM) and the Uhlmann curvature matrix (UCM), respectively, with weak compatibility corresponding to the vanishing of the relevant UCM elements. Here, we develop a symmetry-projection framework that classifies phase generators into subspace-preserving and subspace-changing sectors. For probe states confined to a symmetry subspace, symmetry projection imposes a common block-diagonal structure on the QFIM and UCM, rendering cross-sector parameters simultaneously free from information cross-talk and measurement incompatibility. When the subspace-changing generators act as scalars within the occupied subspace, the corresponding QFIM block reduces to four times the symmetrized covariance matrix, even for mixed probe states. For parity-protected collective $\mathrm{SU}(2)$ systems, this structure singles out the transverse anti-squeezed quadrature and the longitudinal mean-spin direction as natural optimal sensing axes. Applied to a dissipative one-axis twisting model, the dynamically generated probe state exhibits identically vanishing UCM elements for transverse--longitudinal parameter pairs, while maintaining nearly balanced, Heisenberg-scaled QFIM components over a broad transient window. Our work opens a route to symmetry-protected, weakly compatible multiparameter sensing in interacting quantum many-body systems.
