2026/08/03 by G. R. Jin, Z. Y. Zhou, W. Yang
Physics and Astronomy · #quant-ph #physics.atom-ph #physics.optics
6.2 pages, 1 figures
arxiv created 2026/08/03 · arxiv updated 2026/08/04
We establish a general symmetry-projection framework for multiparameter quantum sensing. Decomposing encoding generators into subspace-preserving and subspace-changing components relative to a symmetry sector identically eliminates all cross-sector elements of the quantum Fisher information matrix (QFIM) and the mean symmetric logarithmic derivative (SLD) commutator matrix. When projected subspace-changing generators act as a scalar within the occupied subspace, the corresponding QFIM block reduces to four times the symmetrized covariance matrix, regardless of probe state purity. For parity-protected collective SU(2) spin systems, this renders the transverse QFIM directly certifiable via spin fluctuations, with the optimal axis aligned with the anti-squeezed quadrature. Applied to a dissipative one-axis-twisting system, our framework reveals that highly mixed transient states can exhibit nearly balanced, Heisenberg-scaled QFIM components for transverse--longitudinal parameter pairs (θy,θz) over a broad time window. Furthermore, while the steady state retains an isotropic transverse QFIM scaling as N2/3, weak compatibility for transverse parameter pairs (θx,θy) exhibits a sharp parity dependence---failing for odd N but restored for even N. The resulting symmetry protection eliminates the Uhlmann curvature for transverse--longitudinal pairs, enabling simultaneous saturation of the multi-parameter quantum Cramér-Rao bound in the asymptotic limit.