Symmetry-Projected Compatible Multiparameter Quantum Sensing

Abstract: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 $\mathrm{SU}(2)$ 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 $(\theta_y,\theta_z)$ over a broad time window. Furthermore, while the steady state retains an isotropic transverse QFIM scaling as $N^2/3$, weak compatibility for transverse parameter pairs $(\theta_x,\theta_y)$ 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.

6.2 pages, 1 figures

Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph); Optics (physics.optics)

arXiv:2608.01831 [quant-ph]

(or arXiv:2608.01831v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.01831 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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