Machine-Learning Prediction of Quantum Fisher Information from Collective Spin and Spectral Features

Abstract: Quantum Fisher information (QFI) is a fundamental quantifier in quantum metrology, determining the ultimate precision achievable in parameter-estimation protocols through the quantum Cramér-Rao bound. However, direct evaluation of the QFI generally requires detailed knowledge of the density matrix, making it increasingly demanding as the Hilbert-space dimension grows. In this work, we investigate the extent to which the QFI of multipartite quantum systems can be predicted from a limited set of experimentally accessible quantities using support vector regression (SVR). By comparing different physically motivated features, we identify a dominant feature set governing QFI and show that the predictive power of collective spin moments alone decreases as system size and consequently Hilbert-space dimension grows. We demonstrate that QFI is governed primarily by the interplay between collective covariance and low-order spectral moments of the density matrix. Our results identify the physically relevant information sectors governing the QFI and demonstrate that accurate estimation of metrological sensitivity can be achieved from a restricted set of experimentally accessible quantities without requiring full quantum-state tomography.