Fisher information of complete quantum measurements
Phys. Rev. A 114, 022465 – Published 26 August, 2026
DOI: https://doi.org/10.1103/9xzl-1xkp
Abstract
Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. In this work, we establish a link between these two aspects within the context of a single informationally complete measurement by employing a suitably adapted operator frame theory. In particular, we derive bounds on the ratio between classical and quantum Fisher information in terms of the spectral properties of the associated frame operator, and relate these bounds to the optimal and least informative directions for parameter encoding. We also demonstrate the connection between our results and Fisher-symmetric informationally complete measurements.
