Enhancing Quantum Metrology with High-order Fisher Information and Experiments

arXiv:2606.27633v2 Announce Type: replace Abstract: Fisher information plays a central role in statistics and quantum metrology, providing the basis for the celebrated Cram\'{e}r-Rao bound. In this work, we introduce a new information measure based on higher-order Fisher information and show that it naturally leads to a generalized uncertainty relation for parameter estimation, which can be regarded as an extension of the Cram\'er-Rao bound. As an application, we analyze the case of quantum phase estimation with a single qubit and compare our theoretical bounds with the well-known established hierarchical bounds. Finally, we experimentally validate the proposed framework using a photonic platform.