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arXiv · 2606.27633

Enhancing Quantum Metrology with High-order Fisher Information and Experiments

Xin-Zhu Liu·Jun-Li Jiang·Yan-Han Yang·Li-Ming Zhao·Xue Yang·Shao-Ming Fei·Ming-Xing Luo
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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.

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Xin-Zhu Liu, Jun-Li Jiang, Yan-Han Yang, Li-Ming Zhao, Xue Yang, Shao-Ming Fei, Ming-Xing Luo. 2026-06-26. Enhancing Quantum Metrology with High-order Fisher Information and Experiments. https://arxiv.org/abs/2606.27633

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