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arXiv · 2509.12579

Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime

Xinglei Yu·Xinzhi Zhao·Liangsheng Li·Xiao-Min Hu·Xiangmei Duan·Haidong Yuan·Chengjie Zhang
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Abstract

Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of $1/t$, where $t$ represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cramér-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.

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Xinglei Yu, Xinzhi Zhao, Liangsheng Li, Xiao-Min Hu, Xiangmei Duan, Haidong Yuan, Chengjie Zhang. 2025-09-16. Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime. https://doi.org/10.1126/sciadv.adk7616

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