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

• URL: http://arxiv.org/abs/2509.12579v1
• Date: Tue, 16 Sep 2025 02:13:37 GMT
• Title: Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
• Authors: Xinglei Yu, Xinzhi Zhao, Liangsheng Li, Xiao-Min Hu, Xiangmei Duan, Haidong Yuan, Chengjie Zhang,
• Abstract summary: We present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime.<n>We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians.<n>Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of $1/t$, where $t$ represents time.
• Score: 2.4952786567436056
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Cram\'{e}r-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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