Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916951075323904 |
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| author | Yu, Xinglei Zhao, Xinzhi Li, Liangsheng Hu, Xiao-Min Duan, Xiangmei Yuan, Haidong Zhang, Chengjie |
| author_facet | Yu, Xinglei Zhao, Xinzhi Li, Liangsheng Hu, Xiao-Min Duan, Xiangmei Yuan, Haidong Zhang, Chengjie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime Yu, Xinglei Zhao, Xinzhi Li, Liangsheng Hu, Xiao-Min Duan, Xiangmei Yuan, Haidong Zhang, Chengjie Quantum Physics 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. |
| title | Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.12579 |