Holevo Cramér-Rao bound for multi-parameter estimation in nonlinear interferometers
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913843506053120 |
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| author | Zhou, Mengyao Ma, Hongmei Chen, Liqing Zhang, Weiping Yuan, Chun-Hua |
| author_facet | Zhou, Mengyao Ma, Hongmei Chen, Liqing Zhang, Weiping Yuan, Chun-Hua |
| contents | Due to the potential of quantum advantage to surpass the standard quantum limit (SQL), the nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement. However, many practical applications require multi-parameter estimation. In this work, we discuss the precision limit of multi-parameter estimation of pure Gaussian states based on nonlinear interferometers, and derive the Holevo Cramér-Rao Bound (HCRB) for the case where both modes undergo displacement estimation. Furthermore, we compare our analytical results with the quantum Cramér-Rao Bound based on the symmetric logarithmic derivative (SLD-CRB), and with the result of the dual homodyne measurement. Through numerical analysis, we find that the HCRB equals the result of the dual homodyne measurement, whereas SLD-CRB is not saturable at small squeezed parameters. Therefore, this indicates that the HCRB is tight. Additionally, we provide intuitive analysis and visual representation of our numerical results in phase space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holevo Cramér-Rao bound for multi-parameter estimation in nonlinear interferometers Zhou, Mengyao Ma, Hongmei Chen, Liqing Zhang, Weiping Yuan, Chun-Hua Quantum Physics Due to the potential of quantum advantage to surpass the standard quantum limit (SQL), the nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement. However, many practical applications require multi-parameter estimation. In this work, we discuss the precision limit of multi-parameter estimation of pure Gaussian states based on nonlinear interferometers, and derive the Holevo Cramér-Rao Bound (HCRB) for the case where both modes undergo displacement estimation. Furthermore, we compare our analytical results with the quantum Cramér-Rao Bound based on the symmetric logarithmic derivative (SLD-CRB), and with the result of the dual homodyne measurement. Through numerical analysis, we find that the HCRB equals the result of the dual homodyne measurement, whereas SLD-CRB is not saturable at small squeezed parameters. Therefore, this indicates that the HCRB is tight. Additionally, we provide intuitive analysis and visual representation of our numerical results in phase space. |
| title | Holevo Cramér-Rao bound for multi-parameter estimation in nonlinear interferometers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.02855 |