The Cramér-Rao approach and global quantum estimation of bosonic states
Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cramér Rao approach which considers local estimation gives the ultimate pr...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-07-22-1806/pdf/ |
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| author | Masahito Hayashi Yingkai Ouyang |
| author_facet | Masahito Hayashi Yingkai Ouyang |
| author_sort | Masahito Hayashi |
| collection | DOAJ |
| description | Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cramér Rao approach which considers local estimation gives the ultimate precision bound of quantum state estimation in terms of the quantum Fisher information. However practical scenarios need not offer much prior information about the parameters to be estimated, and the local estimation setting need not apply. In general, it is unclear whether the Cramér-Rao approach is applicable for global estimation instead of local estimation. In this paper, we find situations where the Cramér-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting, where we only use one copy of the bosonic quantum state in the large number of bosons setting. Our result highlights the importance of caution when using the results of the Cramér-Rao approach to extrapolate to the global estimation setting. |
| format | Article |
| id | doaj-art-4b32a42ff2fd4b5bb593e8291ffc7f00 |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-4b32a42ff2fd4b5bb593e8291ffc7f002025-08-20T03:08:13ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-07-019180610.22331/q-2025-07-22-180610.22331/q-2025-07-22-1806The Cramér-Rao approach and global quantum estimation of bosonic statesMasahito HayashiYingkai OuyangQuantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cramér Rao approach which considers local estimation gives the ultimate precision bound of quantum state estimation in terms of the quantum Fisher information. However practical scenarios need not offer much prior information about the parameters to be estimated, and the local estimation setting need not apply. In general, it is unclear whether the Cramér-Rao approach is applicable for global estimation instead of local estimation. In this paper, we find situations where the Cramér-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting, where we only use one copy of the bosonic quantum state in the large number of bosons setting. Our result highlights the importance of caution when using the results of the Cramér-Rao approach to extrapolate to the global estimation setting.https://quantum-journal.org/papers/q-2025-07-22-1806/pdf/ |
| spellingShingle | Masahito Hayashi Yingkai Ouyang The Cramér-Rao approach and global quantum estimation of bosonic states Quantum |
| title | The Cramér-Rao approach and global quantum estimation of bosonic states |
| title_full | The Cramér-Rao approach and global quantum estimation of bosonic states |
| title_fullStr | The Cramér-Rao approach and global quantum estimation of bosonic states |
| title_full_unstemmed | The Cramér-Rao approach and global quantum estimation of bosonic states |
| title_short | The Cramér-Rao approach and global quantum estimation of bosonic states |
| title_sort | cramer rao approach and global quantum estimation of bosonic states |
| url | https://quantum-journal.org/papers/q-2025-07-22-1806/pdf/ |
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