Multiparameter function estimation for general Hamiltonians
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918485286715392 |
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| author | Abbasgholinejad, Erfan Muleady, Sean R. Bringewatt, Jacob Conlon, Lorcan O. Gorshkov, Alexey V. |
| author_facet | Abbasgholinejad, Erfan Muleady, Sean R. Bringewatt, Jacob Conlon, Lorcan O. Gorshkov, Alexey V. |
| contents | Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04136 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiparameter function estimation for general Hamiltonians Abbasgholinejad, Erfan Muleady, Sean R. Bringewatt, Jacob Conlon, Lorcan O. Gorshkov, Alexey V. Quantum Physics Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems. |
| title | Multiparameter function estimation for general Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.04136 |