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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2505.16715 |
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| _version_ | 1866913853137223680 |
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| author | Chen, Kean Wang, Qisheng Yu, Zhan Zhang, Zhicheng |
| author_facet | Chen, Kean Wang, Qisheng Yu, Zhan Zhang, Zhicheng |
| contents | We consider a fundamental task in quantum information theory, estimating the values of $\operatorname{tr}(Oρ)$, $\operatorname{tr}(Oρ^2)$, ..., $\operatorname{tr}(Oρ^k)$ for an observable $O$ and a quantum state $ρ$. We show that $\widetildeΘ(k)$ samples of $ρ$ are sufficient and necessary to simultaneously estimate all the $k$ values. This means that estimating all the $k$ values is almost as easy as estimating only one of them, $\operatorname{tr}(Oρ^k)$. As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling for quantum many-body systems. Moreover, we extend our approach to estimating general functionals by polynomial approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous Estimation of Nonlinear Functionals of a Quantum State Chen, Kean Wang, Qisheng Yu, Zhan Zhang, Zhicheng Quantum Physics We consider a fundamental task in quantum information theory, estimating the values of $\operatorname{tr}(Oρ)$, $\operatorname{tr}(Oρ^2)$, ..., $\operatorname{tr}(Oρ^k)$ for an observable $O$ and a quantum state $ρ$. We show that $\widetildeΘ(k)$ samples of $ρ$ are sufficient and necessary to simultaneously estimate all the $k$ values. This means that estimating all the $k$ values is almost as easy as estimating only one of them, $\operatorname{tr}(Oρ^k)$. As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling for quantum many-body systems. Moreover, we extend our approach to estimating general functionals by polynomial approximation. |
| title | Simultaneous Estimation of Nonlinear Functionals of a Quantum State |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.16715 |