Unified formalism and adaptive algorithms for optimal quantum state, detector and process tomography
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arXiv
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| Autores principales: | , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908522705321984 |
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| author | Xiao, Shuixin Wang, Xiangyu Wang, Yuanlong Hou, Zhibo Zhang, Jun Petersen, Ian R. Yan, Wen-Zhe Yonezawa, Hidehiro Nori, Franco Xiang, Guo-Yong Dong, Daoyi |
| author_facet | Xiao, Shuixin Wang, Xiangyu Wang, Yuanlong Hou, Zhibo Zhang, Jun Petersen, Ian R. Yan, Wen-Zhe Yonezawa, Hidehiro Nori, Franco Xiang, Guo-Yong Dong, Daoyi |
| contents | Quantum tomography is a standard technique for characterizing, benchmarking and verifying quantum systems/devices and plays a vital role in advancing quantum technology and understanding the foundations of quantum mechanics. Achieving the highest possible tomography accuracy remains a central challenge. Here we unify the infidelity metrics for quantum state, detector and process tomography in a single index $1-F(\hat S,S)$, where $S$ represents the true density matrix, POVM element, or process matrix, and $\hat S$ is its estimator. We establish a sufficient and necessary condition for any tomography protocol to attain the optimal scaling $1-F= O(1/N) $ where $N$ is the number of state copies consumed, in contrast to the $O(1/\sqrt{N})$ worst-case scaling of static methods. Guided by this result, we propose adaptive algorithms with provably optimal infidelity scalings for state, detector, and process tomography. Numerical simulations and quantum optical experiments validate the proposed methods, with our experiments reaching, for the first time, the optimal infidelity scaling in ancilla-assisted process tomography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified formalism and adaptive algorithms for optimal quantum state, detector and process tomography Xiao, Shuixin Wang, Xiangyu Wang, Yuanlong Hou, Zhibo Zhang, Jun Petersen, Ian R. Yan, Wen-Zhe Yonezawa, Hidehiro Nori, Franco Xiang, Guo-Yong Dong, Daoyi Quantum Physics Quantum tomography is a standard technique for characterizing, benchmarking and verifying quantum systems/devices and plays a vital role in advancing quantum technology and understanding the foundations of quantum mechanics. Achieving the highest possible tomography accuracy remains a central challenge. Here we unify the infidelity metrics for quantum state, detector and process tomography in a single index $1-F(\hat S,S)$, where $S$ represents the true density matrix, POVM element, or process matrix, and $\hat S$ is its estimator. We establish a sufficient and necessary condition for any tomography protocol to attain the optimal scaling $1-F= O(1/N) $ where $N$ is the number of state copies consumed, in contrast to the $O(1/\sqrt{N})$ worst-case scaling of static methods. Guided by this result, we propose adaptive algorithms with provably optimal infidelity scalings for state, detector, and process tomography. Numerical simulations and quantum optical experiments validate the proposed methods, with our experiments reaching, for the first time, the optimal infidelity scaling in ancilla-assisted process tomography. |
| title | Unified formalism and adaptive algorithms for optimal quantum state, detector and process tomography |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.05988 |