Optimality Condition for the Petz Map
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912382761041920 |
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| author | Li, Bikun Wang, Zhaoyou Zheng, Guo Wong, Yat Jiang, Liang |
| author_facet | Li, Bikun Wang, Zhaoyou Zheng, Guo Wong, Yat Jiang, Liang |
| contents | In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied. Notably, while perfect recovery is generally infeasible for most quantum channels of finite dimension, the Petz map remains a versatile tool with near-optimal performance in recovering quantum states. This work introduces and proves, for the first time, the necessary and sufficient conditions for the optimality of the Petz map in terms of entanglement fidelity. In some special cases, the violation of this condition can be easily characterized by a simple commutator that can be efficiently computed. We provide multiple examples that substantiate our new findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23622 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimality Condition for the Petz Map Li, Bikun Wang, Zhaoyou Zheng, Guo Wong, Yat Jiang, Liang Quantum Physics In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied. Notably, while perfect recovery is generally infeasible for most quantum channels of finite dimension, the Petz map remains a versatile tool with near-optimal performance in recovering quantum states. This work introduces and proves, for the first time, the necessary and sufficient conditions for the optimality of the Petz map in terms of entanglement fidelity. In some special cases, the violation of this condition can be easily characterized by a simple commutator that can be efficiently computed. We provide multiple examples that substantiate our new findings. |
| title | Optimality Condition for the Petz Map |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.23622 |