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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.11664 |
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| _version_ | 1866912073518153728 |
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| author | Wang, Xin Hou, Xu-Yang Tang, Jia-Chen Guo, Hao |
| author_facet | Wang, Xin Hou, Xu-Yang Tang, Jia-Chen Guo, Hao |
| contents | In this paper, we systematically establish the mathematical foundation for the $\text{U}^N(1)$ quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the $\text{U}^N(1)$ principal bundle and derive a Pythagorean-like distance decomposition equation. Additionally, we offer a comprehensive comparison of its properties with those of the U(1) principal bundle description of the pure-state QGT. Finally, we prove a fundamental inequality for the $\text{U}^N(1)$ QGT and discuss its physical implication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematical Foundation of the U$^N(1)$ Quantum Geometric Tensor Wang, Xin Hou, Xu-Yang Tang, Jia-Chen Guo, Hao Mathematical Physics In this paper, we systematically establish the mathematical foundation for the $\text{U}^N(1)$ quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the $\text{U}^N(1)$ principal bundle and derive a Pythagorean-like distance decomposition equation. Additionally, we offer a comprehensive comparison of its properties with those of the U(1) principal bundle description of the pure-state QGT. Finally, we prove a fundamental inequality for the $\text{U}^N(1)$ QGT and discuss its physical implication. |
| title | Mathematical Foundation of the U$^N(1)$ Quantum Geometric Tensor |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.11664 |