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arXiv · 2410.11664

Mathematical Foundation of the U$^N(1)$ Quantum Geometric Tensor

Xin Wang·Xu-Yang Hou·Jia-Chen Tang·Hao Guo
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Abstract

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.

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Xin Wang, Xu-Yang Hou, Jia-Chen Tang, Hao Guo. 2024-10-15. Mathematical Foundation of the U$^N(1)$ Quantum Geometric Tensor. https://arxiv.org/abs/2410.11664

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