Xin Wang, Xu-Yang Hou, Jia-Chen Tang, & Hao Guo (2024). Mathematical Foundation of the UN(1) Quantum Geometric Tensor. arXiv:2410.11664v1 [math-ph].
This paper aims to establish a rigorous mathematical foundation for the UN(1) quantum geometric tensor (QGT) applied to mixed quantum states, extending its applicability beyond the realm of pure states.
The authors utilize the framework of UN(1) principal bundles to systematically derive the UN(1) QGT for mixed states. They draw parallels with the established U(1) principal bundle description of the pure-state QGT, highlighting the generalization achieved in their work.
The UN(1) QGT offers a robust framework for characterizing the geometric and topological properties of mixed quantum states. Its invariance under local UN(1) gauge transformations makes it a suitable tool for analyzing the real distances between these states. The fundamental inequality derived for the UN(1) QGT further strengthens its theoretical foundation and suggests potential applications in diverse areas of quantum physics.
This research significantly contributes to the field of quantum information geometry by extending the concept of the QGT to mixed states, which are ubiquitous in realistic physical systems. This opens up new avenues for investigating the geometry of quantum state spaces and its implications for quantum information processing and quantum technologies.
While the paper lays a strong mathematical foundation, further exploration of the UN(1) QGT's applications in specific physical systems and its connection to other quantum geometric concepts is encouraged. Investigating the experimental measurability of the UN(1) QGT and its potential advantages over other distance measures for mixed states would be valuable future research directions.
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by Xin Wang, Xu... om arxiv.org 10-16-2024
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