Quantifying Uhlmann curvature from Yang-Mills action and its implications in quantum multiparameter estimation

Quantum Physics [Submitted on 17 Apr 2026] Quantifying Uhlmann curvature from Yang-Mills action and its implications in quantum multiparameter estimation Yi-Lin Ge, Bing-Shu Hu, Ling-Yun Deng, Xiao-Ming Lu The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum states is still an open problem. Inspired by the Yang-Mills action in non-Abelian gauge theory, we propose a scalar quantifying the Uhlmann curvature and establish its connection to the measurement incompatibility in quantum multiparameter estimation problems. We show that this curvature measure is gauge invariant, reparametrization invariant, and vanishes if and only if the Uhlmann curvature vanishes. We also explicitly calculate the Uhlmann curvature for the joint estimation of phase and phase diffusion as an example. Comments: 5 pages, 1 figure Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15752 [quant-ph]   (or arXiv:2604.15752v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15752 Focus to learn more Submission history From: Yi-Lin Ge [view email] [v1] Fri, 17 Apr 2026 06:54:17 UTC (16 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)