Weighted Berry curvature and global geometry of mixed quantum states

Quantum Physics arXiv:2609.21355 (quant-ph) [Submitted on 18 Sep 2026] Title:Weighted Berry curvature and global geometry of mixed quantum states Authors:Dominik Kuczyński, Erik Sjöqvist View a PDF of the paper titled Weighted Berry curvature and global geometry of mixed quantum states, by Dominik Kuczy\'nski and 1 other authors View PDF HTML (experimental) Abstract:We examine the geometric interpretation of the quantum geometric tensor proposed in [Phys. Rev. B {\bf 110}, 035404 (2024)] for mixed quantum states, focusing on its imaginary part, which is proportional to a weighted sum of the Berry curvatures of the eigenstates of the density operator. While the real part naturally decomposes into Fisher--Rao and weighted Fubini--Study contributions, we show that the imaginary part does not, in general, coincide with the curvature of a connection on a globally defined U(1) line bundle whose holonomy yields a mixed-state geometric phase. Using a two-level system as an explicit example, we demonstrate that its surface integral depends on the choice of surface bounded by the same closed path, with ambiguities that are not integer multiples of $2\pi$. Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other) Cite as: arXiv:2609.21355 [quant-ph] (or arXiv:2609.21355v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.21355 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Erik Sjoqvist [view email] [v1] Fri, 18 Sep 2026 06:11:21 UTC (8 KB) Full-text links: Access Paper: View a PDF of the paper titled Weighted Berry curvature and global geometry of mixed quantum states, by Dominik Kuczy\'nski and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.other References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)