Quantum states supported by matroids

Quantum Physics arXiv:2607.15548 (quant-ph) [Submitted on 17 Jul 2026] Title:Quantum states supported by matroids Authors:Xiaowei Huang, Fei Shi, Lijun Zhang, Lvzhou Li View a PDF of the paper titled Quantum states supported by matroids, by Xiaowei Huang and 2 other authors View PDF HTML (experimental) Abstract:In this work, we establish a structural correspondence between quantum states and matroid theory. This connection demonstrates that key properties of quantum states, including entanglement and measurement, can be characterized in purely combinatorial terms via matroids, despite the apparent conceptual distance between these two fields. Using this framework, we show that a matroid-supported state is genuinely entangled when its underlying matroid is connected. Moreover, a uniform superposition over all bases of a matroid is genuinely entangled if and only if the matroid is connected. We also demonstrate that a local measurement in the $Z$-basis on such a state yields another matroid-supported state, whose underlying matroid is a minor of the original one. Inspired by matroid duality, we further propose a notion of quantum state duality, uncovering a deep structural symmetry in state transformations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.15548 [quant-ph] (or arXiv:2607.15548v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.15548 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Phys. Rev. A 113, 062452,2026 Related DOI: https://doi.org/10.1103/mx1w-k8fg Focus to learn more DOI(s) linking to related resources Submission history From: Lvzhou Li [view email] [v1] Fri, 17 Jul 2026 01:39:20 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum states supported by matroids, by Xiaowei Huang and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)