Encoding matroids into quantum states

Quantum Physics arXiv:2607.02736 (quant-ph) [Submitted on 2 Jul 2026] Title:Encoding matroids into quantum states Authors:Nathan Ferreira, Alison A. Silva, Giuliano G. La Guardia, Fabiano M. Andrade View a PDF of the paper titled Encoding matroids into quantum states, by Nathan Ferreira and Alison A. Silva and Giuliano G. La Guardia and Fabiano M. Andrade View PDF HTML (experimental) Abstract:Efficient representations of multipartite quantum states play a fundamental role in quantum information theory, providing both conceptual insight and practical tools for characterizing entanglement. Motivated by the axiomatic framework for graph states [Phys. Rev. A 85, 062313 (2012)] and its subsequent extension to hypergraph states [Phys. Rev. A 87, 022311 (2013)], we introduce an axiomatic construction of \emph{matroid states}, a new family of multipartite quantum states associated with matroids. Our constructions are based on a set of axioms analogous to those that define graph and hypergraph states, yielding a consistent quantum representation of arbitrary matroids. Two ways of constructing matroid states are proposed: the first is defined in terms of circuits, and the second in terms of independent sets. In both approaches, we establish the existence of universal global operators that satisfy desirable properties such as locality, symmetry, commutativity, and are associated with the combinatorial structure of matroids. Furthermore, we establish a hierarchy connecting graph, matroid, and hypergraph states within a unified framework. Additionally, we show how to obtain an arbitrary graph state by applying suitable families of matroid states, whose corresponding operators are the generators of the stabilizer subgroup of the graph state. These results identify matroid theory as a natural combinatorial language for the efficient description of multipartite quantum states and open new perspectives for the investigation of quantum entanglement and related combinatorial structures. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Combinatorics (math.CO) Cite as: arXiv:2607.02736 [quant-ph] (or arXiv:2607.02736v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.02736 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Fabiano Andrade [view email] [v1] Thu, 2 Jul 2026 20:12:42 UTC (43 KB) Full-text links: Access Paper: View a PDF of the paper titled Encoding matroids into quantum states, by Nathan Ferreira and Alison A. Silva and Giuliano G. La Guardia and Fabiano M. AndradeView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: math math-ph math.CO math.MP 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?)