Asymptotic entanglement in circle stabilizer states and states forbidding arbitrary vertex-minors

Quantum Physics arXiv:2608.21526 (quant-ph) [Submitted on 21 Aug 2026] Title:Asymptotic entanglement in circle stabilizer states and states forbidding arbitrary vertex-minors Authors:Kenneth Goodenough, Marcelo Sales View a PDF of the paper titled Asymptotic entanglement in circle stabilizer states and states forbidding arbitrary vertex-minors, by Kenneth Goodenough and 1 other authors View PDF HTML (experimental) Abstract:Stabilizer states play a central role in quantum information theory, and understanding their entanglement has motivated a large body of work. A well-studied question in particular is when a stabilizer state $|\psi\rangle$ can be transformed into another stabilizer state $|\phi\rangle$ using only single-qubit Clifford operations and Pauli measurements. If this is possible, we say that $|\phi\rangle$ is a vertex-minor of $|\psi\rangle$. Assuming Geelen's weak structural conjecture on vertex-minors, we establish the following general statement. For any fixed stabilizer state $|\phi\rangle$, the entanglement in stabilizer states $|\psi\rangle$ that do not contain $|\phi\rangle$ as a vertex-minor is asymptotically constrained. More concretely, we show that the distance of any sufficiently rank-connected $|\psi\rangle$ not containing $|\phi\rangle$ as a vertex-minor grows as $O(\log n)$, and prove similar results for the so-called locally accessible information, a quantity that captures the amount of information that can be learned through single-qubit Pauli measurements. Our results rely on (i) connecting the above two entanglement measures to rank functions of multimatroids, (ii) connecting the rank functions of circle stabilizer states to rank functions on $4$-regular multigraphs, which asymptotically constrains the entanglement of circle stabilizer states, and (iii) using Geelen's weak structural conjecture on vertex-minors to `lift' the previous result to sufficiently connected states in proper vertex-minor-closed families of stabilizer states. Our results establish a connection between asymptotic stabilizer entanglement and forbidden vertex-minors, with direct implications for the entanglement that can be generated in quantum devices. Comments: Subjects: Quantum Physics (quant-ph); Combinatorics (math.CO) Cite as: arXiv:2608.21526 [quant-ph] (or arXiv:2608.21526v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.21526 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kenneth Goodenough [view email] [v1] Fri, 21 Aug 2026 18:03:42 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Asymptotic entanglement in circle stabilizer states and states forbidding arbitrary vertex-minors, by Kenneth Goodenough and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: math math.CO 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?)