The injective norm of CSS quantum error-correcting codes

Quantum Physics arXiv:2510.23736 (quant-ph) [Submitted on 27 Oct 2025] Title:The injective norm of CSS quantum error-correcting codes Authors:Stephane Dartois, Gilles Zémor View a PDF of the paper titled The injective norm of CSS quantum error-correcting codes, by Stephane Dartois and Gilles Z\'emor View PDF HTML (experimental) Abstract:In this paper, we compute the injective norm - a.k.a. geometric entanglement - of standard basis states of CSS quantum error-correcting codes. The injective norm of a quantum state is a measure of genuine multipartite entanglement. Computing this measure is generically NP-hard. However, it has been computed exactly in condensed-matter theory - notably in the context of topological phases - for the Kitaev code and its extensions, in works by Orús and collaborators. We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states. In doing so, we uncover an interesting connection to matroid theory and Edmonds' intersection theorem. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Combinatorics (math.CO) MSC classes: 81P42, 81P45, 81P73, 05B35 Cite as: arXiv:2510.23736 [quant-ph] (or arXiv:2510.23736v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.23736 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Stephane Dartois [view email] [v1] Mon, 27 Oct 2025 18:06:02 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled The injective norm of CSS quantum error-correcting codes, by Stephane Dartois and Gilles Z\'emorView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)