Quantum Anticodes

Quantum Physics arXiv:2512.13891 (quant-ph) [Submitted on 15 Dec 2025] Title:Quantum Anticodes Authors:ChunJun Cao, Giuseppe Cotardo, Brad Lackey View a PDF of the paper titled Quantum Anticodes, by ChunJun Cao and 2 other authors View PDF HTML (experimental) Abstract:This work introduces a symplectic framework for quantum error correcting codes in which local structure is analyzed through an anticode perspective. In this setting, a code is treated as a symplectic space, and anticodes arise as maximal symplectic subspaces whose elements vanish on a prescribed set of components, providing a natural quantum analogue of their classical counterparts. This framework encompasses several families of quantum codes, including stabilizer and subsystem codes, provides a natural extension of generalized distances in quantum codes, and yields new invariants that capture local algebraic and combinatorial features. The notion of anticodes also naturally leads to operations such as puncturing and shortening for symplectic codes, which in turn provide algebraic interpretations of key phenomena in quantum error correction, such as the cleaning lemma and complementary recovery and yield new descriptions of weight enumerators. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) MSC classes: 81P73, 94B99 Cite as: arXiv:2512.13891 [quant-ph] (or arXiv:2512.13891v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.13891 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Giuseppe Cotardo [view email] [v1] Mon, 15 Dec 2025 20:49:03 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Anticodes, by ChunJun Cao and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.IT math math.IT 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?)