A Symplectic Proof of the Quantum Singleton Bound
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Quantum Physics arXiv:2602.20186 (quant-ph) [Submitted on 21 Feb 2026] Title:A Symplectic Proof of the Quantum Singleton Bound Authors:Frederick Dehmel, Shilun Li View a PDF of the paper titled A Symplectic Proof of the Quantum Singleton Bound, by Frederick Dehmel and Shilun Li View PDF HTML (experimental) Abstract:We present a symplectic linear-algebraic proof of the Quantum Singleton Bound for stabiliser quantum error-correcting codes together with a Lean4 formalisation of the linear-algebraic argument. The proof is formulated in the language of finite-dimensional symplectic vector spaces modelling Pauli operators and relies on distance-based erasure correctability and the cleaning lemma. Using a dimension-counting argument within the symplectic stabiliser framework, we derive the bound \( k + 2(d - 1) \le n \) for any [[n, k, d]] stabiliser code. This approach isolates the algebraic structure underlying the bound and avoids the heavier analytic machinery that appears in entropy-based proofs, while remaining well-suited to formal verification. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) MSC classes: 81P70, 94B05, 15A63 Cite as: arXiv:2602.20186 [quant-ph] (or arXiv:2602.20186v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.20186 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Frederick Dehmel [view email] [v1] Sat, 21 Feb 2026 06:05:05 UTC (6 KB) Full-text links: Access Paper: View a PDF of the paper titled A Symplectic Proof of the Quantum Singleton Bound, by Frederick Dehmel and Shilun LiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)