Zero-Error List Decoding for Classical-Quantum Channels

Quantum Physics arXiv:2601.09786 (quant-ph) [Submitted on 14 Jan 2026] Title:Zero-Error List Decoding for Classical-Quantum Channels Authors:Marco Dalai, Filippo Girardi, Ludovico Lami View a PDF of the paper titled Zero-Error List Decoding for Classical-Quantum Channels, by Marco Dalai and 2 other authors View PDF HTML (experimental) Abstract:The aim of this work is to study the zero-error capacity of pure-state classical-quantum channels in the setting of list decoding. We provide an achievability bound for list-size two and a converse bound holding for every fixed list size. The two bounds coincide for channels whose pairwise absolute state overlaps form a positive semi-definite matrix. Finally, we discuss a remarkable peculiarity of the classical-quantum case: differently from the fully classical setting, the rate at which the sphere-packing bound diverges might not be achievable by zero-error list codes, even when we take the limit of fixed but arbitrarily large list size. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph) Cite as: arXiv:2601.09786 [quant-ph] (or arXiv:2601.09786v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.09786 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Filippo Girardi [view email] [v1] Wed, 14 Jan 2026 19:00:02 UTC (443 KB) Full-text links: Access Paper: View a PDF of the paper titled Zero-Error List Decoding for Classical-Quantum Channels, by Marco Dalai and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.IT math math-ph math.IT 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?)