Random Access Codes: Explicit Constructions, Optimality, and Classical-Quantum Gaps
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Quantum Physics arXiv:2604.21274 (quant-ph) [Submitted on 23 Apr 2026] Title:Random Access Codes: Explicit Constructions, Optimality, and Classical-Quantum Gaps Authors:Ruho Kondo, Yuki Sato, Hiroshi Yano, Yota Maeda, Kosuke Ito, Naoki Yamamoto View a PDF of the paper titled Random Access Codes: Explicit Constructions, Optimality, and Classical-Quantum Gaps, by Ruho Kondo and 5 other authors View PDF HTML (experimental) Abstract:A random access code (RAC) encodes an $L$-bit string into a $k$-bit $(L>k)$ message from which any designated source bit can be recovered with high probability. Its quantum counterpart, a quantum random access code (QRAC), replaces the $k$-bit message with $k$ qubits. While upper bounds on the decoding success probability have long been studied in both classical and quantum settings, explicit constructions of optimal codes are known only in special cases, even for classical RACs. In this paper, we develop a constructive framework for classical $(L,k)$-RACs under both average- and worst-case criteria. We show that optimal code design reduces to selecting $2^k$ points in $\{0,1\}^L$ and $[0,1]^L$ for the average- and worst-case criteria, respectively, so as to minimize a distance-like objective. This characterization yields explicit constructions for general $(L,k)$. For $k=L-1$, we further obtain closed-form optimal encoders and decoders for both criteria, and show that the resulting classical $(L,L-1)$-RACs attain the corresponding proved upper bounds. We also show that these optimal classical codes induce $(L,L-1)$-QRACs that attain a conjectured upper bound on the decoding success probability. Numerical optimization suggests little difference between RACs and QRACs in the average-case setting, but a potentially large classical-quantum gap in the worst-case nonasymptotic regime. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2604.21274 [quant-ph] (or arXiv:2604.21274v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.21274 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ruho Kondo [view email] [v1] Thu, 23 Apr 2026 04:36:05 UTC (118 KB) Full-text links: Access Paper: View a PDF of the paper titled Random Access Codes: Explicit Constructions, Optimality, and Classical-Quantum Gaps, by Ruho Kondo and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)