Measurement Geometry for Quantum Random Access Codes: Beyond Nayak Bound and Toward Optimality
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Quantum Physics arXiv:2606.12700 (quant-ph) [Submitted on 10 Jun 2026] Title:Measurement Geometry for Quantum Random Access Codes: Beyond Nayak Bound and Toward Optimality Authors:Seiseki Akibue, Rudy Raymond, Suguru Tamaki, Kosei Teramoto View a PDF of the paper titled Measurement Geometry for Quantum Random Access Codes: Beyond Nayak Bound and Toward Optimality, by Seiseki Akibue and 3 other authors View PDF HTML (experimental) Abstract:Quantum random access codes (QRACs) ask how well N classical bits can be encoded into M qubits while allowing any single bit to be recovered. Although the Nayak bound remains the standard general upper bound on the decoding probability, numerical evidence suggests a stronger upper bound in the small-qubit regime. In this work, we formulate the optimal decoding probability in terms of decoding measurements, reformulating QRAC design as a spectral problem for noncommuting measurements. Using this formulation, we give an elementary proof of the Nayak bound by simplifying the Chernoff-bound argument. Moreover, we refine the argument to obtain upper bounds that improve over Nayak's bound in the entire finite-size regime. The equality conditions of our bounds justify defining mutually unbiased projector-valued measurements (MUPVMs), a generalization of mutually unbiased bases. We show that decoding measurement of any two-qubit QRAC attaining the conjectured bound must form MUPVMs. We also show that any MUPVM, assisted by one ancillary qubit, yields a QRAC with optimal N-scaling decoding probability. Finally, we propose a new MUPVM-based construction for the (M+2,M)-QRAC family attaining the conjectured bound. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2606.12700 [quant-ph] (or arXiv:2606.12700v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12700 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Seiseki Akibue [view email] [v1] Wed, 10 Jun 2026 21:41:58 UTC (1,079 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement Geometry for Quantum Random Access Codes: Beyond Nayak Bound and Toward Optimality, by Seiseki Akibue and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: math math-ph 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?) 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?)