Quantum-Enhanced Zero-Error Communication and Storage under Positional Uncertainty
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Quantum Physics arXiv:2605.28945 (quant-ph) [Submitted on 27 May 2026] Title:Quantum-Enhanced Zero-Error Communication and Storage under Positional Uncertainty Authors:Arnau Diebra, David González-Lociga, Mark Hillery, John Calsamiglia, Emili Bagan View a PDF of the paper titled Quantum-Enhanced Zero-Error Communication and Storage under Positional Uncertainty, by Arnau Diebra and 4 other authors View PDF HTML (experimental) Abstract:Permutation channels model communication and storage scenarios in which the positional identity of the physical carriers is partially or completely lost, so that the transmitted information is only accessible up to an unknown reordering. Here we show that quantum mechanics can dramatically enhance zero-error communication through such channels. For cyclic reorderings of $n$ $d$-level systems, and in the absence of positional metadata, the number of classical zero-error messages scales asymptotically as $d^n/n$, whereas quantum protocols can fully recover the identity-channel value $d^n$. Ancilla-assisted protocols further increase this number to $d^{2n}/n$, enabling dense coding under positional uncertainty. We also analyze dihedral permutation channels and derive general Pólya-like formulas for the number of distinguishable messages in a broad class of permutation groups. Finally, for the symmetric group $S_n$, corresponding to complete scrambling of the information carriers, the number of distinguishable messages scales as $n^{d-1}$ classically, compared with $n^{d(d+1)/2-1}$ for quantum protocols and $n^{d^2-1}$ in the ancilla-assisted setting. Our results establish a fundamental quantum advantage for communication and storage under positional uncertainty. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.28945 [quant-ph] (or arXiv:2605.28945v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.28945 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Arnau Diebra Huertas [view email] [v1] Wed, 27 May 2026 18:00:05 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum-Enhanced Zero-Error Communication and Storage under Positional Uncertainty, by Arnau Diebra and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)