A conjecture on a tight norm inequality in the finite-dimensional l_p
Summarize this article with:
Quantum Physics arXiv:2603.24017 (quant-ph) [Submitted on 25 Mar 2026] Title:A conjecture on a tight norm inequality in the finite-dimensional l_p Authors:A. S. Holevo, A. V. Utkin View a PDF of the paper titled A conjecture on a tight norm inequality in the finite-dimensional l_p, by A. S. Holevo and 1 other authors View PDF Abstract:We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We conclude with a brief survey of solutions for kin problems which anyhow concern minimization of the output entropy of certain quantum channel and rely upon the symmetry properties of the problem. Key words and phrases: $l_p $-norm, Rényi entropy, tight inequality, maximization of a convex function. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Functional Analysis (math.FA) Cite as: arXiv:2603.24017 [quant-ph] (or arXiv:2603.24017v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.24017 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Holevo [view email] [v1] Wed, 25 Mar 2026 07:24:55 UTC (33 KB) Full-text links: Access Paper: View a PDF of the paper titled A conjecture on a tight norm inequality in the finite-dimensional l_p, by A. S. Holevo and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: math math-ph math.FA 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?)