A conjecture on a tight norm inequality in the finite-dimensional l_p

Quantum Physics [Submitted on 25 Mar 2026] A conjecture on a tight norm inequality in the finite-dimensional l_p A. S. Holevo, A. V. Utkin 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: 16 pages, one figure 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 Submission history From: Alexander Holevo [view email] [v1] Wed, 25 Mar 2026 07:24:55 UTC (33 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: math math-ph math.FA math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)