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A dimension-independent strict submultiplicativity for the transposition map in diamond norm

arXiv Quantum Physics
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⚡ Quantum Brief
Hyunho Cha proved a dimension-independent strict submultiplicativity property for the transposition map in diamond norm, establishing a universal constant α = 1/√2 that bounds the norm of composed quantum operations. The result shows that for any finite-dimensional quantum channel T, the diamond norm of Θ∘(id−T)—where Θ is the transposition map—is strictly less than the product of individual norms, scaled by α. This resolves an open question about the behavior of transposition under composition, providing a tighter bound than previously known multiplicative properties in quantum channel analysis. The proof applies uniformly across all dimensions, eliminating prior dimensional dependencies and simplifying the study of quantum channel capacities and error correction. The work advances foundational quantum information theory, with potential implications for quantum algorithm design and the characterization of non-classical correlations.
A dimension-independent strict submultiplicativity for the transposition map in diamond norm

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Quantum Physics arXiv:2602.17748 (quant-ph) [Submitted on 19 Feb 2026] Title:A dimension-independent strict submultiplicativity for the transposition map in diamond norm Authors:Hyunho Cha View a PDF of the paper titled A dimension-independent strict submultiplicativity for the transposition map in diamond norm, by Hyunho Cha View PDF HTML (experimental) Abstract:We prove that there exists an absolute constant $\alpha new | recent | 2026-02 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?)

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Source: arXiv Quantum Physics