Optimal convex approximation of quantum channels based on $\alpha$-affinity
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Quantum Physics arXiv:2606.05745 (quant-ph) [Submitted on 4 Jun 2026] Title:Optimal convex approximation of quantum channels based on $α$-affinity Authors:Liqiang Zhang, Chengling Fu, Liuyong Cheng, Guohui Yang, Changshui Yu View a PDF of the paper titled Optimal convex approximation of quantum channels based on $\alpha$-affinity, by Liqiang Zhang and Chengling Fu and Liuyong Cheng and Guohui Yang and Changshui Yu View PDF HTML (experimental) Abstract:Determining the minimal distance between a target channel and a convex hull of predefined set of implementable channels is a fundamental problem in quantum resource theory, and provides key guidance for experimental implementations. In this work, we develop a unified analytical framework for optimal convex approximation of quantum channels based on the quantum $\alpha$-affinity measure. We construct a channel distance metric induced by the {\alpha}-affinity and the ChoiJamiolkowski isomorphism, which satisfies the required properties of a well-defined channel distance. Subsequently, we present an optimization framework for the convex approximation of quantum channels, and derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families, obtaining closed-form expressions for the optimal parameters and the minimal approximation distance. This framework is further applied to the amplitude-damping channel, yielding the explicit form of its optimal approximation and the associated minimal {\alpha}-affinity distance. In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05745 [quant-ph] (or arXiv:2606.05745v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.05745 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Liqiang Zhang [view email] [v1] Thu, 4 Jun 2026 06:18:32 UTC (297 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal convex approximation of quantum channels based on $\alpha$-affinity, by Liqiang Zhang and Chengling Fu and Liuyong Cheng and Guohui Yang and Changshui YuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)