Optimal convex approximation of quantum channels based on $\alpha$-affinity

Quantum Physics [Submitted on 4 Jun 2026] Optimal convex approximation of quantum channels based on α-affinity Liqiang Zhang, Chengling Fu, Liuyong Cheng, Guohui Yang, Changshui Yu 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: 24 pages, 3 figures 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 Submission history From: Liqiang Zhang [view email] [v1] Thu, 4 Jun 2026 06:18:32 UTC (297 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 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?)