CPDNN quantum channels with qubit output are CPCP

Quantum Physics [Submitted on 17 Mar 2026] CPDNN quantum channels with qubit output are CPCP Hyunho Cha The resource theory for nonnegativity of quantum amplitudes distinguishes completely positive completely positive (CPCP) quantum channels from the larger and more tractable class of completely positive doubly nonnegative (CPDNN) quantum channels. It was left open whether there exists a qutrit-to-qubit quantum channel \(\Phi:M_3\to M_2\) that is CPDNN but not CPCP. We answer this question in the negative and prove the stronger statement that every CPDNN quantum channel \(\Phi:M_n\to M_2\) is CPCP for every \(n\in\mathbb N\). Equivalently, for qubit-output quantum channels the doubly nonnegative relaxation is exact. Comments: 4 pages Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.16962 [quant-ph]   (or arXiv:2603.16962v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.16962 Focus to learn more Submission history From: Hyunho Cha [view email] [v1] Tue, 17 Mar 2026 06:22:31 UTC (5 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 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?)