Optimal pure state cloning and transposition are complementary channels
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Quantum Physics arXiv:2603.23628 (quant-ph) [Submitted on 24 Mar 2026] Title:Optimal pure state cloning and transposition are complementary channels Authors:Vanessa Brzić, Dmitry Grinko, Michał Studziński, Marco Túlio Quintino View a PDF of the paper titled Optimal pure state cloning and transposition are complementary channels, by Vanessa Brzi\'c and 3 other authors View PDF HTML (experimental) Abstract:State cloning and state transposition are fundamental transformations which, despite being desirable, cannot be perfectly implemented in quantum theory. In this work, we determine the optimal approximation for transforming $N$ qudits into $K$ copies of their transposition and prove the optimal fidelity for pure input states. We further show that the optimal qudit \(N\!\to\!K\) transposition map is the complementary channel of the optimal universal symmetric \(N\!\to\!N\!+\!K\) quantum cloning machine on pure states, implying that both tasks can be simultaneously realised by the same quantum operation and attain the same optimal fidelity. We then present an explicit quantum circuit that simultaneously implements optimal \(N\!\to\!K\) transposition and \(N\!\to\!N\!+\!K\) cloning and discuss its gate efficiency. Lastly, we investigate mixed-state \(N\!\to\!1\) qudit transposition and find the optimal performance in terms of white noise visibility, yielding the optimal structural physical approximation of state transposition in the multicopy regime. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.23628 [quant-ph] (or arXiv:2603.23628v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.23628 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Vanessa Brzić [view email] [v1] Tue, 24 Mar 2026 18:11:29 UTC (121 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal pure state cloning and transposition are complementary channels, by Vanessa Brzi\'c and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)