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Optimal pure state cloning and transposition are complementary channels

arXiv Quantum Archived Mar 26, 2026 ✓ Full text saved

arXiv:2603.23628v1 Announce Type: new 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

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Quantum Physics [Submitted on 24 Mar 2026] Optimal pure state cloning and transposition are complementary channels Vanessa Brzić, Dmitry Grinko, Michał Studziński, Marco Túlio Quintino 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: 5 pages, 1 figure 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 Submission history From: Vanessa Brzić [view email] [v1] Tue, 24 Mar 2026 18:11:29 UTC (121 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?)

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