Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging
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Quantum Physics arXiv:2605.16935 (quant-ph) [Submitted on 16 May 2026] Title:Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging Authors:Wenlong Sun, Gang Lu, Yuanfeng Jin View a PDF of the paper titled Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging, by Wenlong Sun and 2 other authors View PDF HTML (experimental) Abstract:Complete quantum charging provides a sharp setting in which to ask how much multipartite entanglement is forced by speed itself. For a closed \(N\)-qubit battery evolving from \(\ket{\downarrow}^{\otimes N}\) to \(\ket{\uparrow}^{\otimes N}\) under a time-independent Hamiltonian, we exactly solve the pure-state depth-constrained speed problem. If the realized trajectory has entanglement depth at most \(k\), then the largest possible QSL-normalized rate \(\eta=\tau_{\rm QSL}/T\) is \(\eta_{\max}(k)=\lceil N/k\rceil^{-1/2}\). Conversely, an observed rate \(\eta\) certifies trajectory entanglement depth at least \(\bigl\lceil N/\lfloor \eta^{-2}\rfloor\bigr\rceil\). The mechanism is block orthogonalization: under a fixed product partition, complete charging forces all blocks to orthogonalize simultaneously, and the quantum speed limit converts this counting constraint into the speed bound. Balanced cluster-flip evolutions saturate the bound, establishing an exact integer staircase frontier. Thus fast complete charging cannot be explained by many small independently charging blocks; in particular, crossing the threshold \(\eta>1/\sqrt2\) certifies, for \(N>1\), the generation of genuine \(N\)-partite entanglement. Subjects: Quantum Physics (quant-ph); Operator Algebras (math.OA) MSC classes: 81P45, 81Q05, 81P40, 82B10 Cite as: arXiv:2605.16935 [quant-ph] (or arXiv:2605.16935v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16935 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gang Lyu [view email] [v1] Sat, 16 May 2026 11:08:17 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging, by Wenlong Sun and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math.OA 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?)