Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective
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Quantum Physics arXiv:2605.16463 (quant-ph) [Submitted on 15 May 2026] Title:Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective Authors:Gang Lyu, Wenlong Sun, Yuanfeng Jin, Hua Nan View a PDF of the paper titled Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective, by Gang Lyu and 2 other authors View PDF HTML (experimental) Abstract:Traditional entanglement distillation follows a post-processing paradigm, a noisy quantum state, after full transmission through a noisy channel, is treated as a static resource to be purified via LOCC (local operations and classical communication). This work demonstrates a fundamentally different paradigm,pre-channel entanglement shaping (PES) -- actively engineering the system-environment coupling before or during channel transmission -- achieves a level of purification capability that is physically unattainable by any post-distillation protocol. We prove this separation using the framework of geometric entropy (quantum relative entropy to separable states). In post-distillation, the protocol can only select low-entropy sub-ensembles from a fixed mixed state, leaving the global geometric entropy unchanged or increased. In contrast, PES \textit{suppresses the rate of geometric entropy production} during channel evolution, resulting in a final state whose relative entropy of entanglement strictly exceeds the maximum achievable by post-distillation from the same channel. We provide explicit qubit channel examples, numerical simulations (with complete code in Appendix), and a geometric interpretation on the state manifold. Our result establishes pre-channel entanglement shaping as a distinct operational resource class, with immediate implications for quantum repeaters and entanglement-assisted communication. Very recently, Li \textit{et al.} experimentally demonstrated that preprocessing the entangling channel with optimally tailored local unitaries achieves entanglement fidelities unreachable by any postprocessing, revealing an intrinsic temporal asymmetry in entanglement distillation~\cite{Li2025}. Subjects: Quantum Physics (quant-ph); Operator Algebras (math.OA) MSC classes: Primary: 81P45, 81P40, Secondary: 94A40, 81P15, 53Z05, 82C10 ACM classes: B.4.5; F.1.1; E.4; F.2.2 Cite as: arXiv:2605.16463 [quant-ph] (or arXiv:2605.16463v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16463 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Gang Lyu [view email] [v1] Fri, 15 May 2026 08:42:31 UTC (716 KB) Full-text links: Access Paper: View a PDF of the paper titled Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective, by Gang Lyu 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?)