Sharp Plucker Geometry for Three-Copy Werner Distillation

Quantum Physics arXiv:2608.02647 (quant-ph) [Submitted on 31 Jul 2026] Title:Sharp Plucker Geometry for Three-Copy Werner Distillation Authors:Tianhao Wu, Qiran Zou View a PDF of the paper titled Sharp Plucker Geometry for Three-Copy Werner Distillation, by Tianhao Wu and Qiran Zou View PDF HTML (experimental) Abstract:Whether negative-partial-transpose entanglement can remain undistillable is a longstanding problem in quantum information theory. We analyze the first unresolved three-copy Werner endpoint using a sharp dimension-free inequality for complementary partial traces and an optimal exterior-square inequality for orthonormal tripartite vectors. The latter identifies local SWAP- parity statistics with metric data of a decomposable Plucker bivector. Together these inequalities prove endpoint nonnegativity for every positive semidefinite rank-two coefficient operator and for the complete normal rank-two sector in arbitrary finite local dimensions. For genuinely nonnormal operators, an exact crossed-Gram criterion proves nonnegativity when one local outpu-input support overlap is at most two, including every system with a qubit-sized factor, and when either support plane contains a product ray. Explicit anti-state and rank-boundary families establish optimality of the constants and the rank restriction. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.02647 [quant-ph] (or arXiv:2608.02647v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.02647 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tianhao Wu [view email] [v1] Fri, 31 Jul 2026 18:01:38 UTC (28 KB) Full-text links: Access Paper: View a PDF of the paper titled Sharp Plucker Geometry for Three-Copy Werner Distillation, by Tianhao Wu and Qiran ZouView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)