Extreme points of absolutely PPT states with exactly three distinct eigenvalues
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Quantum Physics arXiv:2603.20717 (quant-ph) [Submitted on 21 Mar 2026] Title:Extreme points of absolutely PPT states with exactly three distinct eigenvalues Authors:Nalan Wang, Lin Chen, Zhiwei Song View a PDF of the paper titled Extreme points of absolutely PPT states with exactly three distinct eigenvalues, by Nalan Wang and 2 other authors View PDF Abstract:Whether the sets of absolutely separable (AS) and absolutely two-qutrit positive-partial-transpose (AP) states are the same has been an open problem in entanglement theory for decades. Since they are both convex sets, we investigate the boundary and extreme points of full-rank two-qutrit AP states with exactly three distinct eigenvalues. We show that every boundary point is an extreme point, with exactly one exception. We explicitly characterize the expressions of such points, each of which turns out to contain at most one parameter in some intervals. When the parameter approaches the ends of intervals, most points become the known extreme points of exactly two distinct eigenvalues. We present our results by tables and figures. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20717 [quant-ph] (or arXiv:2603.20717v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.20717 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nalan Wang [view email] [v1] Sat, 21 Mar 2026 08:52:03 UTC (780 KB) Full-text links: Access Paper: View a PDF of the paper titled Extreme points of absolutely PPT states with exactly three distinct eigenvalues, by Nalan Wang and 2 other authorsView PDFTeX 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?)