Extreme points of absolutely PPT states with exactly three distinct eigenvalues

Quantum Physics [Submitted on 21 Mar 2026] Extreme points of absolutely PPT states with exactly three distinct eigenvalues Nalan Wang, Lin Chen, Zhiwei Song 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: 48 pages,8 figures,7 tables 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 Submission history From: Nalan Wang [view email] [v1] Sat, 21 Mar 2026 08:52:03 UTC (780 KB) Access Paper: 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?)