2013/08/05 by Kil-Chan Ha, Seung-Hyeok Kye
Computer Science · Mathematics · Physics and Astronomy · #Absolutely convex set #Algebraic structures and combinatorial models #Combinatorics #Computer science #Convex analysis #Convex body #Convex combination #Convex hull #Convex optimization #Convex polytope #Convex set #Extreme point #Geometry #Mathematical analysis #Mathematics #Proper convex function #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Regular polygon #Separable space #Set (abstract data type) #Subderivative #math.OA #msc:15A30 #msc:46L05 #msc:81P15 #quant-ph
paper · pdf · doi:10.1142/s1230161214500097
published in Open Systems & Information Dynamics 21(04), 1450009 (World Scientific) · 14 pages, 2 figures
arxiv created 2013/08/05 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the convex set of all 3 ⊗ 3 states with positive partial transposes, we show that one can take two extreme points whose convex combinations belong to the interior of the convex set. Their convex combinations may be even in the interior of the convex set of all separable states. In general, we need at least mn extreme points to get an interior point by their convex combination, for the case of the convex set of all m ⊗ n separable states. This shows a sharp distinction between PPT states and separable states. We also consider the same questions for positive maps and decomposable maps.