Geometry of the faces for separable states arising from generalized Choi maps

TL;DR

This paper explores the geometric structure of separable and entangled states in quantum information, providing examples of boundary states and analyzing their convex cone properties to deepen understanding of PPT states.

Contribution

It introduces new examples of boundary separable states within the convex cone of PPT states and analyzes their geometric structures, revealing insights into entanglement and separability.

Findings

Identified boundary separable states within the PPT cone

Analyzed the geometric structure of minimal faces generated by these states

Discovered a large class of entangled states with positive partial transposes

Abstract

We exhibit examples of separable states which are on the boundary of the convex cone generated by all separable states but in the interior of the convex cone generated by all PPT states. We also analyze the geometric structures of the smallest face generated by those examples. As a byproduct, we obtain a large class of entangled states with positive partial transposes.