Faces for two qubit separable states and the convex hulls of trigonometric moment curves

Abstract

We analyze the facial structures of the convex set consisting of all two qubit separable states. One of faces is a four dimensional convex body generated by the trigonometric moment curve arising from polyhedral combinatorics. Another one is an eight dimensional convex body, which is the convex hull of a homeomorphic image of the two dimensional sphere. Extreme points consist of points on the surface, and any two of them determines an edge. We also reconstruct the trigonometric moment curve in any even dimensional affine space using the qubit-qudit systems, and characterize the facial structures of the convex hull.

References in corpus (3)

• Qubit-qudit states with positive partial transpose
• Separable states with unique decompositions
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states

Cited by in corpus (6)

• Geometry for separable states and construction of entangled states with positive partial transposes
• Moment curves and cyclic symmetry for positive Grassmannians
• Boundary of the set of separable states
• Construction of exposed indecomposable positive linear maps between matrix algebras
• The number of product vectors and their partial conjugates in a pair of spaces
• Global geometric difference between separable and Positive partial transpose states