The geometry of bipartite qutrits including bound entanglement

TL;DR

This paper explores the geometric structure of bipartite qutrit states, introducing a symmetric simplex and identifying bound entangled regions using entanglement witnesses.

Contribution

It constructs a geometric analog to the qubit tetrahedron for qutrits and identifies bound entangled states within this structure.

Findings

Identification of bound entangled regions within the simplex

Construction of a geometric framework for bipartite qutrits

Use of entanglement witnesses to detect bound entanglement

Abstract

We investigate the state space of bipartite qutrits. We construct an analog to the "magic" tetrahedron for bipartite qubits--a magic simplex W. It is formed by all convex combination of nine Bell states which are constructed using the Weyl operators. Due to the high symmetry it is enough to consider certain typical slices through W. Via optimal entanglement witnesses we find regions of bound entangled states inside W.