Geometric entanglement witnesses and bound entanglement

TL;DR

This paper explores the use of geometric entanglement witnesses within the Hilbert-Schmidt space to detect and quantify bound entangled states, providing practical examples involving two-qutrit states in the magic simplex.

Contribution

It introduces a geometric approach to constructing entanglement witnesses for bound entanglement detection and quantification, with specific examples in the two-qutrit state space.

Findings

Demonstrates how geometric entanglement witnesses can identify bound entangled states.

Provides explicit examples within the magic simplex of two-qutrit states.

Shows the effectiveness of geometric methods in entanglement detection.

Abstract

We study entanglement witnesses that can be constructed with regard to the geometrical structure of the Hilbert-Schmidt space, i.e. we present how to use these witnesses in the context of quantifying entanglement and the detection of bound entangled states. We give examples for a particular three-parameter family of states that are part of the \emph{magic simplex} of two-qutrit states.