Entanglement witnesses and geometry of entanglement of two--qutrit states

TL;DR

This paper explores the geometric structure of two-qutrit entanglement, constructing witnesses, calculating measures, and identifying bound entangled states to improve understanding and detection methods.

Contribution

It introduces a geometric approach to entanglement witnesses, calculates the Hilbert--Schmidt measure for specific states, and presents a new method to detect and distinguish bound entanglement.

Findings

Calculated Hilbert--Schmidt measure for two-qutrit states.

Discovered new regions of bound entangled states.

Provided a method to distinguish entangled from separable states.

Abstract

We construct entanglement witnesses with regard to the geometric structure of the Hilbert--Schmidt space and investigate the geometry of entanglement. In particular, for a two--parameter family of two--qutrit states that are part of the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three--parameter family of states. In this way we discover new regions of bound entangled states. Furthermore we outline how to use our method to distinguish entangled from separable states.