Characterizing entanglement with geometric entanglement witnesses

TL;DR

This paper introduces a geometric approach to detect and classify bipartite quantum states, including entangled, bound entangled, and separable states, across arbitrary dimensions using entanglement witnesses based on Hilbert-Schmidt geometry.

Contribution

It presents a novel method for constructing geometric entanglement witnesses that can identify different types of quantum states in any dimension, simplifying the detection process.

Findings

Successfully classified states in the two-qutrit magic simplex

Demonstrated the effectiveness of geometric witnesses in detecting bound entanglement

Provided a unified framework for state characterization across dimensions

Abstract

We show how to detect entangled, bound entangled, and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert-Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the "magic simplex", i.e. the set of Bell-state mixtures of arbitrary dimension.