Optimal witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry

TL;DR

This paper introduces a method to derive optimal entanglement witnesses for three-qubit states by leveraging the properties of GHZ-symmetric states, simplifying the detection of entanglement.

Contribution

It presents a novel approach utilizing GHZ symmetry to analytically construct optimal entanglement witnesses for three-qubit states.

Findings

Derived explicit forms of optimal entanglement witnesses for GHZ-symmetric states

Simplified the process of entanglement detection in three-qubit systems

Provided analytical tools for characterizing complex quantum states

Abstract

Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for three-qubit entanglement.