A study of separability criteria for mixed three-qubit states

TL;DR

This paper investigates the separability of noisy GHZ-W three-qubit states, identifying the most effective criteria for different classes and discovering entangled states with positive partial transpose.

Contribution

It introduces new necessary criteria for separability and identifies entangled states with positive partial transpose in a specific three-qubit mixture.

Findings

Partial transposition and matrix element criteria are most effective for separability detection.

Identified a set of entangled states with positive partial transpose.

Established the strength of existing criteria for this class of states.

Abstract

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.