Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

TL;DR

This paper provides a characterization of the separability of three-qubit GHZ diagonal states using entries, simplifying the process of checking separability without state decomposition, and confirms the sufficiency of Gühne's criterion.

Contribution

It introduces a new entry-based criterion for separability of three-qubit GHZ diagonal states and simplifies existing criteria using entanglement witnesses.

Findings

Necessary criterion of Gühne is sufficient for separability

Separable states can be checked without decomposition into pure product states

Simplified formula for full separability of GHZ diagonal states

Abstract

We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of G\"uhne for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.