Entanglement and genuine entanglement of three qubit GHZ diagonal states

TL;DR

This paper provides a complete analytical criterion for determining full separability and genuine entanglement in three-qubit GHZ diagonal states, simplifying entanglement analysis in these quantum states.

Contribution

It introduces a necessary and sufficient separability criterion for three-qubit GHZ diagonal states, advancing understanding of their entanglement properties.

Findings

Exact entanglement calculation for some GHZ diagonal states

Entanglement depends only on the largest diagonal element

Complete solution to entanglement classification for these states

Abstract

We analytically prove the necessary and sufficient criterion for the full separability of three-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal states. The corresponding entanglement is exactly calculable for some GHZ diagonal states and is tractable for the others using the relative entropy of entanglement. We show that the biseparable criterion and the genuine entanglement are determined only by the biggest GHZ diagonal element regardless of all the other smaller diagonal elements. We have completely solved the entanglement problems of three-qubit GHZ diagonal states.