Genuine Entanglement of Four Qubit Cluster Diagonal States

TL;DR

This paper analytically determines the genuine entanglement of four-qubit cluster diagonal states by simplifying the conditions and deriving explicit formulas for different parameter regions, advancing understanding of quantum entanglement.

Contribution

It reduces the complexity of entanglement criteria for four-qubit cluster states and provides explicit formulas for their genuine entanglement.

Findings

Only 4 parameters are relevant for entanglement characterization.

Explicit formulas for genuine entanglement are derived for seven parameter regions.

The approach simplifies entanglement analysis in four-qubit cluster states.

Abstract

We reduce the necessary and sufficient biseparable conditions of the four qubit cluster diagonal state to concise forms. Only 4 out of the 15 parameters are proved to be relevant in specifying the genuine entanglement of the state. Using the relative entropy of entanglement as the entanglement measure, we analytically find the genuine entanglement of all the four qubit cluster diagonal states. The formulas of the genuine entanglement are of five kinds, for seven different parameter regions of entanglement.