The entanglement of some non-two-colorable graph states

TL;DR

This paper precisely evaluates the entanglement in specific non-two-colorable graph states, improving bounds for certain configurations and proposing a new upper bound based on graph state definitions.

Contribution

It provides exact entanglement calculations for six- and nine-vertex graph states and introduces an improved upper bound for five-vertex ring graph states.

Findings

Exact entanglement values for six- and nine-vertex graph states.

Improved upper bound of 2.9275 for five-vertex ring graph state.

Proposed new upper bound based on graph state properties.

Abstract

We exactly evaluate the entanglement of a six vertex and a nine vertex graph states which correspond to non ''two-colorable'' graphs. The upper bound of entanglement for five vertices ring graph state is improved to 2.9275, less than upper bound determined by LOCC. An upper bound of entanglement is proposed based on the definition of graph state.