Calculation of entanglement in graph states up to five-qubit based on generalized concurrence

TL;DR

This paper introduces a new classification method for entanglement in graph states using generalized concurrence, revealing detailed categorization of multi-qubit states and comparing it with local complementation equivalence.

Contribution

The paper presents a novel classification scheme for graph state entanglement based on generalized concurrence, applicable up to five-qubit states.

Findings

Eight three-qubit graph state categories

Sixty-four four-qubit graph state categories

One thousand twenty-four five-qubit graph state classes

Abstract

We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states are in ten classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule.