Multipartite entanglement in four-qubit cluster-class states

TL;DR

This paper uses quantitative complementarity relations to analyze multipartite correlations in four-qubit cluster-class states, establishing new measures and hierarchies of entanglement.

Contribution

It introduces a set of hierarchy entanglement measures and proves the multipartite correlation as an entanglement monotone in four-qubit cluster states.

Findings

Average multipartite correlation $E_{ms}$ is an entanglement monotone.

Mixed three-tangle is compatible with QCRs as a correlation measure.

Hierarchy entanglement measures are rigorously derived.

Abstract

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation $E_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum states. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.