Permutation-invariant monotones for multipartite entanglement characterization

TL;DR

This paper investigates the permutational properties of multipartite entanglement monotones, highlighting the importance of permutation invariance, and proposes a new invariant monotone to better characterize genuine 4-qubit entanglement.

Contribution

The authors identify non-invariance in existing monotones and introduce a new permutation-invariant monotone for accurate multipartite entanglement measurement.

Findings

One of the examined monotones is not permutation-invariant.

The new monotone effectively measures genuine 4-qubit entanglement.

Insights into multipartite entanglement characterization are provided.

Abstract

In this work we consider the permutational properties of multipartite entanglement monotones. Based on the fact that genuine multipartite entanglement is a property of the entire multi-qubit system, we argue that ideal definitions for its characterizing quantities must be permutation-invariant. Using this criterion, we examine the three 4-qubit entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A. 72, 012337]. By expressing them in terms of quantities whose permutational properties can be easily derived, we find that one of these monotones is not permutation-invariant. We propose a permutation-invariant entanglement monotone to replace it, and show that our new monotone properly measures the genuine 4-qubit entanglement in 4-qubit cluster-class states. Our results provide some useful insights in understanding multipartite entanglement.