Permutation-invariant monotones for multipartite entanglement characterization
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.
Keywords
Cite
@article{arxiv.0804.3461,
title = {Permutation-invariant monotones for multipartite entanglement characterization},
author = {Xi-Jun Ren and Wei Jiang and Xingxiang Zhou and Zheng-Wei Zhou and Guang-Can Guo},
journal= {arXiv preprint arXiv:0804.3461},
year = {2009}
}
Comments
Submitted to Phys.Rev.A