Permutation-invariant monotones for multipartite entanglement characterization
Xi-Jun Ren, Wei Jiang, Xingxiang Zhou, Zheng-Wei Zhou, Guang‐Can Guo · Physical Review A · 2008
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 multiqubit system, we argue that ideal definitions for its characterizing quantities must be permutation invariant. Using this criterion, we examine the three four-qubit entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A 72, 012337 (2005)]. 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 four-qubit entanglement in four-qubit cluster-class states. Our results provide some useful insights in understanding multipartite entanglement.