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.

Submitted to Phys.Rev.A

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• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• Simple forms of SLOCC equivalent four-qubit \c{hi} state