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arXiv · 0804.3461

Permutation-invariant monotones for multipartite entanglement characterization

Xi-Jun Ren·Wei Jiang·Xingxiang Zhou·Zheng-Wei Zhou·Guang-Can Guo
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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.

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Xi-Jun Ren, Wei Jiang, Xingxiang Zhou, Zheng-Wei Zhou, Guang-Can Guo. 2008-04-22. Permutation-invariant monotones for multipartite entanglement characterization. https://doi.org/10.1103/physreva.78.012343

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