Entangled three-qubit states without concurrence and three-tangle
Abstract
We provide a complete analysis of mixed three-qubit states composed of a GHZ state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this ``monogamy'' can be lifted for mixed states by virtue of vanishing tangle measures.
Cite
@article{arxiv.quant-ph/0606071,
title = {Entangled three-qubit states without concurrence and three-tangle},
author = {Robert Lohmayer and Andreas Osterloh and Jens Siewert and Armin Uhlmann},
journal= {arXiv preprint arXiv:quant-ph/0606071},
year = {2007}
}
Comments
10 RevTeX pages, 3 figures, abstract and conclusions substantially extended