Entangled three-qubit states without concurrence and three-tangle

Details Entangled three-qubit states without concurrence and three-tangle Entangled three-qubit states without concurrence and three-tangle

2006-06-08

arxiv.org/abs/quant-ph/0606071v2

Phys. Rev. Lett. 97, 260502 (2006)

Physics

Quantum Physics

10 RevTeX pages, 3 figures, abstract and conclusions substantially extended

Scientific paper

10.1103/PhysRevLett.97.260502

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.

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