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Entangled three-qubit states without concurrence and three-tangle

Robert Lohmayer·Andreas Osterloh·Jens Siewert·Armin Uhlmann
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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.

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Robert Lohmayer, Andreas Osterloh, Jens Siewert, Armin Uhlmann. 2006-09-12. Entangled three-qubit states without concurrence and three-tangle. https://doi.org/10.1103/physrevlett.97.260502

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