Entangled three-qubit states without concurrence and three-tangle.
TLDR
By studying the Coffman-Kundu-Wootters inequality, it is found 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.Abstract:
We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger 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.read more
Citations
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References
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TL;DR: In this paper, it was shown that the Greenberger-Horne-Zeilinger state and a W state retain maximally bipartite entanglement when any one of the three qubits is traced out.
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TL;DR: Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.