Lohmayer Robert, Osterloh Andreas, Siewert Jens, Uhlmann Armin
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev Lett. 2006 Dec 31;97(26):260502. doi: 10.1103/PhysRevLett.97.260502. Epub 2006 Dec 29.
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.
我们对由一个格林伯格-霍恩-泽林格（Greenberger-Horne-Zeilinger）态和一个与其正交的W态组成的混合三量子比特态进行了全面分析。我们给出了三纠缠度的最优分解和凸顶。此外，我们提供了一种分析方法来判定任意三量子比特的秩为2的态的三纠缠度是否为零。与两量子比特混合态的性质相比，这些结果凸显了有趣的差异，并且可为未来多体混合态纠缠研究提供定量参考。通过研究科夫曼-昆杜-伍特斯（Coffman-Kundu-Wootters）不等式，我们发现，虽然对于纯态，不等价纠缠类型的量严格相加，但对于混合态，由于纠缠度度量为零，这种“一夫一妻制”可以被打破。
