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Monogamy Inequality in terms of Negativity for Three-Qubit States

Yong-Cheng Ou·Heng Fan
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Abstract

We propose a new entanglement measure to quantify three qubits entanglement in terms of negativity. A monogamy inequality analogous to Coffman-Kundu-Wootters (CKW) inequality is established. This consequently leads to a definition of residual entanglement, which is referred to as three-$π$ in order to distinguish from three-tangle. The three-$π$ is proved to be a natural entanglement measure. By contrast to the three-tangle, it is shown that the three-$π$ always gives greater than zero values for $W$ and GHZ classes, implying there always exists three-way entanglement for them, and three-tangle generally underestimates three-way entanglement of a given system. This investigation will offer an alternative tool to understand genuine multipartite entanglement.

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Yong-Cheng Ou, Heng Fan. 2007-04-04. Monogamy Inequality in terms of Negativity for Three-Qubit States. https://doi.org/10.1103/physreva.75.062308

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