Monogamy inequality in terms of negativity for three-qubit states

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