Monogamy Inequality in terms of Negativity for Three-Qubit States

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-$\pi$ in order to distinguish from 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 $W$ 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.