Three-Tangle of Three-Qubit Werner States Using Symmetry

We use the symmetry of three-qubit Werner states to compute analytically the three-party entanglement measure known as three-tangle for these states. The computation shows that three-qubit Werner states have vanishing three-tangle. Also the optimal pure-state decompositions realizing the vanishing three-tangle are found. Moreover, the Coffman-Kundu-Wootters inequality is checked by computing one-tangle and concurrences of Werner states. It is found that the one-tangle is always greater than the sum of squared concurrences and three-tangle.