For pure symmetric three-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal{C}$, the three-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for symmetric $n$-qubit states derived from their Majorana representation, we derive the explicit achievable region of triples $(\mathcal{C},\tau ,\kappa )$.

• Received 30 May 2017

DOI:https://doi.org/10.1103/PhysRevA.96.062310