Genuine multiparticle entanglement of permutationally invariant states

We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of PPT mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.