Entanglement classification via a single entanglement measure

We show that a single polynomial entanglement measure is enough to verify equivalence between generic n-qubit states under stochastic local operations with classical communication (SLOCC). SLOCC operations may be represented geometrically by Möbius transformations on the roots of the entanglement measure on the Bloch sphere. Moreover, we show how the roots of the three-tangle measure classify four-qubit generic states, and propose a method to obtain the normal form of a four-qubit state, which bypasses the possibly infinite iterative procedure.