system, as well as the inequivalence between bipartite and tripartite entanglement, can be easily understood from the non-increasing character of these measures under LOCC. In addittion, the 3-tangle allows for a systematic and practical identification of which class under SLOCC any pure state belongs to.

For each $\kappa=A,B$ and $C$ we can regard the three-qubit system as a bipartite system, with qubit $\kappa$, say $A$ for concreteness, being one part of the system and the remaining two qubits, $B$ and $C$, being the other. Correspondingly, a state ${\mbox{$| \psi \rangle$}}$ of the three qubits can be viewed as a bipartite state ${\mbox{$| \psi_{A(BC)} \rangle$}}$. For bipartite states several measures are known, which are entanglement monotones [@Vi00J]; that is, which cannot be increased, on average, under LOCC. For instance, we already mentioned the entropy of entanglement $E(\psi)$ for asymptotic conversions –given by the entropy $S_A$ of the eigenvalues of $\rho_A$— and the monotone $E_2(\psi)$ for the single copy case —which is given by the smallest eigenvalue $\lambda_2$ of $\rho_A$. They all satisfy that vanish for product states (corresponding to $\rho_A$ with rank 1) while having a positive value for any other state (corresponding to $\rho_A$ with rank 2). Thus we can 