section V more general multipartite systems are considered. Section VI contains some conclusions. Finally, appendix A to C prove, respectively, some needed results related to SLOCC, the monotonicity of the 3-tangle under LOCC and the fact that ${\mbox{$| W \rangle$}}$ retains optimally bipartite entanglement when one qubit is traced out.

Kinds of entanglement under Stochastic LOCC
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In this work we define as equivalent the entanglement of two states ${\mbox{$| \psi \rangle$}}$ and ${\mbox{$| \phi \rangle$}}$ of a multipartite system iff local protocols exist that allow the parties to convert each of the two states into the other one with some a priori probability of success. In this approach, we follow the definition for stochastic equivalence as given in [@Be99][^2]. The underlying motivation for this definition is that, if the entanglement of is ${\mbox{$| \psi \rangle$}}$ and ${\mbox{$| \phi \rangle$}}$ is equivalent, then the two states can be used to perform the same tasks, although the probability of a successful performance of the task may depend on the state that is being used.

Invertible local operators
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Sensible enough, this classification would remain useless if in practice we would not be able to find out which states are related by 