W \rangle$}}$ is maximally robust under disposal of any one of the three qubits, in the sense that the remaining reduced density matrices[^1] $\rho_{AB}$, $\rho_{BC}$ and $\rho_{AC}$ retain, according to several criteria, the greatest possible amount of entanglement, compared to any other state of three qubits, either pure or mixed.

We will finally analyze entanglement under SLOCC in more general multipartite systems. We will show that, for most of these systems, there is typically no chance at all to transform locally a given state into some other if they are chosen randomly, because the space of entangled pure states depends on more parameters than those that can be modified by acting locally on the subsystems.

The paper is organized as follows. In section II we characterize mathematically the equivalence relation established by stochastic conversions under LOCC, and illustrate its performance by applying it to the well-known bipartite case. In section III we move to consider a system of three qubits, for which we prove the existence of 6 classes of states under SLOCC —including the 2 genuinely tripartite ones—. Section IV is devoted to study the endurance of the entanglement of the state ${\mbox{$| W \rangle$}}$ against particle losses. In 