particular case of SLOCC, states equivalent under LU are also equivalent under SLOCC, the new classification being a coarse graining of the previous one.

The main aim of this work is to identify and characterize all possible kinds of pure-state entanglement of three qubits under SLOCC. Unentangled states, and also those which are product in one party while entangled with respect to the remaining two, appear as expected, trivial cases. More surprising is the fact that there are two different kinds of genuine tripartite entanglement. Indeed, we will show that any (non-trivial) tripartite entangled state can be converted, by means of SLOCC, into one of two standard forms, namely either the GHZ state [@Gr89] =1/(|000+|111) \[GHZ\], or else a second state |W=1/(|001+|010+|100) \[W\], and that this splits the set of genuinely trifold entangled states into two sets which are unrelated under LOCC. That is, we will see that if ${\mbox{$| \psi \rangle$}}$ can be converted into the state ${\mbox{$| GHZ \rangle$}}$ in (\[GHZ\]) and ${\mbox{$| \phi \rangle$}}$ can be converted into the state ${\mbox{$| W \rangle$}}$ in (\[W\]), then it is not possible to transform, not even with only a very small probability of success, ${\mbox{$| \psi \rangle$}}$ into ${\mbox{$| 