that 3 product terms always do the job, for instance $(\sqrt{c}{\mbox{$| 1 \rangle$}}+ \sqrt{d}{\mbox{$| 0 \rangle$}}){\mbox{$| 00 \rangle$}}$, $\sqrt{a}{\mbox{$| 0 \rangle$}}{\mbox{$| 01 \rangle$}}$ and $\sqrt{b}{\mbox{$| 0 \rangle$}}{\mbox{$| 10 \rangle$}}$ once we took the original state into the standard, unique form = + + + , \[Wclass\] where $a, b, c >0$, and $d \equiv 1- (a + b+ c) \geq 0$.

The parties can locally obtain the state (\[Wclass\]) from the state ${\mbox{$| W \rangle$}}$ in (\[W\]), which we choose as a representative of the class —and whose study we postpone for later on—, by application of an ILO of the form (

[ll]{} &\
0 &

) (

[ll]{} & 0\
0 &

) (

[ll]{} 1 & 0\
0 & 1

).

Before moving to relate these classes by means of non–invertible local operators, we note that states within the GHZ-class and the W-class depend, respectively, on 5 and 3 parameters that cannot be changed by means of LU. Previous works [@Li97; @Sc; @Ac00; @Ca00] have shown that a generic state of three qubits depends, up to LU, on 5 parameters. This means that states tipically belong to the GHZ-class, or equivalently, that a [*generic*]{} pure state of 