=c\_+s\_\
=c\_+s\_\
=c\_+s\_ and $K=(1+2 c_\delta s_\delta c_\alpha c_\beta c_\gamma c_\varphi)^{-1} \in
(1/2,\infty)$ is a normalization factor. The ranges for the five parameters are $\delta \in (0,\pi/4], \alpha,\beta,\gamma \in (0,\pi/2]$ and $\varphi \in
[0,2\pi)$.

All these states are in the same equivalence class as the ${\mbox{$| GHZ \rangle$}}$ (\[GHZ\]) under SLOCC. Indeed, the ILO (

[ll]{} c\_& s\_c\_e\^[i]{}\
0 & s\_s\_e\^[i ]{}

) (

[ll]{} 1 & c\_\
0 & s\_

) (

[ll]{} 1 & c\_\
0 & s\_

), applied to ${\mbox{$| GHZ \rangle$}}$ produces the state (\[GHZclass\]).

The GHZ state is a remarkable representative of this class. It is maximally entangled in several senses [@Gi98]. For instance, it maximally violates Bell-type inequalities, the mutual information of measurement outcomes is maximal, it is maximally stable against (white) noise and one can locally obtain from a GHZ state with unit propability an EPR state shared between any two of the three parties. Another relevant feature is that when any one of the three qubits is traced out, the remaining two are in a separable —and therefore unentangled— state.

[**W-class**]{}\
Let us move to analyze the case where R$(\rho_{BC})$ contains only one product vector. We already argued that decomposition (\[2deco\]) 