Figure 1

Lower bound to the residual four-tangle ${\tau }_{q_1|q_2|q_3|q_4}^{(4)\text{low}}$ versus the parameter $a$ (here assumed real) for the normal-form states: $|G_{abc}^2⟩$ with $b=c=a$ (red solid line), $|G_{ab}^3⟩$ with $b=a/4$ (green dashed line), $|G_{ab}^4⟩$ with $b=a/2$ (blue dotted line), $|G_a^5⟩$ (magenta dot-dashed line), $|G_a^6⟩$ (black dot-dot-dashed line). The residuals stay non-negative for general choices of the parameters $a$, $b$, $c$.