### Entanglement Polytope Explorer

Here, we only show the full-dimensional entanglement polytopes, corresponding to genuinely four-qubit entangled quantum states in $\mathbb C^2 \otimes \mathbb C^2 \otimes \mathbb C^2 \otimes \mathbb C^2$. Since the polytopes are four-dimensional, please use the right-hand side slider to fix the eigenvalues of the first qubit.

$\lambda_1^{\max}$
No. Class Description Vertices Faces Perms
1 $L_{0_{7\oplus \bar{1}}}$ Origin (0.5,0.5,0.5,0.5) replaced by (0.75,0.5,0.5,0.5). 12 13 4
2 $L_{0_{5\oplus 3}}$ Vertices (0.5,0.5,0.5,0.5) and (1,0.5,0.5,0.5) missing. 10 13 4
3 $L_{a_4}$ ($a=0$) Vertices (0.5,1,0.5,0.5), (0.5,0.5,0.5,1), (0.5,0.5,0.5,0.5) missing. 9 14 6
4 $L_{\text{ab}_3}$ ($b=-a$) All three-partite entangled vertices missing. 8 16 1
5 $L_{\text{ab}_3}$ ($a=b=0$) W-state. All three- and four-partite entangled vertices missing. 7 9 1
6 $L_{a_2b_2}$ ($b = -a$) Vertices (0.5,1,0.5,0.5), (0.5,0.5,0.5,1) missing. 10 14 6
7 $G_{\text{abcd}}$ (generic) Generic polytope. 12 12 1