Fig. 7
From: A geometric formulation to measure global and genuine entanglement in three-qubit systems
Partial section of the entanglement–polytope \(\mathcal {P}\) along the plane \(\Pi _i\) defined by the vertices \(\vec {S}\), \(\vec {B}_i\) and \(\vec {G}\). The orthogonal projection of \(\vec {\lambda }_{\psi } \in \mathcal {P}\) on the line-segment \(\overline{SB_i} \subset \mathcal {P}\) (written \(\vec {p}_i\)), as well as the rejection of \(\vec {\lambda }_{\psi }\) from \(\overline{SB_i}\) (denoted \(\vec {q}_i\)) are useful for introducing diverse entanglement measures (see discussion in the main text). If \(\vec {\lambda }_{\psi }\) is located in \(\Pi _i\) (as shown in the figure), then \(\vec {q}_i\) is also located in \(\Pi _i\). In general, both \(\vec {q}_i\) and \(\vec {\lambda }_{\psi }\) localize the same (arbitrary) point of \(\mathcal {P}\), the former from \(\vec {p}_i\) on the line-segment \(\overline{SB_i}\), the latter from the vertex \(\vec {S}\).
