Fig. 8
From: A geometric formulation to measure global and genuine entanglement in three-qubit systems
The arithmetic mean \(\xi (\psi )\) introduced in Eq. (19) vanishes for fully separable states and is normalized to 1 for the GHZ–state. (a) The points \(\vec {\lambda }_{\psi } \in \mathcal {P}\) average higher values \(\xi\) as they get closer to the vertex \(\vec {G} \in \mathcal {P}\). (b) Condition \(\xi (\psi ) = \xi _0\), with \(\xi _0 = {\text {constant}}\), defines planes transverse to the line segment \(\overline{SG}\) whose points represent states \(\vert \psi \rangle \in \mathcal {H}\) with the same degree of entanglement. The \(\xi _0\)–planes shown in the figure correspond to \(\xi _0 = 1/3, 2/3\), and 5/6.
