Fig. 12
From: A geometric formulation to measure global and genuine entanglement in three-qubit systems
Entanglement measures \(\mu (\psi )\), \(F_{123} (\psi )\) and \(\mathcal {C}_{{\text {GME}}} (\psi )\) for the state \(\vert \psi _{\theta } \rangle\) given in Eq. (23). At \(\theta =0\) the state becomes \(\vert 111 \rangle\), so it is fully separable. However, it is maximally entangled at \(\theta = \theta _0 = 2\pi /3\), since it is local unitary equivalent to the GHZ–state. At \(\theta = \pi\) the state is equal to \(\vert W \rangle\). Consistently, the measures range between 0 and 1, reaching their maximum (\(=1\)) at \(\theta _0\). Measure \(\mu\) defines a lower bound, as it produces lower values than the results of the other two measures, except at \(\theta = \theta _0\).
