Maximally entangled three-qubit states via geometric measure of entanglement

Understand

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound.

• However, for multipartite states the standard Schmidt decomposition generally does not exist.
• We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states.
• The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and W states emerge as extreme members in this family of maximally entangled states.