We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states and derive analytical formulas for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.

• Received 8 November 2009

DOI:https://doi.org/10.1103/PhysRevA.82.032301