Maximizing the geometric measure of entanglement

The characterization of the maximally achievable entanglement in a given physical system is relevant, as entanglement is known to be a resource for various quantum information tasks. This holds especially for pure multiparticle quantum states, where the problem of maximal entanglement is not only of physical interest, but also closely related to fundamental mathematical problems in multilinear algebra and tensor analysis. We propose an algorithmic method to find maximally entangled states of several particles in terms of the geometric measure of entanglement. Besides identifying physically interesting states our results deliver insights to the problem of absolutely maximally entangled states; moreover, our methods can be generalized to identify maximally entangled subspaces.