Geometric multipartite entanglement measures

We report on a geometric formulation of multipartite entanglement measures which sets a generalization of the partial formulation of a few-qubit entanglement scenario reported in Ref. [1]. By means of the permutation group of N = 3 elements, we first propose a measure which satisfactorily reproduces the entanglement values reported in the literature for tripartite entangled states. We then give a measure for the general, multipartite entanglement case and show that this corrects some inconsistencies previously reported in Refs. [2, 3, 4]. The proposed N-qubit entanglement polynomial measure accurately reproduces standard results that are amenable to experimental verification.