Nilpotent polynomials approach to four-qubit entanglement

We apply the general formalism of nilpotent polynomials (Mandilara et al 2006 Phys. Rev. A 74 022331) to the problem of pure-state multipartite entanglement classification in four qubits. In addition to establishing contact with the existing results, we explicitly show how the nilpotent formalism naturally suggests constructions of entanglement measures invariant under the required unitary or invertible class of local operations. A candidate measure of four-partite entanglement is also suggested, and its behaviour numerically tested on random pure states.