An algebraic approach to the study of multipartite entanglement

We introduce a simple algebraic approach to the study of multipartite entanglement for pure states together with a class of suitable functionals able to detect the entanglement. On this basis, we reproduce some known results. Indeed, by investigating the properties of the introduced functionals, we show that a subset of such class is strictly connected to the purity. Moreover, we provide a direct and basic solution to the problem of simultaneous maximization of three appropriate functionals for three-qubit states, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of the GHZ states.