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

Quantum Physics