Entanglement, mixedness, and spin-flip symmetry in multiple-qubit systems

A relationship between a recently introduced multipartite entanglement measure, state mixedness, and spin-flip symmetry is established for any finite number of qubits. It is also shown that, for those classes of states invariant under the spin-flip transformation, there is a complementarity relation between multipartite entanglement and mixedness. A number of example classes of multiple-qubit systems are studied in light of this relationship.