  Recently, a new type of symmetry for three-qubit quantum states was
introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It
includes the operations which leave the three-qubit standard GHZ state
unchanged. This symmetry is powerful as it yields families of mixed states that
are, on the one hand, complex enough from the physics point of view and, on the
other hand, simple enough mathematically so that their properties can be
characterized analytically. We show that by using the properties of
GHZ-symmetric states it is straightforward to derive optimal witnesses for
three-qubit entanglement.
