  Greenberger-Horne-Zeilinger (GHZ) states and their mixtures exhibit
fascinating properties. A complete basis of GHZ-states can be constructed by
properly choosing local basis rotations. We demonstrate this experimentally for
the Hilbert space C2x4 by entangling two photons in polarisation and orbital
angular momentum. Mixing GHZ-states unmasks different entanglement features
based on their particular local geometrical connectedness. In particular, a
specific GHZ-state in a complete orthonormal basis has a twin GHZ-state for
which equally mixing leads to full separability in opposition to any other
basis-state. Exploiting these local geometrical relations provides a toolbox
for generating specific types of multipartite entanglement, each providing
different benefits in outperforming classical devices. Our experiment, based on
hybrid entangled entanglement, investigates these GHZs properties showing a
good stability and fidelity and allowing a scaling in degrees of freedom and
advanced operational manipulations.
