Geometry of GHZ Type Quantum States

For tripartite states there is still no general tool to discriminate between separablility and different types of entanglement. Some special entanglement measures, adjusted to the usage for multipartite system were studied, and especially applied to generalized GHZ and W states. States with entangled entanglement and some of their corresponding geometrical structures are examined. Similar to the magic simplex in the two qubit case the geometrical structure of simplices plays an important role in the investigation of relations, symmetries and entanglement properties of tripartite qubit states. For GHZ symmetric states the entanglement status and border lines for regions of different types of entanglement can be found. Via local unitary transformation these informations could also be used for a simplex of states with entangled entanglement. Using basis states as building blocks and entangling them in a special way we are able to construct GHZ type state for arbitrary many particles in a very straightforward method. Finally with help of a Bloch representation we gained some interesting geometrical insights into the structure of tripartite qubit states.