Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms o f which the state can be written in a unique form. This leads to a canonica l form which generalizes the two-quantum-bit Schmidt decomposition. It is u niquely characterized by the five entanglement parameters. It leads to a co mplete classification of the three-quantum-bit states. It shows that the ri ght outcome of an adequate local measurement always erases all entanglement between the other two parties.