  We consider a single copy of a pure four-partite state of qubits and
investigate its behaviour under the action of stochastic local quantum
operations assisted by classical communication (SLOCC). This leads to a
complete classification of all different classes of pure states of four-qubits.
It is shown that there exist nine families of states corresponding to nine
different ways of entangling four qubits. The states in the generic family give
rise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit
entanglement distributed among the four parties. The concept of concurrence and
3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to
a seven parameter family of entanglement monotones. Finally, the SLOCC
operations maximizing all these entanglement monotones are derived, yielding
the optimal single copy distillation protocol.
