  All mixed states of two qubits can be brought into normal form by the action
of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$.
These normal forms can be obtained by considering a Lorentz singular value
decomposition on a real parameterization of the density matrix. We show that
the Lorentz singular values are variationally defined and give rise to
entanglement monotones, with as a special case the concurrence. Next a
necessary and sufficient criterion is conjectured for a mixed state to be
convertible into another specific one with a non-zero probability. Finally the
formalism of the Lorentz singular value decomposition is applied to tripartite
pure states of qubits. New proofs are given for the existence of the GHZ- and
W-class of states, and a rigorous proof for the optimal distillation of a
GHZ-state is derived.
