  We investigate the behavior of quantum states under stochastic local quantum
operations and classical communication (SLOCC) for fixed numbers of qubits. We
explicitly exhibit the homomorphism between complex and real groups for
two-qubits, and use the latter to describe the effect of SLOCC operations on
two-qubit states. We find an expression for the polarization Lorentz group
invariant length, which is the Minkowskian analog of the quantum state purity,
the corresponding Euclidean length. The construction presented is immediately
generalizable to any finite number of qubits.
