Entanglement of mixed states in systems of n qubits

With the help of geometric algebra, we define a sequence of unitary operators that fulfills a controllability condition and whose operation on a reference or pass state spans the complete Hilbert space. The unitary operators can be classified according to their ability to induce entanglement, and the operators that can entangle a system provide a natural parametrization of the process. The entanglement of pure states is measured using reduced traces, and this can be extended to define a measure of the entanglement of mixed states in a system of n qubits. Practical expressions for average state fidelity of n-qubit systems have also been obtained.