  The evolution of two qubits coupled by a general nonlocal interaction is
studied in two distinct regimes. In the first regime the purity of the
individual qubits is interchanged through the entanglement shared by the two.
We illustrate how this can be a mechanism for decoherence. In the second
regime, the interaction entangles two initially pure qubits. The dynamical maps
for the reduced unitary evolution of both initially simply separable and
not-simply-separable states are found. We outline a protocol for optimizing the
entanglement generation subject to constraints.
