  We analyze rigorously the dynamics of the entanglement between two qubits
which interact only through collective and local environments. Our approach is
based on the resonance perturbation theory which assumes a small interaction
between the qubits and the environments. The main advantage of our approach is
that the expressions for (i) characteristic time-scales, such as decoherence,
disentanglement, and relaxation, and (ii) observables are not limited by finite
times. We introduce a new classification of decoherence times based on
clustering of the reduced density matrix elements. The characteristic dynamical
properties such as creation and decay of entanglement are examined. We also
discuss possible applications of our results for superconducting quantum
computation and quantum measurement technologies.
