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We analyze rigorously the dynamics of the entanglement between two qubitswhich interact only through collective and local environments. Our approach isbased on the resonance perturbation theory which assumes a small interactionbetween the qubits and the environments. The main advantage of our approach isthat the expressions for (i) characteristic time-scales, such as decoherence,disentanglement, and relaxation, and (ii) observables are not limited by finitetimes. We introduce a new classification of decoherence times based onclustering of the reduced density matrix elements. The characteristic dynamicalproperties such as creation and decay of entanglement are examined. We alsodiscuss possible applications of our results for superconducting quantumcomputation and quantum measurement technologies.

Evolution of Entanglement of Two Qubits Interacting through Local and Collective Environments