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We study decoherence of two non-interacting qubits. The environment and itsinteraction with the qubits are modelled by random matrices. Decoherence,measured in terms of purity, is calculated in linear response approximation.Monte Carlo simulations illustrate the validity of this approximation and ofits extension by exponentiation. The results up to this point are also used tostudy one qubit decoherence. Purity decay of entangled and product states arequalitatively similar though for the latter case it is slower. Numericalstudies for a Bell pair as initial state reveal a one to one correspondencebetween its decoherence and its internal entanglement decay. For strong andintermediate coupling to the environment this correspondence agrees with theone for Werner states. In the limit of a large environment the evolutioninduces a unital channel in the two qubits, providing a partial explanation forthe relation above.Comment: 32 pages, 11 figure

Decoherence of two-qubit systems: a random matrix description