Control of purity and entanglement of two two-qubits dispersively coupled to a eld with a reservoir are inves-
tigated. Initially the qubits are entangled, while the eld is either in a coherent state or a statistical mixture of two
coherent states. For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially
transposed density matrix. A measure related to the mutual entropy, namely the index of entropy, is employed to
measure the entanglement. Its results agree well with the negativity. It is found that the entanglement and purity have
strong sensitivity to phase damping. The asymptotic behaviour of the states of the eld, the two two-qubits, and the
total system fall into mixed states.