Control of purity and entanglement for two spatially two-separated qubits via phase damping

Control of purity and entanglement of two two-qubits dispersively coupled to a field with a reservoir are investigated. Initially the qubits are entangled, while the field 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 eigen values 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 field, the two two-qubits, and the total system fall into mixed states.