  The Kraus form of the completely positive dynamical maps is appealing from
the mathematical and the point of the diverse applications of the open quantum
systems theory. Unfortunately, the Kraus operators are poorly known for the
two-qubit processes. In this paper, we derive the Kraus operators for a pair of
interacting qubit, while the strength of the interaction is arbitrary. One of
the qubits is subjected to the x-projection spin measurement. The obtained
results are applied to calculate the dynamics of the initial entanglement in
the qubits system. We obtain the loss of the correlations in the finite time
interval; the stronger the inter-qubit interaction, the longer lasting
entanglement in the system.
