We study how phase decoherence through intrinsic decoherence leads to growing entropy and a strong
degradation of the maximum generated entanglement as a measure of information content of ionic
state due to ion-laser interaction with a trapped ion. We calculate the partial entropy of the particle
(atom or trapped ion) and field subsystems as well as the total entropy. The total entropy is shown
to increase with time. Thus, the partial field or atomic entropy cannot be used as a direct measure of
the particle–field entanglement. We find that, at least qualitatively, the difference between the total
entropy and the sum of field and atom partial entropies can be used as an entanglement measure,
when compared with an established entanglement measure based on the negativity of the eigenvalues
of the partially transposed density matrix. We find a very strong sensitivity of the maximum generated
entanglement on the decoherence and the chosen intrinsic decoherence parameter