By assuming a hierarchical interaction with the environments within the Houtappel approximation, decoherence effects on a Quantum Information System (QIS) are studied. In order to avoid a harmful "always on" effect it is assumed that such interaction happens in a single one step. As a result the decoherence times are quantized and inversely proportional to the strength of the couplings of the QIS with the environment. The decoherence is manifested as a liberated heat by the QIS. By Landauer's principle this effect erases the information. Our theoretical results are applied to three different Nuclear Magnetic Resonance systems. Bounds to the probability of erasing the information are imposed for these systems.