The qubit (or a system of two quantum dots) has become a standard paradigm for studying quantum information processes. Our focus is decoherence due to interaction of the qubit with its environment, leading to noise. We consider quantum noise generated by a dissipative quantum bath. A detailed comparative study with the results for a classical noise source such as generated by a telegraph process, enebles us to set limits on the pplicability of this process $\nu is à \nu is$ its quantum counterpart, as well as lend handle on the parameters that can be tuned for analysing decoherence. Both Ohmic and non-Ohmic dissipations are treated and appropriate limits are analysed for facilitating comparison with the telegraph process.