  We study the dephasing of a single qubit coupled to a bosonic bath. In
particular, we investigate the case when the bath is initially prepared in a
pure state known as the Schr\"odinger cat. In clear contradistinction to the
time-evolution of an initial coherent state, the time evolutions of the purity
and the coherence factor now depend on the particular choice of the
Schr\"odinger cat state. We also demonstrate that the evolution of the
entanglement of a two--qubit system depends on the initial conditions in a
similar way.
