Dephasing of qubits by the Schrödinger cat

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 Schrödinger 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 Schrödinger 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.