  We show via an explicit example that quantum anomalies can lead to
decoherence of a single quantum qubit through phase relaxation. The anomaly
causes the Hamiltonian to develop a non-self-adjoint piece due to the
non-invariance of the domain of the Hamiltonian under symmetry transformation.
The resulting decoherence originates completely from the dynamics of the system
itself and not, as usually considered, from interactions with the environment.
