Decoherence of a Single Qubit from Quantum Anomaly

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.