Redundant information encoding in QED during decoherence

Decoherence processes in quantum electrodynamics due to neglecting either the radiation [L. Landau, Z. Phys. 45, 430 (1927)] or the charged matter [N. Bohr and L. Rosenfeld, K. danske vidensk. Selsk, Math.-Fys. Medd. XII, 8 (1933)] have been studied from the dawn of the theory. However what happens in between, when a part of the radiation may be observed, as is the case in many real-life situations, has not been analyzed yet. We present such an analysis for a non-relativistic, point-like charge and thermal radiation. In the dipole approximation, we solve the dynamics and show that there is a regime where, despite of the noise, the observed field carries away almost perfect and hugely redundant information about the charge momentum. We analyze a partial charge-field state and show that it approaches a so called spectrum broadcast structure.