  We study information-theoretic aspects of the infrared sector of quantum
electrodynamics, using the dressed-state approach pioneered by Chung, Kibble,
Faddeev-Kulish and others. In this formalism QED has an IR-finite S-matrix
describing the scattering of electrons dressed by coherent states of photons.
We show that measurements sensitive only to the outgoing electronic degrees of
freedom will experience decoherence in the electron momentum basis due to
unobservable photons in the dressing. We make some comments on possible
refinements of the dressed-state formalism, and how these considerations relate
to the black hole information paradox.
