  In theories with long-range forces like QED or perturbative gravity, only
rates that include emitted soft radiation are non-vanishing. Independently of
detector resolution, finite observables can only be obtained after integrating
over the IR-component of this radiation. This integration can lead to some loss
of quantum coherence. In this note, however, we argue that it should in general
not lead to full decoherence. Based on unitarity, we suggest a way to define
non-vanishing off-diagonal pieces of the IR-finite density matrix. For this
IR-finite density matrix, we estimate the dependence of the loss of quantum
coherence, i.e. of its purity, on the scattering kinematics.
