  Accelerated charges emit electromagnetic radiation. According to classical
electrodynamics if the charges move along sufficiently close trajectories they
emit coherently, i.e., their emitted energy scales quadratically with their
number rather than linearly. By investigating the emission by a two-electron
wave packet in the presence of an electromagnetic plane wave within
strong-field QED, we show that quantum effects deteriorate the coherence
predicted by classical electrodynamics even if the typical quantum nonlinearity
parameter of the system is much smaller than unity. We explain this result by
observing that coherence effects are also controlled by a new quantum parameter
which relates the recoil undergone by the electron with the width of its wave
packet in momentum space.
