  When an ultrarelativistic electron beam collides with a sufficiently intense
laser pulse, radiation-reaction effects can strongly alter the beam dynamics.
In the realm of classical electrodynamics, radiation reaction has a beneficial
effect on the electron beam as it tends to reduce its energy spread. Here, we
show that when quantum effects become important, radiation reaction induces the
opposite effect, i.e., the electron beam spreads out after interacting with the
laser pulse. We identify the physical origin of this opposite tendency in the
intrinsic stochasticity of photon emission, which becomes substantial in the
full quantum regime. Our numerical simulations indicated that the predicted
effects of the stochasticity can be measured already with presently available
lasers and electron accelerators.
