  Quantum discord-breaking channels were previously defined as the local
channels that act on subsystem $A$ to produce classical-quantum states across
system $AB$. However, unlike entanglement, discord is asymmetric. Here, we
characterise the discord-breaking channels that act on subsystem $B$, thus
completing the overall description of discord-breaking channels. We then
introduce the notion of discord-annihilating channels, which act globally on
system $AB$ to destroy quantum discord, and find their closed form.
Discord-annihilating channels have clear operational description, involving
subspace projections on subsystem $A$ and conditional preparation of fixed
states on subsystem $B$.
