For a separable Hilbert space $H$, we consider a quantum channel $\Phi: B(H)\to B(H)$ constructed with a finite number $k$ of Kraus operators $E_1,…,E_k$. We show that many important properties of $\Phi$ such as its minimum output entropies depend only on the $C*$-algebra generated by $E_i$ and not $H$. Then we investigate examples arising from free groups, and show that — unlike in finite dimension examples — free probability equips us with the ability to study regularized quantities. Then, we revisit the problem of additivity of minimum output entropies. In the commuting operator setup, we supply a non-random example of non-additive quantum channel. This is joint work with Sang-Gyun Youn (Queen’s).