# Convex approximations of quantum channels. (arXiv:1709.03805v1 [quant-ph])

unavailable quantum channel $\Phi $ having at our disposal a single use of a

given set of other channels $\{\Psi_i \}$. The problem is recast to look for

the least distinguishable channel from $\Phi $ among the convex set $\sum_i p_i

\Psi_i$, and the corresponding optimal weights $\{ p_i \}$ provide the optimal

convex mixing of the available channels $\{\Psi_i \}$. For single-qubit

channels we study specifically the cases where the available convex set

corresponds to covariant channels or to Pauli channels, and the desired target

map is an arbitrary unitary transformation or a generalized damping channel.