  These notes are based on the lectures given by the second author at the
School on Optimal Transport on Quantum Structures at Erd\"os Center in
September 2022. The focus of the exposition is on two recently introduced
approaches on quantum optimal transport: one based on quantum channels as
generalized transport plans, the other based on the notion of
Hamming-Wasserstein distance of order 1 on multiple-qubit systems. The material
is presented in an elementary manner with a focus on the finite-dimensional
setting.
