Most types channel capacities associated to a given quantum channel are quantified using mutual informations (sometimes classical, sometimes quantum, sometimes regularised), which is not surprising given the classical counterparts of these results. On the other hand, the quantum capacity is quantified via the (regularised) coherent information instead. Explicit proofs are discussed for example in Preskill's notes and Watrous' books, and rely on showing that one can work out quantum codes whose associated rate is given by this coherent information.
Without going into the (generally quite lengthy) details of these proofs, is there any intuition as to why quantifying quantum capacity turns out to involve the coherent information rather than some kind of mutual information?
