Super-additivity of quantum capacity in simple channels

The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits super-additive quantum capacity when combined with qudit erasure channels. Here we consider the ``generalized platypus channel'', prove that it has computable channel capacities, such as both private and classical capacity equal to $1$, and in particular, the generalized platypus channel still displays the super-additivity of quantum capacity when combined with qudit erasure channels and multilevel amplitude damping channels respectively.