Superadditivity of classical capacity revisited

We introduce new type of superadditivity for classical capacity of quantum channels, which involves the properties of channels’ environment. By imposing different restrictions on the total energy contained in channels’ environment we can consider different types of superadditivity. Using lossy bosonic and additive noise quantum channels as examples, we demonstrate that their capacities can be either additive or superadditive depending on the values of channels parameters. The parameters corresponding to transition between the additive and superadditive cases are related with recently found critical and supercritical parameters for Gaussian channels.