Average output entropy for quantum channels

We study the regularized average Renyi output entropy S¯r reg of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for βr reg , a quantity which we conjecture to be equal to S¯r reg . We find an explicit form for βr reg for some entanglement-breaking channels and also for the qubit depolarizing channel Δλ as a function of the parameter λ. We prove equality of the two quantities in some cases, in particular, we conclude that for Δλ both are non-analytic functions of the variable λ.