  We study the regularized average Renyi output entropy $\bar{S}_{r}^{\reg}$ 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
$\beta_{r}^{\reg}$, a quantity which we conjecture to be equal to $\Srreg$. We
find an explicit form for $\beta_{r}^{\reg}$ for some entanglement-breaking
channels, and also for the qubit depolarizing channel $\Delta_{\lambda}$ as a
function of the parameter $\lambda$. We prove equality of the two quantities in
some cases, in particular we conclude that for $\Delta_{\lambda}$ both are
non-analytic functions of the variable $\lambda$.

Quantum Physics