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Average output entropy for quantum channels

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 $β_{r}^{\reg}$, a quantity which we conjecture to be equal to $\Srreg$. We find an explicit form for $β_{r}^{\reg}$ for some entanglement-breaking channels, and also for the qubit depolarizing channel $Δ_λ$ as a function of the parameter $λ$. We prove equality of the two quantities in some cases, in particular we conclude that for $Δ_λ$ both are non-analytic functions of the variable $λ$.