Average output entropy for quantum channels

Abstract

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 ${\Delta }_{\lambda }$ 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 $\lambda$.

32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channels

References in corpus (3)

• Aspects of generic entanglement
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Non-additivity of Renyi entropy and Dvoretzky's Theorem