Strong converse theorems using Rényi entropies (Q2820904)

For many processes such as quantum communication via a noisy channel, the error \(\varepsilon_n\) corresponding to using the resource \(n\) times increases with \(n\) as \(\varepsilon_n\geq 1-\exp(-K\cdot n)\). This inequality is known as the \textit{strong converse property}.NEWLINENEWLINEIn this paper, the authors prove this property for different tasks such as state redistribution, data compression, etc. To prove these results, the authors use the quantum analog \(S_\alpha(\rho)=(1-\alpha)^{-1}\cdot \log(\text{Tr}(\rho^\alpha))\) of Rényi's entropy and the corresponding quantum analogue of Rényi's relative entropy.