Ke Li

We provide the sandwiched Renyi divergence of order alphaın(1/2,1), as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of quantum tasks. Specifically, we consider (a) smoothing of the max-relative entropy, (b) quantum privacy amplification, and (c) quantum information decoupling. We solve the problem of determining the exact strong converse exponents for these three tasks, with the performance being measured by the fidelity or purified distance. The results are given in terms of the sandwiched Renyi divergence of order alphaın(1/2,1), and its induced quantum Renyi conditional entropy and quantum Renyi mutual information. This is the first time to find the precise operational meaning for the sandwiched Renyi divergence with Renyi parameter in the interval alphaın(1/2,1).