@article {2317, title = {Quantum Channel Simulation and the Channel{\textquoteright}s Smooth Max-Information}, year = {2018}, abstract = {

We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel\&$\#$39;s smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel\&$\#$39;s smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel\&$\#$39;s smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

}, url = {https://arxiv.org/abs/1807.05354}, author = {Kun Fang and Xin Wang and Marco Tomamichel and Mario Berta} }