The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime.

翻译：中等偏差机制关注信息处理任务在渐近框架下的有限块长权衡，即在通信代价趋近于容量型量的同时误差趋于零。我们针对多种完全量子通信任务找到了这些权衡的精确刻画，包括量子信源编码、量子态分割、纠缠辅助量子信道编码和纠缠辅助量子信道模拟。我们推导的主要技术工具是部分平滑最大信息与假设检验相对熵之间的紧密关系。这使得我们能够在中等偏差机制下获得独立同分布状态的部分平滑最大信息的展开式。