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:中度偏差制度所关注的是,通信成本与无药制下的信息处理任务错误之间的沟通成本和差错之间有一定的分块长度的权衡,因为通信成本接近一个类似能力的数量,差错同时消失。 我们发现,对于各种完全量子通信任务,包括量子源编码、量子状态分解、缠绕辅助量子信道编码和缠绕辅助量子通道模拟,这些权衡的精确特征。 我们得出的主要技术工具是部分顺畅的最大信息与假设测试相对增温之间的紧密关系。 这使得我们得以扩大部分顺畅的最大信息,用于i. d. 的中度偏差制度国家。