论文标题
通过量子通道的经典交流的简单而更严格的实现性
Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
论文作者
论文摘要
信息理论中的可实现性是指实现基本任务的规定性能基准的编码策略。在量子信息理论中，精心设计的Hayashi-Nagaoka操作员不平等是证明具有大量单发性可实现性界限的必不可少的技术，因为它有效地类似于在各种问题中遇到的工会。在这项工作中，我们表明，相当不错的测量自然也起着工会的作用。它的明智应用大大简化了通过优雅的三行证明，用于古典量子（C-Q）通道编码的单发性可实现性的推导。 拟议的分析享有以下有利的功能。 （i）既定的单次界限承认了封闭式表达，就像著名的孔伏螺旋体定理中一样。也就是说，通过C-Q通道发送$ M $消息的错误概率是由将联合通道输入输入状态与$（M-1）$解耦产品状态区分开的最小错误的上限。 （ii）我们的结合以统一的方式直接产生渐近造成的渐近偏差，较小的偏差和中等偏差状态。 （iii）不再需要应用Hayashi-Nagaoka操作员不平等的系数。因此，派生的一声结合可以依靠Hayashi-Nagaoka操作员不平等，使现有的结果更加锐化。特别是，我们获得了最紧密的$ε$ - 一击容量，用于迄今为止C-Q通道编码，提高了渐近场景中的三阶编码率。 （iv）我们的结果适用于无限维的希尔伯特空间。 （v）所提出的方法适用于通过量子侧信息来得出经典数据压缩的单次可实现性，对量子通道的纠缠辅助经典通信以及各种量子网络信息处理协议。
Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an essential technique in proving a wealth of one-shot achievability bounds since it effectively resembles a union bound in various problems. In this work, we show that the pretty-good measurement naturally plays a role as the union bound as well. A judicious application of it considerably simplifies the derivation of one-shot achievability for classical-quantum (c-q) channel coding via an elegant three-line proof. The proposed analysis enjoys the following favorable features. (i) The established one-shot bound admits a closed-form expression as in the celebrated Holevo-Helstrom Theorem. Namely, the error probability of sending $M$ messages through a c-q channel is upper bounded by the minimum error of distinguishing the joint channel input-output state against $(M-1)$ decoupled products states. (ii) Our bound directly yields asymptotic results in the large deviation, small deviation, and moderate deviation regimes in a unified manner. (iii) The coefficients incurred in applying the Hayashi-Nagaoka operator inequality are no longer needed. Hence, the derived one-shot bound sharpens existing results relying on the Hayashi-Nagaoka operator inequality. In particular, we obtain the tightest achievable $ε$-one-shot capacity for c-q channel coding heretofore, improving the third-order coding rate in the asymptotic scenario. (iv) Our result holds for infinite-dimensional Hilbert space. (v) The proposed method applies to deriving one-shot achievability for classical data compression with quantum side information, entanglement-assisted classical communication over quantum channels, and various quantum network information-processing protocols.
