发表机构
The Chinese University of Hong Kong, Shenzhen; The Hong Kong University of Science and Technology (Guangzhou); National University of Singapore（香港中文大学（深圳）; 香港科技大学（广州）; 新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文猜想并近似证明了量子退极化信道输出的主化关系，从而获得经典容量的紧致三阶展开，表明纠缠码字和集体解码最多带来O(log log n)比特的改进。
AI 中文摘要
量子信息理论中的一个核心挑战是，在允许跨多个信道使用的相干操作时，确定纠缠是否为信息处理提供优势。对于退极化信道，King关于最小输出熵可加性的证明排除了在渐近主导阶下经典通信的这种优势，同时为高阶优势留下了可能性。在这项工作中，我们猜想退极化信道输出的一个主化关系，并证明了该猜想的近似版本。我们的证明结合了移位对数行列式的精确排序与乘积态输出谱的反集中界，改进了King基于Schatten范数的分析。作为直接应用，我们获得了量子退极化信道经典容量的紧致三阶展开。因此，纠缠码字和集体解码最多可以将消息大小相对于乘积编码策略改进$O(\log \log n)$比特，这加深了我们对有限块长机制中纠缠作用的理解。
英文摘要
A central challenge in quantum information theory is to determine whether entanglement provides an advantage for information processing when coherent operations across multiple channel uses are allowed. For depolarizing channels, King's proof of the additivity of the minimum output entropy rules out such an advantage for classical communication at leading asymptotic order, while leaving open the possibility of an advantage for higher orders. In this work, we conjecture a majorization relation for the outputs of depolarizing channels and prove an approximate version of this conjecture. Our proof combines an exact ordering of shifted log-determinants with an anti-concentration bound for the spectrum of the product-state output, refining King's analysis based on Schatten norms. As a direct application, we obtain a tight third-order expansion for the classical capacity of quantum depolarizing channels. Consequently, entangled codewords and collective decoding can improve the message size over the product-coding strategy by at most $O(\log \log n)$ bits, sharpening our understanding of the role of entanglement in the finite-blocklength regime.
Comments15 pages, no figure
