发表机构
RIKEN Hakubi Research Team, RIKEN Pioneering Research Institute (PRI) and RIKEN Center for Quantum Computing (RQC); Scuola Normale Superiore; Institute for Quantum Information, RWTH Aachen University; Department of Electrical and Computer Engineering, National University of Singapore; Centre for Quantum Technologies, National University of Singapore（理化学研究所博后研究团队、先导研究院和量子计算中心; 意大利高等师范学院; 亚琛工业大学量子信息研究所; 新加坡国立大学电气与计算机工程系; 新加坡国立大学量子技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨将量子信息中的误差度量从最小扩展改为最大扩展对操作任务的影响，发现信道编码和资源蒸馏不受影响，而信道模拟和资源稀释的速率改用Belavkin-Staszewski相对熵，且已知可逆性结果失效。
AI 中文摘要
量子信息中常用的距离度量，如迹距离或基于保真度的净化距离，是经典信息论中相应距离度量的最小扩展。然而，这种扩展经典距离的方式并非唯一，还可以定义一系列其他扩展。本文研究了当误差度量改为经典距离度量的最大扩展时，量子信息处理任务如何受到影响，这给操作任务施加了更严格的误差要求。我们发现，某些任务（如信道编码或量子资源蒸馏）的性能完全不受此变化影响。然而，对于其他任务（如信道模拟和量子资源稀释），我们证明其速率不再由标准（Umegaki）量子相对熵的函数给出，而是基于Belavkin-Staszewski相对熵的函数。我们的结果将Belavkin-Staszewski相对熵与操作任务联系起来，并揭示已知的量子信息可逆性结果（包括反向香农定理和量子资源变换的渐近可逆性）在最大距离度量下不再成立。
英文摘要
The measures of distance frequently used in quantum information, such as trace distance or fidelity-based purified distance, are the smallest extensions of the corresponding distance measures in classical information theory. However, this way of extending classical distances is not unique, and a whole spectrum of other extensions can be defined. Here we study the question of how quantum information processing tasks are affected by a change of the error metrics to the maximal extensions of the classical distance measures, imposing more demanding error requirements on operational tasks. We find that the performance of some tasks, such as channel coding or quantum resource distillation, is not affected whatsoever by this change. However, for other tasks such as channel simulation and quantum resource dilution, we show that the rates are now given not by functions of the standard (Umegaki) quantum relative entropy, but ones based on the Belavkin-Staszewski relative entropy. Our results connect the Belavkin-Staszewski relative entropy with operational tasks and reveal that known reversibility results in quantum information, including the reverse Shannon theorem and the asymptotic reversibility of quantum resource transformations, no longer hold under maximal distance measures.
Comments28+4 pages
