广义振幅阻尼信道经典容量的一个相当紧致的逆界
The classical capacity of generalized amplitude-damping channels and its strong-converse exponent
- School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对广义振幅阻尼信道经典容量这一开放问题，本文通过松弛关联度量推导出可高效计算的逆界，数值显示该界在非零温度下与Holevo信息几乎重合，显著优于现有结果。
AI中文摘要：
量子信道的经典容量是指以可忽略的错误传输经典信息的最高速率。尽管许多基本量子信道的容量已被确定，但广义振幅阻尼信道的容量在量子香农理论中仍是一个开放问题。在本工作中，我们重新审视了Brandão等人[Phys. Rev. Lett. 106, 230502 (2011)]引入的一个逆界，该逆界通过一个关联度量来上界经典容量。对于广义振幅阻尼信道，我们推导出该度量的一个松弛形式，使得逆界可高效计算。数值比较表明，我们的界在一般情况下相当紧致，并在非零温度下与Holevo信息几乎重合，在整个参数范围内显著优于现有界。
英文摘要：
The classical capacity of a quantum channel generally requires regularization because input codewords may be entangled across channel uses. We remove this regularization for generalized amplitude-damping channels (GADCs) and determine their exact strong-converse exponent throughout the full parameter range. The exponent is a single-letter transform of the sandwiched Rényi Holevo information and is attained by product input codewords with collective decoding. The key ingredient is a decomposition of the joint output into positive operators whose triangular factors have identical scalar Gram matrices after norm compression. A sharp triangular Schatten-norm compression inequality then establishes maximum output norm multiplicativity for diagonally sandwiched GADCs tensored with arbitrary completely positive maps. This yields additivity of the sandwiched Rényi Holevo information at every order above one. Consequently, the classical capacity equals the known one-copy Holevo information and admits a scalar optimization. Thus, entangled input codewords improve neither the capacity nor the optimal exponential decay of decoding success above capacity.
