依赖于输入维数和输入能量的量子信道信息特征的均匀连续性界
量子物理
2021-09-28 v5 信息论
数学物理
math.IT
math.MP
摘要
我们获得了量子信道基本信息特征的连续性界，这些界依赖于其输入维度（如果有限）和输入能量界（如果输入维度无限）。我们特别关注多模量子振荡器作为输入系统的情况。首先，我们证明了单个信道和信道的 个副本的输出条件互信息的连续性界。然后，我们获得了输出 Holevo 量相对于信道和输入系综同时变化的变差估计。结果得到了依赖于输入维度的量子信道基本容量的紧和近紧连续性界。它们补充了依赖于输出维度的 Leung-Smith 连续性界。最后，我们得到了无限维能量约束信道基本容量的紧和近紧连续性界，相对于生成量子信道强收敛的能量约束 Bures 距离。
引用
@article{arxiv.1610.08870,
title = {Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy},
author = {M. E. Shirokov},
journal= {arXiv preprint arXiv:1610.08870},
year = {2021}
}
备注
34 pages, in v.2 we add specifications of all the results for the case of multi-mode quantum oscillator (as input system), in v.3 the diamond-norm topology on the set of channels is replaced by the strong (pointwise) convergence topology, in v.4 the continuity bounds for energy-constrained channel capacities are improved (made tight or close-to-tight), v.5 is the journal version. arXiv admin note: text overlap with arXiv:1604.00568