论文标题
利用对称性的量子能力的有效界限的层次结构
A hierarchy of efficient bounds on quantum capacities exploiting symmetry
论文作者
论文摘要
实现信息处理任务的最佳率通常是根据正规信息度量来表征的。在许多量子任务的情况下，我们不知道如何计算此类数量。在这里，我们在最近引入的$ d^{\＃} $中利用对称性，以便在各种正则数量上获得半标准编程界限的层次结构。作为应用程序，我们提供了一般程序，以对正则化的Umegaki通道发散以及经典能力和量子通道的双向辅助量子能力提供有效的界限。特别是，我们获得了振幅阻尼通道的能力的略有改进。我们还证明，对于固定的输入和输出尺寸，可以将任何两个量子通道之间的正则夹层rényi发散近似于$ 1/ε$的$ε$准确度。
Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries in the recently introduced $D^{\#}$ in order to obtain a hierarchy of semidefinite programming bounds on various regularized quantities. As applications, we give a general procedure to give efficient bounds on the regularized Umegaki channel divergence as well as the classical capacity and two-way assisted quantum capacity of quantum channels. In particular, we obtain slight improvements for the capacity of the amplitude damping channel. We also prove that for fixed input and output dimensions, the regularized sandwiched Rényi divergence between any two quantum channels can be approximated up to an $ε$ accuracy in time that is polynomial in $1/ε$.
