Relative Entropy Convergence for Depolarizing Channels
Relative Entropy Convergence for Depolarizing Channels
复制标题
去极化通道的相对熵收敛
DOI：
10.1063/1.4939560
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Wolf
中科院分区：
文献类型：
--
作者：
Alexander Muller;Daniel Stilck França;M. Wolf
本文利用相对熵研究了连续时间去极化信道下满秩不动点的态的收敛性。在这种情况下，相对熵上界的最佳指数由log-Sobolev-1常数给出。我们的主要结果是这个常数的计算。作为应用，我们利用去极化通道的log-Sobolev-1常数改进了von-Neumann熵的不等式。这一结果是比较类似的边界最近得到的金等人。我们显示了一个版本的平斯克不等式，这是最佳的和紧密的，如果我们固定的第二个参数的相对熵。最后，我们考虑了完全去极化信道张量幂的log-Sobolev-1常数，并利用量子版的Shearer不等式证明了一个一致的下界。
We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von-Neumann entropy. This result is compared to similar bounds obtained recently by Kim et al. and we show a version of Pinsker's inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer's inequality to prove a uniform lower bound.