We show that a sequence $\{\Phi_n\}$ of quantum channels strongly converges to a quantum channel $\Phi_0$ if and only if there exist a common environment for all the channels and a corresponding sequence $\{V_n\}$ of Stinespring isometries strongly converging to a Stinespring isometry $V_0$ of the channel $\Phi_0$. We also give a quantitative description of the above characterization of the strong convergence in terms of the appropriate metrics on the sets of quantum channels and Stinespring isometries. As a result, the uniform selective continuity of the complementary operation with respect to the strong convergence is established. We show discontinuity of the unitary dilation by constructing a strongly converging sequence of channels which can not be represented as a reduction of a strongly converging sequence of unitary channels. The Stinespring representation of strongly converging sequences of quantum channels allows to prove the lower semicontinuity of the entropic disturbance as a function of a pair (channel, input ensemble). Some corollaries of this property are considered.

中文翻译：

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量子通道的强收敛：Stinespring 膨胀的连续性和幺正膨胀的不连续性

我们表明，当且仅当存在所有通道的公共环境和相应的序列 $\{V_n\}$ 时，量子通道的序列 $\{\Phi_n\}$ 强烈收敛到量子通道 $\Phi_0$ Stinespring 等轴测图强烈收敛到通道 $\Phi_0$ 的 Stinespring 等轴测图 $V_0$。我们还根据量子通道集和 Stinespring 等距的适当度量对强收敛的上述特征进行了定量描述。结果，建立了关于强收敛的互补操作的均匀选择性连续性。我们通过构建一个强收敛的通道序列来显示酉扩张的不连续性，该序列不能表示为强烈收敛的酉通道序列的减少。量子通道强收敛序列的 Stinespring 表示允许证明熵扰动的下半连续性作为一对（通道，输入集合）的函数。考虑了此属性的一些推论。