Using elementary techniques from analytic perturbation theory of Hermitian matrices, we devise a simple strategy to detect positive quantum capacities of quantum channels and their complements. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Our main result leads to simplified proofs of certain existing structure theorems for the class of degradable quantum channels, and an extension of their applicability to the larger class of more capable quantum channels.

翻译：使用赫米提安基体分析扰动理论的基本技术,我们设计了一个简单的战略来检测量子信道及其补充的正量子能力。几个值得注意的例子,例如脱极和转移分解渠道(包括Werner-Holevo频道 ) 、 脱裂渠道、 普遍的保利渠道、 多层振幅障碍渠道 以及( 并置) 双向单向共变式通道, 从而恰当地展示了我们的方法的实用性。 我们的主要结果导致简化了某些现有可降解量子通道等级结构理论的证明,以及将其适用于更大级别的更能容量的量子频道。