We consider various forms of a process, which we call gluing , for combining two or more complementary quantum channel pairs $({\mathcal B}, {\mathcal C})$ to form a composite. One type of gluing combines a perfect channel with a second channel to produce a generalized erasure channel pair $({\mathcal B}_{g}, {\mathcal C}_{g})$ . We consider two cases in which the second channel is (i) an amplitude-damping, or (ii) a phase-damping qubit channel; (ii) is the dephrasure channel of Leditzky et al. For both (i) and (ii), $({\mathcal B}_{g}, {\mathcal C}_{g})$ depends on the damping parameter $0\leq p\leq 1$ and a parameter $0 \leq \lambda \leq 1$ that characterizes the gluing process. In both cases we study $Q^{(1)}({\mathcal B}_{g})$ and $Q^{(1)}({\mathcal C}_{g})$ , where $Q^{(1)}$ is the channel coherent information, and determine the regions in the $(p, \lambda)$ plane where each is zero or positive, confirming previous results for (ii). A somewhat surprising result for which we lack any intuitive explanation is that $Q^{(1)}({\mathcal C}_{g})$ is zero for $\lambda \leq 1/2$ when $p=0$ , but is strictly positive (though perhaps extremely small) for all values of $\lambda > 0$ when $p$ is positive by even the smallest amount. In addition we study the nonadditivity of $Q^{(1)}({\mathcal B}_{g})$ for two identical channels in parallel. It occurs in a well-defined region of the $(p, \lambda)$ plane in case (i). In case (ii) we have extended previous results for the dephrasure channel without, however, identifying the full range of $(p, \lambda)$ values where nonadditivity occurs. Again, an intuitive explanation is lacking.

中文翻译：

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使用广义擦除通道的量子容量的正性和非可加性

我们考虑各种形式的过程，我们称之为 胶合 , 用于组合两个或多个互补量子通道对 $({\mathcal B}, {\mathcal C})$ 以形成复合体。一种类型的粘合将一个完美的通道与第二个通道结合在一起，以产生一个广义擦除通道 一对 $({\mathcal B}_{g}, {\mathcal C}_{g})$ . 我们考虑两种情况，其中第二个通道是 (i) 幅度阻尼通道，或 (ii) 相位阻尼量子位通道；(ii) 是措辞渠道 莱迪茨基 等。 对于 (i) 和 (ii)， $({\mathcal B}_{g}, {\mathcal C}_{g})$ 取决于阻尼参数 $0\leq p\leq 1$ 和一个参数 $0 \leq \lambda \leq 1$ 这是粘合过程的特征。在这两种情况下，我们研究 $Q^{(1)}({\mathcal B}_{g})$ 和 $Q^{(1)}({\mathcal C}_{g})$ ， 在哪里 $Q^{(1)}$ 是信道相干信息，并确定区域 $(p, \lambda)$ 其中每个都是零或正的平面，证实了（ii）的先前结果。我们缺乏任何直观解释的有点令人惊讶的结果是 $Q^{(1)}({\mathcal C}_{g})$ 为零 $\lambda \leq 1/2$ 什么时候 $p=0$ ，但对于 的所有值都严格为正（尽管可能非常小） $\lambda > 0$ 什么时候 $p$ 即使是最小的量也是正的。此外，我们研究了非可加性 $Q^{(1)}({\mathcal B}_{g})$ 用于两个相同的并行通道。它发生在一个明确的区域 $(p, \lambda)$ 飞机在情况（i）。在情况 (ii) 中，我们已经扩展了 dephrasure 通道的先前结果，但没有确定所有范围 $(p, \lambda)$ 发生不可加性的值。同样，缺乏直观的解释。