Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380], our results on super-additivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

翻译：确定量子信道的容量是量子信息理论中的一个基本问题。尽管有严格的编码定理量化了量子信道中的信息流动，但由于超可加效应，其容量仍难以理解。研究这些现象对于加深我们对量子信息的理解至关重要，然而，简单而清晰的超可加信道示例却非常稀少。在此，我们研究了一类称为鸭嘴兽信道的信道族。其最简单的成员——一个qutrit信道——在与多种qubit信道联合使用时，显示出相干信息的超可加性。更高维度的族成员则显示与擦除信道一起时的量子容量超可加性。受伴生论文[IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380]中引入的“自旋对齐猜想”的约束，我们关于量子容量超可加性的结果可推广到更低维度的信道以及更广泛的参数范围。特别地，超可加性发生在两个各自具有大容量的弱可加信道之间，这与先前的结果形成鲜明对比。值得注意的是，一种新颖的单一传输策略在所有示例中均实现了超可加性。我们的结果表明，超可加性比之前认为的更为普遍。它可以在各种信道中发生，即使当两个参与信道都具有大量子容量时也是如此。