Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture," which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [Phys. Rev. Lett. 130, 200801 (2023); arXiv:2202.08377], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

翻译：理解量子通道及其容量的奇异行为是量子信息理论的一个关键目标。本文研究了一个极其简单、低维、单参数的量子通道族，该族具有奇特的量子信息理论特征。作为该族中最简单的例子，我们聚焦于一个qutrit到qutrit的通道，它直观地通过将简单可降解通道与完全无用的量子比特通道混合而成。这种混合使得该通道的容量表现出各种有趣的行为。例如，该通道的私有容量和经典容量一致且可显式计算，尽管该通道不属于任何已知信息量具有可加性的类别。此外，若一个清晰且引人注目的猜想成立，则该通道的量子容量可被显式计算。这个“自旋对齐猜想”可能具有独立意义，我们在某些特例中证明了它，并提供了额外的数值证据支持其有效性。最后，我们以两种方式推广了该qutrit通道，所得通道及其容量表现出同样丰富的特性。在伴随论文[Phys. Rev. Lett. 130, 200801 (2023); arXiv:2202.08377]中，我们进一步展示了该qutrit通道在与多种辅助通道联合传输量子信息时，表现出此前未知的超可加性。