Generic Nonadditivity of Quantum Capacity in Simple Channels

Abstract

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 superadditivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of superadditive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display superadditivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display superadditivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture"introduced in our companion paper [F. Leditzky, D. Leung, V. Siddhu, G. Smith, and J. A. Smolin, The platypus of the quantum channel zoo, IEEE Transactions on Information Theory (IEEE, 2023), 10.1109/TIT.2023.3245985], our results on superadditivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, superadditivity 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 superadditivity in all examples. Our results show that superadditivity 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.