Generic nonadditivity of quantum capacity in simple channels

TL;DR

This paper demonstrates that super-additivity of quantum capacity is common across various simple channels, using the novel platypus channels, challenging previous assumptions about capacity additivity in quantum information theory.

Contribution

Introduces the family of platypus channels as simple examples exhibiting super-additivity of quantum capacity, expanding understanding of quantum channel capacities.

Findings

Super-additivity occurs in simple channels like platypus channels.

Super-additivity is observed between channels with large individual capacities.

A single transmission strategy achieves super-additivity across all examples.

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 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.