Additivity of the Quantum and Classical Capacities of Quantum Channels

Abstract

Quantum channels enable communication through the transmission of quantum states. Quantum Shannon theory investigates these channels, aiming to characterize their capacity for information transmission under various conditions. While this characterization is well-established for classical communication channels, quantum channels exhibit significantly more complex and mathematically intricate behavior, making a complete understanding elusive. A key challenge is the phenomenon of non-additivity, where combining quantum channels can enhance information flow by leveraging quantum effects. In this work, we focus on two types of non-additivity: those of classical capacity and quantum capacity.

We present new constructive counterexamples demonstrating the non-additivity of the minimum output p-Renyi entropy for p>2. These examples achieve non-additivity at lower values of p than previously known constructions of the same dimension. We also show that several plausible generalizations of antisymmetric spaces -- such as through alternative symmetries or higher tensor powers -- cannot produce non-additivity using current techniques.

Additionally, we advance the study of resonant multilevel amplitude damping channels. We analytically derive their degradability regions, previously inferred using a heuristic assumption supported by numerical evidence, and formulate conjectures on their capacity based on our own numerical evidence. Specifically, we conjecture that their coherent information is optimized on diagonal states and that they are always weakly additive. However, we find that coherent information activation is possible, as strong non-additivity arises in certain regions when combined with erasure channels.