Superadditivity in trade-off capacities of quantum channels

TL;DR

This paper explores the superadditivity phenomenon in the dynamic capacity of quantum channels, demonstrating that channels with additive capacities can exhibit superadditive combined capacities, challenging previous assumptions.

Contribution

It provides the first proof-of-principle conditions and explicit constructions for quantum channels exhibiting superadditivity in combined capacities.

Findings

Superadditivity can occur in classical-quantum capacities of quantum channels.

Explicit constructions of channels with superadditive capacities are provided.

Superadditivity challenges the assumption that additive individual capacities imply additive combined capacities.

Abstract

In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we want to optimally use a quantum channel for general communication purpose. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity, and it is largely unknown if this could lead to an superadditive double or triple resource capacity. For example, if a channel has an additive classical and quantum capacity, can the classical-quantum capacity be superadditive? In this work, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple capacity region.