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.Comment: 15 pages. v2: typo correcte