  Finding the optimal encoding strategies can be challenging for communication
using quantum channels, as classical and quantum capacities may be
superadditive. Entanglement assistance can often simplify this task, as the
entanglement-assisted classical capacity for any channel is additive, making
entanglement across channel uses unnecessary. If the entanglement assistance is
limited, the picture is much more unclear. Suppose the classical capacity is
superadditive, then the classical capacity with limited entanglement assistance
could retain superadditivity by continuity arguments. If the classical capacity
is additive, it is unknown if superadditivity can still be developed with
limited entanglement assistance. We show this is possible, by providing an
example. We construct a channel for which, the classical capacity is additive,
but that with limited entanglement assistance can be superadditive. This shows
entanglement plays a weird role in communication and we still understand very
little about it.
