# Superadditivity of the Classical Capacity with Limited Entanglement Assistance

## TL;DR

This paper demonstrates that limited entanglement assistance can induce superadditivity in the classical capacity of quantum channels, revealing complex roles of entanglement in quantum communication.

## Contribution

The authors construct a quantum channel where classical capacity is additive but becomes superadditive with limited entanglement assistance, highlighting new phenomena in quantum information theory.

## Key findings

- Limited entanglement assistance can induce superadditivity.
- Classical capacity can be additive while assisted capacity is superadditive.
- Entanglement's role in quantum communication is more complex than previously understood.

## Abstract

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.