Forgetting boosts the classical environment-assisted and private capacity

A channel capacity is non-convex if the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities. This implies that there is a concrete communication scenario in which a sender can increase the transmission rate by forgetting which channel acts on the channel input. Previously, this surprising property had only been shown for the quantum capacity. Here we prove that both the private and classical environment-assisted capacities are non-convex.