Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel

TL;DR

This paper demonstrates that unlike classical channels, the private and environment-assisted capacities of quantum channels are non-convex, revealing fundamental differences in quantum information theory.

Contribution

It extends the non-convexity property from quantum capacity to private and environment-assisted capacities of quantum channels, highlighting new theoretical insights.

Findings

Private capacity is non-convex.

Environment-assisted capacity is non-convex.

Non-convexity applies beyond quantum capacity.

Abstract

The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.