Activation of zero-error classical capacity in low-dimensional quantum systems

TL;DR

This paper investigates the activation phenomenon of zero-error classical capacity in low-dimensional quantum systems, showing that activation occurs only under specific conditions and providing examples in qubit systems.

Contribution

It demonstrates that activation of zero-error classical capacity in qubit systems is limited to noiseless channels and provides explicit examples of activation in low-dimensional systems.

Findings

Activation occurs only with noiseless qubit channels.

Zero-error capacity of two qubit channels cannot be activated.

Examples of activation in low-dimensional quantum systems are provided.

Abstract

Channel capacities of quantum channels can be nonadditive even if one of two quantum channels has no channel capacity. We call this phenomenon \emph{activation} of the channel capacity. In this paper, we show that when we use a quantum channel on a qubit system, only a noiseless qubit channel can generate the activation of the zero-error classical capacity. In particular, we show that the zero-error classical capacity of two quantum channels on qubit systems cannot be activated. Furthermore, we present a class of examples showing the activation of the zero-error classical capacity in low-dimensional systems.