All unital qubit channels are $4$-noisy operations

TL;DR

This paper demonstrates that all unital qubit channels can be realized using a 4-dimensional environment in a specific interaction model, and shows that sometimes a 3-dimensional environment is necessary.

Contribution

It proves that any unital qubit channel can be implemented as a 4-noisy operation and provides a lower bound example requiring at least 3 dimensions.

Findings

All unital qubit channels are 4-noisy operations.

A specific unital qubit channel requires at least a 3-dimensional environment.

The implementation involves a unitary interaction with a maximally mixed environment.

Abstract

We show that any unital qubit channel can be implemented by letting the input system interact unitarily with a $4$-dimensional environment in the maximally mixed state and then tracing out the environment. We also provide an example where the dimension of such an environment has to be at least $3$.