Unital qubit channels are $3$-noisy

Abstract

The algebraic and environmental characteristics of mixed unitary quantum operations are investigated. It is established that the composition of two uniformly n-mixed unitary channels is itself n-noisy, and this n-noisy property is shown to be an invariant under unitary equivalence. Furthermore, by utilizing majorization and the divisibility of Kraus rank-four unital qubit channels, we demonstrate that any unital qubit channel can be physically simulated using a three-dimensional maximally mixed environment. Together, these results advance the classification and physical realization of noisy quantum channels.