All unital qubit channels are $4$-noisy operations. (arXiv:1802.01337v1 [quant-ph])

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 $3$.

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