Independently established Pauli structure

The linear certificate then concerns the physically twirled complete task, not automatically the original channel. For example, a coherent rotation $e^{-i\theta Z/2}$ has original error $|\sin (\theta /2)|$, whereas its twirl has error ${\sin }^2(\theta /2)$. Imperfect randomization gates require their own allowance. An unimplemented mathematical twirl is not evidence that the hardware channel is Pauli.