  This note shows that adaptive strategies do not offer additional advantages
for learning and testing Pauli channels with entangled input. First, the tight
query complexity of learning Pauli channels with entangled input is established
for the general norm $l_p$. In particular, the complexities for the $l_{1}$,
$l_2$ and $l_\infty$ norms are improved or matched compared to previous results
using entanglement in the literature. We also settle the query complexity to
test if Pauli channels are white noise sources across $l_p$. Additionally, we
demonstrate that the query complexity of estimating the noise level of a Pauli
channel, characterized by the entropy of its error distribution and the count
of non-zero probabilities, is $\Theta(4^n/n)$. Further, $\Theta(4^n/n)$ queries
are sufficient to estimate the diamond norm between two Pauli channels.
