  Understanding the noise affecting a quantum device is of fundamental
importance for scaling quantum technologies. A particularly important class of
noise models is that of Pauli channels, as randomized compiling techniques can
effectively bring any quantum channel to this form and are significantly more
structured than general quantum channels. In this paper, we show fundamental
lower bounds on the sample complexity for learning Pauli channels in diamond
norm with unentangled measurements. We consider both adaptive and non-adaptive
strategies. In the non-adaptive setting, we show a lower bound of
$\Omega(2^{3n}\epsilon^{-2})$ to learn an $n$-qubit Pauli channel. In
particular, this shows that the recently introduced learning procedure by
Flammia and Wallman is essentially optimal. In the adaptive setting, we show a
lower bound of $\Omega(2^{2.5n}\epsilon^{-2})$ for
$\epsilon=\mathcal{O}(2^{-n})$, and a lower bound of
$\Omega(2^{2n}\epsilon^{-2} )$ for any $\epsilon > 0$. This last lower bound
even applies for arbitrarily many sequential uses of the channel, as long as
they are only interspersed with other unital operations.
