  Quantum entanglement is a crucial resource for learning properties from
nature, but a precise characterization of its advantage can be challenging. In
this work, we consider learning algorithms without entanglement to be those
that only utilize states, measurements, and operations that are separable
between the main system of interest and an ancillary system. Interestingly, we
show that these algorithms are equivalent to those that apply quantum circuits
on the main system interleaved with mid-circuit measurements and classical
feedforward. Within this setting, we prove a tight lower bound for Pauli
channel learning without entanglement that closes the gap between the
best-known upper and lower bound. In particular, we show that
$\Theta(2^n\varepsilon^{-2})$ rounds of measurements are required to estimate
each eigenvalue of an $n$-qubit Pauli channel to $\varepsilon$ error with high
probability when learning without entanglement. In contrast, a learning
algorithm with entanglement only needs $\Theta(\varepsilon^{-2})$ copies of the
Pauli channel. The tight lower bound strengthens the foundation for an
experimental demonstration of entanglement-enhanced advantages for Pauli noise
characterization.
