  We explore the role of $\textit{collective measurements}$ on precision in
estimation of a single parameter. Collective measurements are represented by
observables which commute with all permutations of the probe particles. We show
that with this constraint, quantum bits(qubits) outperform classical
bits(non-superposable bits) in optimizing precision. Specifically, we prove
that while precision in a collective measurement is loosely bounded by
$O\left(\frac{1}{N}\right)$ for $N$ classical bits, using qubits it is tightly
bounded by $O\left(\frac{1}{N^2}\right)$. This bound is consistent with quantum
metrology protocols with the collective measurement requiring an entangled
probe state to saturate. Finally, we construct a canonical measurement protocol
that saturates this bound.
