  The ultimate precision limit in estimating the Larmor frequency of $N$
unentangled rotating spins is well established, and is highly important for
magnetometers, gyroscopes and many other sensors. However this limit assumes
perfect, single addressing, measurements of the spins. This requirement is not
practical in NMR spectroscopy, as well as other physical systems, where a
weakly interacting external probe is used as a measurement device. Here we show
that in the framework of quantum nano-NMR spectroscopy, in which these
limitations are inherent, the ultimate precision limit is still achievable
using control and a finely tuned measurement.
