  Quantum number-path entanglement is a resource for super-sensitive quantum
metrology and in particular provides for sub-shotnoise or even
Heisenberg-limited sensitivity. However, such number-path entanglement has
thought to have been resource intensive to create in the first place ---
typically requiring either very strong nonlinearities, or nondeterministic
preparation schemes with feed-forward, which are difficult to implement. Very
recently, arising from the study of quantum random walks with multi-photon
walkers, as well as the study of the computational complexity of passive linear
optical interferometers fed with single-photon inputs, it has been shown that
such passive linear optical devices generate a superexponentially large amount
of number-path entanglement. A logical question to ask is whether this
entanglement may be exploited for quantum metrology. We answer that question
here in the affirmative by showing that a simple, passive, linear-optical
interferometer --- fed with only uncorrelated, single-photon inputs, coupled
with simple, single-mode, disjoint photodetection --- is capable of
significantly beating the shotnoise limit. Our result implies a pathway forward
to practical quantum metrology with readily available technology.
