  We consider estimating a small transverse displacement of an optical beam
over a line-of-sight propagation path: a problem that has numerous important
applications ranging from establishing a lasercom link, single-molecule
tracking, guided munition, to atomic force microscopy. We establish the
ultimate quantum limit of the accuracy of sensing a beam displacement, and
quantify the classical-quantum gap. Further, using normal-mode decomposition of
the Fresnel propagation kernel, and insights from recent work on
entanglement-assisted sensing, we find a near-term realizable
multi-spatio-temporal-mode continuous-variable entangled-state probe and a
receiver design, which attains the quantum precision limit. We find a
Heisenberg-limited sensitivity enhancement in terms of the number of entangled
temporal modes, and a curious super-Heisenberg quantum enhanced scaling in
terms of the number of entangled spatial modes permitted by the
diffraction-limited beam propagation geometry.
