  We present a quantum sensing scheme achieving the ultimate quantum
sensitivity in the estimation of the transverse displacement between two
photons interfering at a balanced beam splitter, based on transverse-momentum
sampling measurements at the output. This scheme can possibly lead to enhanced
high-precision nanoscopic techniques, such as super-resolved single-molecule
localization microscopy with quantum dots, by circumventing the requirements in
standard direct imaging of cameras resolution at the diffraction limit, and of
highly magnifying objectives. Interestingly, we show that our interferometric
technique achieves the ultimate spatial precision in nature irrespectively of
the overlap of the two displaced photonic wavepackets, while its precision is
only reduced of a constant factor for photons differing in any non-spatial
degrees of freedom. This opens a new research paradigm based on the interface
between spatially resolved quantum interference and quantum-enhanced spatial
sensitivity.
