Estimation with ultimate quantum precision of the transverse displacement between two photons via two-photon interference sampling measurements

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, the ultimate spatial precision in nature is achieved irrespectively of the overlap of the two displaced photonic wavepackets. This opens a new research paradigm based on the interface between spatially resolved quantum interference and quantum-enhanced spatial sensitivity.