Ultimate quantum sensitivity in the estimation of the delay between two interfering photons through frequency-resolving sampling

We demonstrate the ultimate sensitivity allowed by quantum physics in the estimation of the time delay between two photons by measuring their interference at a beam-splitter through frequency resolving sampling measurements. This sensitivity can be increased quadratically by decreasing the photonic temporal bandwidth even at values smaller than the time delay when standard two photon interferometers become inoperable and without adapting the path of the reference photon, nor the need of time-resolving detectors with unfeasible high resolution. Applications can range from more feasible imaging of nanostructures, including biological samples, and nanomaterial surfaces to quantum enhanced estimation based on frequency-resolved boson sampling in optical networks.