Post-selected enhancement of phase sensitivity in a two-path interferometer

Post-selected metrology can exceed the standard quantum limit of single photon interference by concentrating all of the available Fisher information in a subset of post-selected outcomes. Here we apply this principle to a standard two-path interferometer, activating the Fisher information concentrated in the low probability output port by transferring the phase sensitivity to the circular polarizations of the photon. We obtain a phase gradient of the post-selected interference fringe that corresponds to that of a four-photon NOON state, providing a direct comparison of the performance of multi-photon interference with single-photon post-selection.