Remote Phase Sensing by Coherent Single Photon Addition

We propose a remote phase sensing scheme inspired by the high sensitivity of the entanglement produced by coherent multimode photon addition on the phase set in the remote heralding apparatus. By exploring the case of delocalized photon addition over two modes containing identical coherent states, we derive the optimal observable to perform remote phase estimation from heralded quadrature measurements. The technique is experimentally tested with calibration measurements and then used for estimating a remote phase with a sensitivity that is found to scale with the intensity of the (local) coherent states, which never interacted with the sample.