  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.
