  Non-Gaussian states of an optical field are important as a proposed resource
in quantum information applications. While conditional preparation is a highly
successful approach to preparing such states, their quality is limited by
detector non-idealities such as dead time, narrow dynamic range, limited
quantum efficiency and dark noise. Mesoscopic photon counters, with peak
performance at higher photon number, offer many practical advantages over
single-photon level conditioning detectors. Here we propose a novel approach
involving displacement of the ancilla field into the regime where mesoscopic
detectors can be used. We explore this strategy theoretically and present
simulations accounting for experimental non-idealities such as loss and
amplification noise, showing that precise photon-number resolution is not
necessary to herald highly nonclassical states. We conclude that states with
strong Wigner negativity can be prepared at high rates by this technique under
experimentally attainable conditions.
