Super-resolving quantum lidar: entangled coherent-state sources with binary-outcome photon counting measurement suffice to beat the shot-noise limit.

We investigate the performance of the super-resolving quantum lidar with the entangled coherent states of light in the presence of loss and noise, especially in the noisy case. An exact analytical expression of the output signal has been derived with the binary-outcome photon counting measurements. Numerical results show that the resolution of our scheme with parity detection is √N (N) times enhanced relative to that of the coherent-state strategy with the same (intensity) detection in the lossless and noiseless cases. The influences of phase diffusion on resolution and sensitivity have been analyzed and discussed. It is found that the super-resolution emerges in the whole diffusion rate regions, whereas the super-sensitivity just exists in the high and low diffusion rate regimes. Comparisons are made with the well known N00N states, the results show that the entangled coherent states performs better resolution and sensitivity than those of the N00N scheme in the whole diffusion regimes. In addition, the effects of photon loss on resolution and sensitivity have also been studied. The phase sensitivity can beat the shot noise limit and the resolution is much better than the Rayleigh diffraction limit in the whole loss regions. Finally, the zero-nonzero photon counting measurement gives much worse sensitivity than that of the parity detection, which is just opposite from the case as demonstrated in a recent coherent-light Mach-Zehnder experiment.