A quantum illumination protocol exploits correlated light beams to enhance the probability of detection of a partially reflecting object lying in a very noisy background. Recently a simple photon-number-detection-based implementation of a quantum illumination-like scheme was provided in Phys. Rev. Lett. 101, 153603 (2013), where the enhancement was preserved despite the loss of nonclassicality. In the present paper, we investigate the source for quantum advantage in that realization. We introduce an effective two-mode description of the light sources and analyze the mutual information (MI) as a quantifier of total correlations in the effective two-mode picture. In the relevant regime of a highly thermalized background, we find that the improvement in the signal-to-noise ratio achieved by the entangled sources over the unentangled thermal ones amounts exactly to the ratio of the effective MIs of the corresponding sources. More precisely, both quantities tend to a common limit specified by the squared ratio of the respective cross correlations. A thorough analysis of the experimental data confirms this theoretical result.
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