Imperfect photon detection in quantum illumination

In quantum illumination, various detection schemes have been proposed for harnessing the remaining quantum correlations of the entanglement-based resource state. To date, the only successful implementation in the microwave domain [R. Assouly, R. Dassonneville, T. Peronnin, A. Bienfait, and B. Huard, Nat. Phys. 19, 1418 (2023)] has relied on a specific mixing operation of the respective return and idler modes, followed by single-photon counting in one of the two mixer outputs. We investigate the performance of this scheme for realistic detection parameters in terms of the detection efficiency, dark-count probability, and photon-number resolution. Furthermore, we take the second mixer output into account and investigate the advantage of correlated photon counting (CPC) for a varying thermal background and optimum postprocessing weighting in CPC. We find that the requirements for photon-number resolution in the two mixer outputs are highly asymmetric due to different associated photon-number expectation values.