Quantum Illumination with three-mode Gaussian State

The quantum illumination is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that the quantum Bhattacharyya bound between ρ (state for target absence) and σ (state for target presence) is less than the previous result derived by two-mode Gaussian state when N_S, average photon number per signal, is less than 0.295. This indicates that the quantum illumination with three-mode Gaussian state gives less error probability compared to that with two-mode Gaussian state when N_S < 0.295.