  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 $\rho$ (state
for target absence) and $\sigma$ (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 $N_S < 0.295$.
