Quantum Illumination with three-mode Gaussian State

Abstract

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 $N_S<0.295$.

11 pages, 1 figure v2: symplectic transformation is changed. Final result is not changed V3: 12 pages, will appear in QIP