Gaussian quantum illumination via monotone metrics

Quantum illumination is to discern the presence or absence of a target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small, the exponential decay constant can be computed using monotone metrics. We explicitly derive analytic formula for the decay constant of an arbitrary Gaussian input state in terms of first- and second-order moments assuming a low reflectivity target. Especially, further assuming large background noise, there is no need of symplectic diagonalization, which highly complicates the computation of decay constants. First, we show that the performance of a displaced two-mode squeezed vacuum (TMSV) state with low squeezing can be similar to that of a TMSV state with high squeezing. Second, we show that it is of utmost importance to prepare an efficient idler memory to outperform coherent states while providing a criterion on the idler memory transmittivity. Finally, we identify the region of physically possible correlations between the signal and idler modes that can outperform coherent states.