Target Detection with Asymmetric Gaussian Classical Correlation

Abstract

We study the characteristics of two-mode classical correlation in Gaussian regime, which is produced by impinging a thermal state into a beam splitter. It is explicitly investigated how a measurement on one mode affects the other. The result enables the distinction between classical and quantum correlations. Then, we show how classically correlated states are advantageous in target detection, specifically for an asymmetric classical correlation with different mean photon numbers in the signal and idler modes. Under on-off detection, the classically correlated states significantly outperform quantum correlated states as the environmental thermal mean photon number increases. Furthermore, we demonstrate the advantage of local Gaussian operations in the target detection.

The paper asks when asymmetric, classically correlated Gaussian light can outperform a two-mode squeezed vacuum (TMSV) in target detection with restricted receivers. The classical source is obtained by splitting a thermal state, allowing independently chosen signal and idler mean photon numbers $N_S$ and $N_I$. Analytical conditional-state calculations compare idler on–off, photon-number-resolving, homodyne, and heterodyne measurements. For the split-thermal source, the conditional signal remains classical; corresponding TMSV measurements can prepare nonclassical states, although heterodyne conditioning produces a coherent state. For target detection using return–idler coincidence clicks, weak-reflection SNR expressions show that a bright classical idler can outperform TMSV at the same transmitted signal energy as background noise increases. At reflectance $\kappa=0.01$, $N_S=1$, and $N_I=100$, the crossover occurs near $N_B=2.04$, and the SNR ratio approaches $25.5$ at high background. For $N_S=0.001$ and $N_I=10^5$, the crossover rises to approximately $N_B=10^3$. The paper also derives approximate quantum-Chernoff error exponents for signal displacement and squeezing. In the bright-idler, bright-background regime, squeezing gives a larger exponent for equal operation parameters $|\alpha|^2=\sinh^2r$ when $N_S>1/2$. At fixed final signal energy, however, displacement performs better than squeezing and can outperform the unmodified source. The classical-over-TMSV result is explicitly receiver-dependent, not an advantage over optimal quantum illumination. The analysis uses weak-reflection approximations; the paper notes that classical sources do not outperform TMSV under photon-number-resolving detection and leaves non-Gaussian signal operations for future study.