Infinite-fold Asymptotic Quantum Advantage in Classical Correlation Sensing

Abstract

We study the hypothesis testing problem of distinguishing between correlated thermal noise and uncorrelated thermal noise of the same average energy on $K$ detectors in asymptotic asymmetric hypothesis testing. We compare the performance of heterodyne or homodyne detection with classical post-processing, the most general quantum strategy (involving any arbitrary measurement), and a simple strategy involving a photonic chip and On-Off detection. When the average received energy per detector goes to zero, the photonic chip strategy asymptotically achieves the optimal decrease in the error, while heterodyne/homodyne measurements do not. Thus, we show that linear optics and On-Off measurement are enough to achieve better detection than classical methods when detecting correlations in thermal optical signals.