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.

DOI: 10.48550/arxiv.2503.17235

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