Imaging thermal sources naturally yields Gaussian states at the receiver, raising the question of whether Gaussian measurements can perform optimally in quantum imaging. In this Letter, we establish no-go theorems on the performance of Gaussian measurements for imaging thermal sources in the limit of mean photon number per temporal mode $\epsilon \to 0$ or source size $L\to 0$. We show that non-Gaussian measurements can outperform any Gaussian measurement in the scaling of the estimation variance with $\epsilon$ (or $L$). We also present several examples to illustrate the no-go results.

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• Imaging & optical processing
• Optical interferometry
• Quantum information processing with continuous variables
• Quantum metrology
• Quantum optics
• Quantum parameter estimation
• Quantum sensing