  In bosonic quantum metrology, the estimate of a loss parameter is typically
performed by means of pure states, such as coherent, squeezed or entangled
states, while mixed thermal probes are discarded for their inferior
performance. Here we show that thermal sources with suitable correlations can
be engineered in such a way to approach, or even surpass, the error scaling of
coherent states in the presence of general Gaussian decoherence. Our findings
pave the way for practical quantum metrology with thermal sources in optical
instruments (e.g., photometers) or at different wavelengths (e.g., far
infrared, microwave or X-ray) where the generation of quantum features, such as
coherence, squeezing or entanglement, may be extremely challenging.
