Thermal quantum metrology in memoryless and correlated environments

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. This decoherence is modeled by including bosonic loss, thermal noise, and even the possibility of environmental correlations, so as to simulate non-Markovian dynamics. 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.