Discrimination of thermal baths by single-qubit probes

Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe. These concepts are illustrated in a linear-optical simulation.