Quantum Probes for Ohmic Environments at Thermal Equilibrium.It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states.  On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium.  In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes.  Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ω c ≲ T (in natural units).  For larger values of ω c , decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.
THERM