Estimating temperature via sequential measurements

We study the efficiency of estimation procedures in which the temperature of an external bath is indirectly recovered by monitoring the transformations induced on a probing system that is put in thermal contact with the bath. In particular we compare the performances of sequential measurement schemes-where the probe is initialized only once and measured repeatedly during its interaction with the bath-with those of measure and re-prepare approaches where instead, after each interaction and measurement stage, the probe is reinitialized into the same fiduciary state. From our analysis it is revealed that the sequential approach, while being in general not capable of providing the best accuracy achievable, is nonetheless more versatile with respect to the choice of the initial state of the probe, yielding on average smaller indetermination levels.