# Estimating Temperature via Sequential Measurements

## TL;DR

This paper compares sequential measurement schemes and measure & re-prepare approaches for estimating bath temperature via a probe, finding sequential methods are more versatile and often yield lower uncertainty despite not always being the most accurate.

## Contribution

It introduces a comparative analysis of sequential and re-prepare measurement strategies for temperature estimation, highlighting the advantages of sequential schemes.

## Key findings

- Sequential schemes are more versatile in initial state choice.
- Sequential methods generally produce smaller uncertainty levels.
- Sequential approaches are not always the most accurate but are more adaptable.

## Abstract

We study the efficiency of estimation procedures where 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 & 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.