The Unruh effect, predicting a thermal reservoir for accelerating systems, calls for a more refined understanding of measurement processes involving quantum systems as thermometers. Conventional models fail to account for the inherent spatial extent of the thermometer, neglecting the complexities associated with accelerated extended quantum systems. Our work builds upon the seminal work of Bell et al. [Z. Phys. C 28, 75 (1985).]. We propose a refined thermometer model incorporating a spin-1/2 particle where the spin acts as a temperature indicator. This refined model demonstrates the ability to effectively measure the temperature under specific, realistic conditions, providing a unique value that essentially averages the local Unruh temperatures throughout the extended quantum system acting as the thermometer.

The Leggett-Garg inequalities have been proposed to identify the quantum behavior of a system; specifically, the violation of macrorealism. They are usually implemented by performing two sequential measurements on quantum systems, calculating the correlators of such measurements and then combining them arriving at Leggett-Garg inequalities. However, this approach only provides sufficient conditions for the violation of macrorealism. Recently, an alternative approach was proposed that uses nondemolition measurements and gives both a necessary and sufficient condition for the violation of macrorealism. By storing the information in a quantum detector, it is possible to construct a quasiprobability distribution whose negative regions unequivocally identify the quantum behavior of the system. Here, we perform a detailed comparison between these two approaches. The use of the IBM quantum simulators allows us to evaluate the performance in real-case situations and to include both the statistical and environmental noise. We find that the nondemolition approach is not only able to always identify the quantum features, but it requires fewer resources than the standard Leggett-Garg inequalities. In addition, while the efficiency of the latter is strongly affected by the presence of the noise, the nondemolition approach results incredibly robust and its efficiency remains unchanged by the noise. These results make the nondemolition approach a viable alternative to the Leggett-Garg inequalities to identify the violation of macrorealism.