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arXiv · 2104.10647

Role of topology in determining the precision of a finite thermometer

Alessandro Candeloro·Luca Razzoli·Paolo Bordone·Matteo G. A. Paris
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Abstract

Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modelling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.

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Alessandro Candeloro, Luca Razzoli, Paolo Bordone, Matteo G. A. Paris. 2021-04-21. Role of topology in determining the precision of a finite thermometer. https://doi.org/10.1103/physreve.104.014136

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