Role of topology in determining the precision of a finite thermometer

• URL: http://arxiv.org/abs/2104.10647v2
• Date: Fri, 30 Jul 2021 15:24:42 GMT
• Title: Role of topology in determining the precision of a finite thermometer
• Authors: Alessandro Candeloro, Luca Razzoli, Paolo Bordone and Matteo G. A. Paris
• Abstract summary: We find that low connectivity is a resource to build precise thermometers working at low temperatures. We compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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