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Abstract
This theoretical PhD project investigates the fundamental limits to the precision with which temperature can be estimated in quantum systems. The first part of the thesis presents a Bayesian formulation of temperature estimation theory, which is based on the thermodynamic length between thermal sample states. We show how the resulting temperature estimation theory can be mapped onto a Euclidean parameter estimation problem, and this insight makes it possible to apply precision bounds developed in this context. When mapping these bound from the Euclidean theory, back to the space of temperatures, it is found that the measure of precision resulting from a framework based on the thermodynamic length, has a natural interpretation as a generalized relative error.
The Bayesian approach to temperature estimation, in which a priori incomplete information is assumed, points to the need of effective adaptive strategies, with which the measurement strategy can be updated as temperature information is extracted. We propose two such adaptive strategies. In the case of equilibrium probe thermometry, we show that no nonadaptive measurement strategy can exhibit Heisenberglike scaling with the probe dimension. Furthermore, it is illustrated that an adaptive strategy can restore Heisenberglike scaling with the probe dimension. These results highlight the essential role of adaptation for thermometry.
The last part of this thesis investigates optimal thermometry under realistic constraints on the available measurements. In particular, we focus on the challenges associated with thermometry at very low temperatures. It is found that finite energyresolution fundamentally constrains the attainable sensitivity of a measurement to temperature in the ultracold regime. The relevance of the derived bounds is illustrated by considering a numerically exact simulation of a probebased thermometry protocol. Furthermore, we investigate fundamental limitations under constraints of measurements with only a finite number of distinguishable outcomes, and derive the associated precision bounds. It is shown that for the majority of manybody quantum systems, there exist coarsegrained measurements achieving a temperature sensitivity comparable to that of the manybody system itself.
The Bayesian approach to temperature estimation, in which a priori incomplete information is assumed, points to the need of effective adaptive strategies, with which the measurement strategy can be updated as temperature information is extracted. We propose two such adaptive strategies. In the case of equilibrium probe thermometry, we show that no nonadaptive measurement strategy can exhibit Heisenberglike scaling with the probe dimension. Furthermore, it is illustrated that an adaptive strategy can restore Heisenberglike scaling with the probe dimension. These results highlight the essential role of adaptation for thermometry.
The last part of this thesis investigates optimal thermometry under realistic constraints on the available measurements. In particular, we focus on the challenges associated with thermometry at very low temperatures. It is found that finite energyresolution fundamentally constrains the attainable sensitivity of a measurement to temperature in the ultracold regime. The relevance of the derived bounds is illustrated by considering a numerically exact simulation of a probebased thermometry protocol. Furthermore, we investigate fundamental limitations under constraints of measurements with only a finite number of distinguishable outcomes, and derive the associated precision bounds. It is shown that for the majority of manybody quantum systems, there exist coarsegrained measurements achieving a temperature sensitivity comparable to that of the manybody system itself.
Original language  English 

Publisher  Department of Physics, Technical University of Denmark 

Number of pages  178 
Publication status  Published  2021 
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 1 Finished

Quantum Thermodynamics and Quantum Information
Jørgensen, M. R. (PhD Student), Huber, M. (Examiner), NeergaardNielsen, J. S. (Examiner), Brask, J. B. (Main Supervisor), Huck, A. (Supervisor) & M?lmer, K. (Examiner)
15/09/2018 → 11/02/2022
Project: PhD