© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1811.03988 · Journal of Physics A Mathematical and Theoretical

Thermometry in the quantum regime: recent theoretical progress

Mohammad Mehboudi, Anna Sanpera, Luis Alfonso Correa

Published Jun 10, 2019• 193 citations

Abstract

Abstract Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

DOI: 10.1088/1751-8121/ab2828

Related papers

Quantum Thermometry

Antonella De Pasquale, Thomas M. Stace

We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, therefore these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.

arXiv:1807.05762•Fundamental theories of physics•Jan 1, 2018•26 citations

Fundamental limits on low-temperature quantum thermometry with finite resolution

Patrick P. Potts, Jonatan Bohr Brask, Nicolas Brunner

While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. {We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty}. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.

arXiv:1711.09827•Quantum•Jul 9, 2019•84 citations

Global quantum thermometry based on the optimal biased bound

Shoukang Chang, Yunbin Yan, Lu Wang +8 more

Thermometry is a fundamental parameter estimation problem that is crucial for the advancement of natural sciences. One widely adopted approach to address this issue is the local thermometry theory, which employs classical and quantum Cramér-Rao bounds as benchmarks for thermometric precision. However, this theory is constrained to decrease temperature fluctuations around a known temperature value, hardly tackling the precision thermometry problem over a wide temperature range. To overcome this limitation, we derive two basic bounds on thermometry precision within a global framework, i.e., classical and quantum optimal biased bounds. By implementing energy measurements on a thermal equilibrium system, the quantum optimal biased bound can be saturated. Furthermore, we demonstrate their thermometry performance through two specific applications: a noninteracting spin- 1 / 2 gas and a thermalized quantum harmonic oscillator. Our results indicate that, compared to local thermometry, global thermometry provides superior temperature estimation performance. Notably, global error bound approaches its local approximation under asymptotic cases. Published by the American Physical Society 2024

arXiv:2305.08397•Physical Review Research•Nov 19, 2024•5 citations

Enhanced precision bound of low-temperature quantum thermometry via dynamical control

Victor Mukherjee, Analía Zwick, Arnab Ghosh +2 more

Abstract High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.

arXiv:1711.09660•Communications Physics•Dec 13, 2019•61 citations

Tight bound on finite-resolution quantum thermometry at low temperatures

Mathias R. Jørgensen, Patrick P. Potts, Matteo G. A. Paris +1 more

This work analyzes the fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. It derives a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero, showing that the variance in any temperature estimate must decrease slower than linearly.

•Jan 1, 2020•35 citations

Tight bound on finite-resolution quantum thermometry at low temperatures

Mathias R. Jørgensen, Patrick P. Potts, Matteo G. A. Paris +1 more

This work analyzes the fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. It derives a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero, showing that the variance in any temperature estimate must decrease slower than linearly.

arXiv:2001.04096•Physical Review Research•Sep 11, 2020•46 citations

Abstract Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, therefore these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.

While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. {We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty}. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.

Thermometry is a fundamental parameter estimation problem that is crucial for the advancement of natural sciences. One widely adopted approach to address this issue is the local thermometry theory, which employs classical and quantum Cramér-Rao bounds as benchmarks for thermometric precision. However, this theory is constrained to decrease temperature fluctuations around a known temperature value, hardly tackling the precision thermometry problem over a wide temperature range. To overcome this limitation, we derive two basic bounds on thermometry precision within a global framework, i.e., classical and quantum optimal biased bounds. By implementing energy measurements on a thermal equilibrium system, the quantum optimal biased bound can be saturated. Furthermore, we demonstrate their thermometry performance through two specific applications: a noninteracting spin- 1 / 2 gas and a thermalized quantum harmonic oscillator. Our results indicate that, compared to local thermometry, global thermometry provides superior temperature estimation performance. Notably, global error bound approaches its local approximation under asymptotic cases. Published by the American Physical Society 2024

Abstract High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.