Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.09827 · Quantum

Fundamental limits on low-temperature quantum thermometry with finite resolution

Patrick P. Potts, Jonatan Bohr Brask, Nicolas Brunner

Published Jul 9, 2019• 84 citations
arXivHTMLPDF

Abstract

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.

DOI
10.22331/q-2019-07-09-161

Related papers

Fundamental limits on low-temperature quantum thermometry

Patrick P. Hofer, 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. This leads to a simple condition under which the uncertainty in the temperature measurement must diverge exponentially with decreasing temperature, as seen in previous works. When this condition is not satisfied, a better scaling becomes possible, even with restricted measurement access. Our approach allows us to identify the mechanism that enables this advantage, which is ultimately limited by the third law of thermodynamics. 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.

•Nov 27, 2017•3 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

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

Thermometry in the quantum regime: recent theoretical progress

Mohammad Mehboudi, Anna Sanpera, Luis Alfonso Correa

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.

arXiv:1811.03988•Journal of Physics A Mathematical and Theoretical•Jun 10, 2019•193 citations

Optimal nonequilibrium thermometry in finite time

Pavel Sekatski, Martí Perarnau-Llobet

What is the minimum time required to take the temperature? In this paper, we solve this question for any process where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so that the probe's evolution is well described by a quantum Markovian master equation. Considering the most general control strategy on the probe (adaptive measurements, arbitrary control on the probe's state and Hamiltonian), we provide bounds on the achievable measurement precision in a finite amount of time, and show that in many scenarios these fundamental limits can be saturated with a relatively simple experiment. We find that for a general class of sample-probe interactions the scaling of the measurement uncertainty is inversely proportional to the time of the process, a shot-noise like behaviour that arises due to the dissipative nature of thermometry. As a side result, we show that the Lamb shift induced by the probe-sample interaction can play a relevant role in thermometry, allowing for finite measurement resolution in the low-temperature regime (more precisely, the measurement uncertainty decays polynomially with the temperature as $T\rightarrow 0$, in contrast to the usual exponential decay with $T^{-1}$). We illustrate these general results for (i) a qubit probe interacting with a bosonic sample, where the role of the Lamb shit is highlighted, and (ii) a collective superradiant coupling between a $N$-qubit probe and a sample, which enables a quadratic decay with $N^2$ of the measurement uncertainty.

•Jul 9, 2021•2 citations

Bayesian quantum thermometry based on thermodynamic length

Mathias R. Jørgensen, Jan Kołodyński, Mohammad Mehboudi +2 more

In this work we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a well-defined measure of estimation precision becomes nontrivial. Furthermore, the construction of a suitable criterion for optimal measurement design must be reexamined to account for the prior uncertainty. We propose a fully Bayesian approach to temperature estimation based on the concept of thermodynamic length, which solves both these problems. As an illustration of this framework, we consider thermal spin-$1/2$ particles and investigate the fundamental difference between two cases: on the one hand, when the spins are probing the temperature of a heat reservoir and, on the other, when the spins themselves constitute the sample.

arXiv:2108.05901•Physical Review A•Apr 1, 2022•26 citations
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.
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. This leads to a simple condition under which the uncertainty in the temperature measurement must diverge exponentially with decreasing temperature, as seen in previous works. When this condition is not satisfied, a better scaling becomes possible, even with restricted measurement access. Our approach allows us to identify the mechanism that enables this advantage, which is ultimately limited by the third law of thermodynamics. 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.
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.
What is the minimum time required to take the temperature? In this paper, we solve this question for any process where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so that the probe's evolution is well described by a quantum Markovian master equation. Considering the most general control strategy on the probe (adaptive measurements, arbitrary control on the probe's state and Hamiltonian), we provide bounds on the achievable measurement precision in a finite amount of time, and show that in many scenarios these fundamental limits can be saturated with a relatively simple experiment. We find that for a general class of sample-probe interactions the scaling of the measurement uncertainty is inversely proportional to the time of the process, a shot-noise like behaviour that arises due to the dissipative nature of thermometry. As a side result, we show that the Lamb shift induced by the probe-sample interaction can play a relevant role in thermometry, allowing for finite measurement resolution in the low-temperature regime (more precisely, the measurement uncertainty decays polynomially with the temperature as T→0T\rightarrow 0T→0, in contrast to the usual exponential decay with T−1T^{-1}T−1). We illustrate these general results for (i) a qubit probe interacting with a bosonic sample, where the role of the Lamb shit is highlighted, and (ii) a collective superradiant coupling between a NNN-qubit probe and a sample, which enables a quadratic decay with N2N^2N2 of the measurement uncertainty.
In this work we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a well-defined measure of estimation precision becomes nontrivial. Furthermore, the construction of a suitable criterion for optimal measurement design must be reexamined to account for the prior uncertainty. We propose a fully Bayesian approach to temperature estimation based on the concept of thermodynamic length, which solves both these problems. As an illustration of this framework, we consider thermal spin-1/21/21/2 particles and investigate the fundamental difference between two cases: on the one hand, when the spins are probing the temperature of a heat reservoir and, on the other, when the spins themselves constitute the sample.