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:2302.03061 · Quantum

Energy measurements remain thermometrically optimal beyond weak coupling

Jonas Glatthard, Karen V. Hovhannisyan, Martí Perarnau-Llobet, Luis Alfonso Correa, Harry J. D. Miller

Published Nov 28, 2023• 9 citations
arXivHTMLPDF

Abstract

We develop a general perturbative theory of finite-coupling quantum thermometry up to second order in probe-sample interaction. By assumption, the probe and sample are in thermal equilibrium, so the probe is described by the mean-force Gibbs state. We prove that the ultimate thermometric precision can be achieved – to second order in the coupling – solely by means of local energy measurements on the probe. Hence, seeking to extract temperature information from coherences or devising adaptive schemes confers no practical advantage in this regime. Additionally, we provide a closed-form expression for the quantum Fisher information, which captures the probe's sensitivity to temperature variations. Finally, we benchmark and illustrate the ease of use of our formulas with two simple examples. Our formalism makes no assumptions about separation of dynamical timescales or the nature of either the probe or the sample. Therefore, by providing analytical insight into both the thermal sensitivity and the optimal measurement for achieving it, our results pave the way for quantum thermometry in setups where finite-coupling effects cannot be ignored.

DOI
10.22331/q-2023-11-28-1190

Related papers

Multispin probes for thermometry in the strong-coupling regime

Marlon Brenes, Dvira Segal

We study the sensitivity of thermometric probes that are composed of $N$ spins coupled to a sample prepared at temperature $T$. Our analysis extends beyond the weak-coupling limit into the strong sample-probe coupling regime. In particular, sample-induced interactions between each of the spins are generated via strong coupling effects and are not fine-tuned among each body composing the probe. By employing the reaction-coordinate mapping to evaluate the noncanonical equilibrium state of the probe at finite coupling, we compute the thermometric sensitivity via the quantum Fisher information through the equilibrium state itself. We find that for single-spin probes $(N=1)$, temperature sensitivity decreases in the regime of weak-to-intermediate coupling strength, however, as the coupling increases we observe much higher sensitivity of the probe in the low-temperature regime. Furthermore, as long as $N>1$, there exist optimal values of the sample-probe interaction energy that allow one to attain enhanced thermometric sensitivity when compared to the maximum achieved precision obtained from thermal Gibbs states at weak coupling, particularly in the regime of low temperature. Finally, we show that this enhanced sensitivity may be observed from suboptimal measurements.

arXiv:2307.04232•Physical Review A•Sep 29, 2023•28 citations

Enhancement of low-temperature thermometry by strong coupling

Luis Alfonso Correa, Martí Perarnau-Llobet, Karen V. Hovhannisyan +3 more

We consider the problem of estimating the temperature $T$ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low $T$ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.

arXiv:1611.10123•Physical Review A•Dec 4, 2017•108 citations

Thermometric machine for ultraprecise thermometry of low temperatures

Ivan Henao, Karen V. Hovhannisyan, Raam Uzdin

Thermal equilibrium states are exponentially hard to distinguish at very low temperatures, making equilibrium quantum thermometry in this regime a formidable task. We present a thermometric scheme that circumvents this limitation, by using a two-level probe that does not thermalize with the sample whose temperature is measured. This is made possible thanks to a suitable interaction that couples the probe to the sample and to an auxiliary thermal bath known to be at a higher temperature. Provided a reasonable upper bound on the temperature of the sample, the resulting 'thermometric machine' drives the probe towards a steady state whose signal-to-noise ratio can achieve values as high as $\mathcal{O}(1/T)$. We also characterize the transient state of the probe and numerically illustrate an extreme reduction in the number of measurements to attain a given precision, as compared to optimal measurements on a thermalized probe.

arXiv:2108.10469•Aug 24, 2021•3 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

Coherence-Enhanced Spatial Quantum Thermometry

Asghar Ullah, Giovanni Scala, Luis L. Sánchez-Soto +1 more

Quantum thermometry has long promised sensitivities beyond classical limits, with recent paradigms highlighting quantum coherence as a primary driver of precision. While most studies focus on single-point temperature estimation, we extend this framework to the spatial domain. We consider a probe two-level system (TLS) coupled asymmetrically to an auxiliary TLS that equilibrates with a sample of profile T(x). The reduced probe state carries coherence in its local basis that remains temperature-sensitive after the probe transition has frozen out, yielding a Fisher information exponentially larger at low temperature than that of a population-only readout. An exact reparametrization converts the thermometric precision into a local spatial distinguishability bound; its validity requires only a sufficiently small relative temperature uncertainty and yields an explicit measurement budget. Adding auxiliary TLSs shifts the array's optimal working temperature upward and broadens the useful sensing window, with the achievable gain ultimately limited by the total available coupling rather than by an indefinite scaling law. Finally, we propose a microwave Mach-Zehnder interferometer that maps the temperature-dependent probe coherence onto an experimentally accessible quadrature observable.

quant-pharXiv:2609.26936•Sep 24, 2026•0 citations

Optimal nonequilibrium thermometry in Markovian environments

Pavel Sekatski, Martí Perarnau-Llobet

What is the minimum time required to take a temperature? In this paper, we solve this question for a large class of processes 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→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 shift is highlighted, and (ii) a collective superradiant coupling between a N -qubit probe and a sample, which enables a quadratic decay with N of the measurement uncertainty.

arXiv:2107.04425•Quantum•Dec 7, 2022•29 citations
We develop a general perturbative theory of finite-coupling quantum thermometry up to second order in probe-sample interaction. By assumption, the probe and sample are in thermal equilibrium, so the probe is described by the mean-force Gibbs state. We prove that the ultimate thermometric precision can be achieved – to second order in the coupling – solely by means of local energy measurements on the probe. Hence, seeking to extract temperature information from coherences or devising adaptive schemes confers no practical advantage in this regime. Additionally, we provide a closed-form expression for the quantum Fisher information, which captures the probe's sensitivity to temperature variations. Finally, we benchmark and illustrate the ease of use of our formulas with two simple examples. Our formalism makes no assumptions about separation of dynamical timescales or the nature of either the probe or the sample. Therefore, by providing analytical insight into both the thermal sensitivity and the optimal measurement for achieving it, our results pave the way for quantum thermometry in setups where finite-coupling effects cannot be ignored.
We study the sensitivity of thermometric probes that are composed of NNN spins coupled to a sample prepared at temperature TTT. Our analysis extends beyond the weak-coupling limit into the strong sample-probe coupling regime. In particular, sample-induced interactions between each of the spins are generated via strong coupling effects and are not fine-tuned among each body composing the probe. By employing the reaction-coordinate mapping to evaluate the noncanonical equilibrium state of the probe at finite coupling, we compute the thermometric sensitivity via the quantum Fisher information through the equilibrium state itself. We find that for single-spin probes (N=1)(N=1)(N=1), temperature sensitivity decreases in the regime of weak-to-intermediate coupling strength, however, as the coupling increases we observe much higher sensitivity of the probe in the low-temperature regime. Furthermore, as long as N>1N>1N>1, there exist optimal values of the sample-probe interaction energy that allow one to attain enhanced thermometric sensitivity when compared to the maximum achieved precision obtained from thermal Gibbs states at weak coupling, particularly in the regime of low temperature. Finally, we show that this enhanced sensitivity may be observed from suboptimal measurements.
We consider the problem of estimating the temperature TTT of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low TTT can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.
Thermal equilibrium states are exponentially hard to distinguish at very low temperatures, making equilibrium quantum thermometry in this regime a formidable task. We present a thermometric scheme that circumvents this limitation, by using a two-level probe that does not thermalize with the sample whose temperature is measured. This is made possible thanks to a suitable interaction that couples the probe to the sample and to an auxiliary thermal bath known to be at a higher temperature. Provided a reasonable upper bound on the temperature of the sample, the resulting 'thermometric machine' drives the probe towards a steady state whose signal-to-noise ratio can achieve values as high as O(1/T)\mathcal{O}(1/T)O(1/T). We also characterize the transient state of the probe and numerically illustrate an extreme reduction in the number of measurements to attain a given precision, as compared to optimal measurements on a thermalized probe.
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.
Quantum thermometry has long promised sensitivities beyond classical limits, with recent paradigms highlighting quantum coherence as a primary driver of precision. While most studies focus on single-point temperature estimation, we extend this framework to the spatial domain. We consider a probe two-level system (TLS) coupled asymmetrically to an auxiliary TLS that equilibrates with a sample of profile T(x). The reduced probe state carries coherence in its local basis that remains temperature-sensitive after the probe transition has frozen out, yielding a Fisher information exponentially larger at low temperature than that of a population-only readout. An exact reparametrization converts the thermometric precision into a local spatial distinguishability bound; its validity requires only a sufficiently small relative temperature uncertainty and yields an explicit measurement budget. Adding auxiliary TLSs shifts the array's optimal working temperature upward and broadens the useful sensing window, with the achievable gain ultimately limited by the total available coupling rather than by an indefinite scaling law. Finally, we propose a microwave Mach-Zehnder interferometer that maps the temperature-dependent probe coherence onto an experimentally accessible quadrature observable.
What is the minimum time required to take a temperature? In this paper, we solve this question for a large class of processes 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→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 shift is highlighted, and (ii) a collective superradiant coupling between a N -qubit probe and a sample, which enables a quadratic decay with N of the measurement uncertainty.