Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies

Mehboudi, Mohammad; Jørgensen, Mathias R.; Seah, Stella; Brask, Jonatan Bohr; Kołodyński, Jan; Perarnau-Llobet, Martí

doi:10.1103/physrevlett.128.130502

Cited by 28 publications

(17 citation statements)

References 54 publications

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“…Lastly, it would be interesting to consider the problem of thermometry with Gaussian measurements in the context of the Bayesian formalism, which has been the subject of few recent works [40][41][42][43]. In particular, since the optimal Gaussian measurement is temperature dependent, this adds an extra challenge into designing optimal thermometry protocols when initial uncertainty about the true temperature is non negligible.…”

Section: Discussionmentioning

confidence: 99%

Thermometry of Gaussian quantum systems using Gaussian measurements

Cenni

Lami

Acín

et al. 2022

Quantum

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We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically, and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This is in contrast to the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while {on/off} photo-detection-like measurements do it for when the temperature tends to zero. Our results therefore pave the way for effective thermometry of Gaussian quantum systems using experimentally realizable measurements.

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Section: Discussionmentioning

confidence: 99%

Thermometry of Gaussian quantum systems using Gaussian measurements

Cenni

Lami

Acín

et al. 2022

Quantum

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“…Instead of continuing to measure at the a priori optimal time t s , we can change the recapture intervals at each measurement so as to maximise the information content of the posterior probability adaptively [37]. Specifically, 1.…”

Section: Adaptive Optimisation Of the Expansion Timementioning

confidence: 99%

“…However, in the experimentally relevant scenario of finite measurement records, with just tens or hundreds of shots, F does not always capture-even qualitatively-the behaviour of optimal temperature estimates. In these cases, one must adopt the more general Bayesian framework [32][33][34], which is only starting to be explored in quantum thermometry [35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Optimal cold atom thermometry using adaptive Bayesian strategies

Glatthard¹,

Rubio²,

Sawant³

et al. 2022

Preprint

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Precise temperature measurements on systems of few ultracold atoms is of paramount importance in quantum technology, but can be very resource-intensive. Here, we put forward an adaptive Bayesian framework that substantially boosts the performance of cold atom temperature estimation. Specifically, we process data from release-recapture thermometry experiments on few potassium atoms cooled down to the microkelvin range in an optical tweezer. We demonstrate that adaptively choosing the release-recapture times to maximise information gain does substantially reduce the number of measurements needed for the estimate to converge to a final reading. Unlike conventional methods, our proposal systematically avoids capturing and processing uninformative measurements. Furthermore, we are able to produce much more reliable estimates, especially when the measured data are scarce and noisy. Likewise, the resulting estimates converge faster to the real temperature in the asymptotic limit. Our method can be adapted to enhance the precision and resource-efficiency of many other techniques running on different experimental setups, thus opening new avenues in quantum thermometry.

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“…Relevant experimental realization of probe thermometry include single-atom probes for ultracold gases [7][8][9], NV centers acting as thermometers of living cells [10,11], and nanoscale electron calorimeters [12][13][14]. Theoretically, much progress has been achieved on characterizing the fundamental precision limits of probe thermometry in frequentist and Bayesian approaches [15][16][17][18][19][20][21][22][23], the precision scaling at ultralow temperatures [24][25][26][27][28], the impact of strong coupling and correlations [29][30][31][32][33][34], measurement back action [35,36], as well as enhanced sensing via non-equilibrium probes [37][38][39][40][41][42][43][44][45][46]. While providing remarkable progress on our understanding of thermometry, previous works are based on the assumption that the probe is measured and subsequently reset or discarded.…”

Section: Introductionmentioning

confidence: 99%

Probe thermometry with continuous measurements

Boeyens,

Annby-Andersson,

Bakhshinezhad

et al. 2023

New J. Phys.

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Temperature estimation plays a vital role across natural sciences. A standard approach is provided by probe thermometry, where a probe is brought into contact with the sample and examined after a certain amount of time has passed. In situations where, for example, preparation of the probe is non-trivial or total measurement time of the experiment is the main resource that must be optimized, continuously monitoring the probe may be preferred. Here, we consider a minimal model, where the probe is provided by a two-level system coupled to a thermal reservoir. Monitoring thermally activated transitions enables real-time estimation of temperature with increasing accuracy over time. Within this framework we comprehensively investigate thermometry in both bosonic and fermionic environments employing a Bayesian approach. Furthermore, we explore adaptive strategies and find a significant improvement on the precision. Additionally, we examine the impact of noise and find that adaptive strategies may suffer more than non-adaptive ones for short observation times. While our main focus is on thermometry, our results are easily extended to the estimation of other environmental parameters, such as chemical potentials and transition rates.

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Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies

Cited by 28 publications

References 54 publications

Thermometry of Gaussian quantum systems using Gaussian measurements

Thermometry of Gaussian quantum systems using Gaussian measurements

Optimal cold atom thermometry using adaptive Bayesian strategies

Probe thermometry with continuous measurements

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