1Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
2University of Potsdam, Institute of Physics and Astronomy, Karl-Liebknecht-Str. 24–25, 14476 Potsdam, Germany
3Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
4Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain
5Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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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.
Popular summary
When the probe–sample coupling is strong, the probe is not in a thermal state when at equilibrium with the sample. It is instead described by the so-called mean-force Gibbs state, which in general has complicated dependence on the coupling parameters and even temperature itself. As a result, the optimal thermometric measurement loses its simplicity, and it remains an open challenge to find general prescriptions for optimal thermometric measurements beyond the weak coupling regime.
Nonetheless, here we prove under minimal assumptions that that—surprisingly—energy measurements of the probe remain nearly optimal even at moderate coupling, beyond the weak coupling regime. This means that sophisticated measurement schemes exploiting coherences or using adaptive strategies do not confer any practical advantage as long as the coupling is not too strong.
Our take-home message? The experimental ability to measure a probe in its local basis will often be sufficient for precise thermometry.
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The above citations are from SAO/NASA ADS (last updated successfully 2023-11-28 12:59:52). The list may be incomplete as not all publishers provide suitable and complete citation data.
Could not fetch Crossref cited-by data during last attempt 2023-11-28 12:59:50: Could not fetch cited-by data for 10.22331/q-2023-11-28-1190 from Crossref. This is normal if the DOI was registered recently.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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- Source: https://quantum-journal.org/papers/q-2023-11-28-1190/
