Thermometry of Gaussian quantum systems using Gaussian measurements

Marina F.B. Cenni1, Ludovico Lami2, Antonio Acín1,3, and Mohammad Mehboudi4

1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
2Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
3ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010, Barcelona, Spain
4Département de Physique Appliquée, Université de Genève, 1205 Genève, Switzerland

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Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:
22 pages. More details are introduced compared to version 1, namely an example with maximum likelihood estimator for thermometry is added

Abstract

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 $\textit{experimentally realizable measurements}$.

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Cited by

[1] Safoura S. Mirkhalaf, Mohammad Mehboudi, and Saleh Rahimi-Keshari, "Operational significance of nonclassicality in nonequilibrium Gaussian quantum thermometry", arXiv:2207.10742.

[2] Muhammad Miskeen Khan, Mohammad Mehboudi, Hugo Terças, Maciej Lewenstein, and Miguel Angel Garcia-March, "Subnanokelvin thermometry of an interacting d -dimensional homogeneous Bose gas", Physical Review Research 4 2, 023191 (2022).

[3] Guim Planella, Marina F. B. Cenni, Antonio Acín, and Mohammad Mehboudi, "Bath-Induced Correlations Enhance Thermometry Precision at Low Temperatures", Physical Review Letters 128 4, 040502 (2022).

[4] Massimo Frigerio, Stefano Olivares, and Matteo G. A. Paris, "Cost-effective estimation of single-mode thermal states by probabilistic quantum metrology", Quantum Science and Technology 7 3, 035011 (2022).

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