Postdoc @ University of Geneva
Friday July 1 – 12.30 BST
Feasible measurements for thermometry of Gaussian quantum systems
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 contrasts with 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 photo-detection-like measurements do it for when the temperature tends to zero. Lastly, we present an example where, despite being sub-optimal, Gaussian measurements can exploit bath induced correlations to enhance thermometry precision at extremely low temperatures. Our results therefore put forward an experimentally realizable thermometry protocol for Gaussian quantum.
2. Phys. Rev. Lett. 128, 040502 (2022)