Thermometry of Gaussian quantum systems using Gaussian measurements

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