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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 <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">experimentally realizable measurements<\/mml:mtext><\/mml:mrow><\/mml:math>.<\/jats:p>","DOI":"10.22331\/q-2022-06-23-743","type":"journal-article","created":{"date-parts":[[2022,6,23]],"date-time":"2022-06-23T15:02:00Z","timestamp":1655996520000},"page":"743","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":19,"title":["Thermometry of Gaussian quantum systems using Gaussian measurements"],"prefix":"10.22331","volume":"6","author":[{"given":"Marina F.B.","family":"Cenni","sequence":"first","affiliation":[{"name":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ludovico","family":"Lami","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik und IQST, Universit\u00e4t Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Ac\u00edn","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"},{"name":"ICREA-Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, 08010, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Mehboudi","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Physique Appliqu\u00e9e, Universit\u00e9 de Gen\u00e8ve, 1205 Gen\u00e8ve, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Mohammad Mehboudi, Anna Sanpera, and Luis A Correa. 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