Álvarez Marcos, AinaraLuis Aina, Alfredo2023-06-222023-06-222022-09-070146-959210.1364/OL.467687https://hdl.handle.net/20.500.14352/72629© Optica Publishing Group ArXiv version includes some of the last recommendations that were not included in the journal version.We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detec-tion of phase-space displacements with a suitably designed quantum ruler. A phase-space-based quantum mutual coherence function is introduced that includes the contribu-tion of the detector. We obtain an universal equality linking resolution with coherence. This is illustrated with the case of Gaussian states and number states. (c) 2022 Optica Publishing Groupengjournal articlehttp://dx.doi.org/10.1364/OL.467687https://opg.optica.orgopen access535OpticsÓptica (Física)2209.19 Óptica Física