Phase-space quantum Wiener-Khintchine theorem

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 Grou