Phase-space quantum Wiener-Khintchine theorem.

Abstract

We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-space-based quantum mutual coherence function is introduced that includes the contribution of the detector. We obtain an universal equality linking resolution with coherence. This is illustrated with the case of Gaussian states and number states.