Phase-space quantum Wiener-Khintchine theorem

TL;DR

This paper develops a quantum analogue of the Wiener-Khintchine theorem using phase-space methods, linking resolution and coherence in quantum optical systems, with applications to Gaussian and number states.

Contribution

It introduces a phase-space quantum mutual coherence function that incorporates detector effects, establishing a universal relation between resolution and coherence.

Findings

Derived a quantum Wiener-Khintchine theorem in phase-space

Established a universal equality linking resolution and coherence

Illustrated results with Gaussian and number states

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-pace 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.