Collins diffraction formula and the Wigner function in entangled state representation

TL;DR

This paper explores the relationship between Collins diffraction formula and the Wigner function within entangled state representation, linking optical transformations with quantum phase space distributions.

Contribution

It establishes a connection between optical diffraction formulas and quantum entangled state representations, introducing the entangled Wigner function for analysis.

Findings

Derived the relationship between Collins diffraction and entangled Wigner function.

Linked output intensity with input probability distribution in phase space.

Extended analysis to both spatial and frequency domains.

Abstract

Based on the correspondence between Collins diffraction formula (optical Fresnel transform) and the transformation matrix element of a three-parameters two-mode squeezing operator in the entangled state representation (Opt. Lett. 31 (2006) 2622) we further explore the relationship between output field intensity determined by the Collins formula and the input field's probability distribution along an infinitely thin phase space strip both in spacial domain and frequency domain. The entangled Wigner function is introduced for recapitulating the result.