# Quasiprobability distribution functions from fractional Fourier transforms

## TL;DR

This paper introduces a new class of complex quasiprobability distribution functions derived from fractional Fourier transforms, linking them to Fresnel transforms and proposing a reconstruction method via atom-field interactions.

## Contribution

It presents a formal framework for quasiprobability functions based on fractional Fourier transforms and connects them to physical reconstruction techniques.

## Key findings

- New quasiprobability functions from fractional Fourier transforms
- Connection to Fresnel transform of characteristic functions
- Proposed method for distribution reconstruction via atom-field interactions

## Abstract

We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions.