# $q$-deformed quadrature operator and optical tomogram

## TL;DR

This paper introduces a $q$-deformed quadrature operator, derives its wavefunctions, and computes the optical tomogram for $q$-deformed coherent states, advancing quantum optics and deformation theory.

## Contribution

It defines a new $q$-deformed quadrature operator and provides analytical expressions for wavefunctions and tomograms of $q$-deformed states, which were not previously available.

## Key findings

- Explicit wavefunctions of $q$-deformed oscillator in quadrature basis
- Analytical expression for the tomogram of $q$-deformed coherent states
- Eigenstates of the $q$-deformed quadrature operator derived

## Abstract

In this letter, we define the homodyne $q$-deformed quadrature operator. Analytic expression for the wavefunctions of $q$-deformed oscillator in the quadrature basis are found. Furthermore, we compute the explicit analytical expression for the tomogram of the $q$-deformed coherent states by finding the eigenstates of the $q$-deformed quadrature operator.