# Generalized Anti-Wick Quantum States

## TL;DR

This paper investigates a class of mixed quantum states called Toeplitz density operators, generalizing anti-Wick operators, and explores their properties using advanced functional analysis tools.

## Contribution

It introduces and analyzes a new class of mixed states called Toeplitz density operators, extending the concept of anti-Wick operators with a rigorous mathematical framework.

## Key findings

- Characterization of Toeplitz density operators as quantum states.
- Connection between Toeplitz operators and anti-Wick operators.
- Application of Feichtinger spaces in the analysis of these operators.

## Abstract

The purpose of this Note is to study a simple class of mixed states and the corresponding density operators (matrices). These operators, which we call quite Toeplitz density operators correspond to states obtained from a fixed function ("window") by position-momentum translations, and reduce in the simplest case to the anti-Wick operators considered long ago by Berezin. The rigorous study of Toeplitz operators requires the use of classes of functional spaces defined by Feichtinger.