# Deformation Quantization of a Certain Type of Open Systems

## TL;DR

This paper presents a method for quantizing certain classical open quantum systems using deformation quantization, ensuring the preservation of complete positivity in their quantum evolution.

## Contribution

It introduces a systematic approach to quantize classical open systems into quantum open systems while maintaining their physical properties.

## Key findings

- Successfully quantized classical open systems preserving complete positivity
- Applied method to linearly coupled harmonic oscillators
- Demonstrated the approach's effectiveness in a standard example

## Abstract

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed.