# General Galilei Covariant Gaussian Maps

## TL;DR

This paper characterizes non-Markovian Gaussian maps that are covariant under Galilean transformations, extending known results and applying them to measures of macroscopicity in quantum systems.

## Contribution

It provides a comprehensive characterization of Galilei covariant Gaussian maps, including non-Markovian cases, and discusses their implications for measures of macroscopicity.

## Key findings

- Reduction to Holevo's Markovian result in the limit
- Extension of macroscopicity measures to non-Markovian maps
- Analysis of dissipation and covariance in quantum maps

## Abstract

We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we characterize translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined in Nimmrichter and Hornbergerl. [Phys. Rev. Lett. 110, 16 (2013)].