# Coarse graining a non-Markovian collisional model

## TL;DR

This paper derives an analytical relation between coarse graining time and environmental correlation time for non-Markovian qubit dynamics, enabling better understanding and modeling of noise effects in quantum systems.

## Contribution

It provides the first analytical relation between coarse graining time and correlation time for non-Markovian quantum dynamics, applicable to various environmental correlation distributions.

## Key findings

- Derived an explicit relation between $t_{CG}$ and $ au$ for a qubit.
- Validated the relation using a collisional model with correlated qutrits.
- Applicable to general environmental correlation distributions.

## Abstract

The dynamics of systems subjected to noise is called Markovian in the absence of memory effects, i.e. when its immediate future only depends on its present. Time correlations in the noise source may generate non-Markovian effects that, sometimes, can be erased by appropriately coarse graining the time evolution of the system. In general, the coarse graining time $t_\text{CG}$ is taken to be much larger than the correlation time $\tau$ but no direct relation between them is established. Here we analytically obtain a relation between $t_\text{CG}$ and $\tau$ for the dynamics of a qubit subjected to a time correlated environment. Our results can be applied in principle to any distribution of the environmental correlations and can be tested through a collisional model where the qubit sequentially interacts with correlated qutrits.