# Completely Positive Divisibility Does Not Mean Markovianity

## TL;DR

This paper demonstrates that in quantum processes, complete positive divisibility does not necessarily imply Markovian behavior, revealing complex non-Markovian correlations using advanced process tensor formalism.

## Contribution

It provides a full classification of non-Markovian quantum processes that are CP-divisible, challenging the assumption that divisibility implies Markovianity in quantum systems.

## Key findings

- CP-divisible quantum processes can be non-Markovian
- Process tensor formalism effectively classifies quantum correlations
- Divisibility does not guarantee Markovianity in quantum dynamics

## Abstract

In the classical domain, it is well-known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely positive (CP) divisible quantum processes can still involve non-Markovian temporal correlations, that we then fully classify using the recently developed process tensor formalism, which generalizes the theory of stochastic processes to the quantum domain.