# Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

## TL;DR

This paper introduces a method to determine the nonclassical nature of open quantum system dynamics by analyzing whether they can be simulated with Hamiltonian ensembles, linking simulation impossibility to quantum correlations.

## Contribution

It proposes a novel approach to assess system-environment correlations through Hamiltonian-ensemble simulation, defining nonclassicality based on simulation feasibility.

## Key findings

- Nonunital dynamics are classified as nonclassical.
- Examples include unital classical and unital nonclassical dynamics.
- Simulation impossibility indicates nonclassical correlations.

## Abstract

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.