# Low dimensional manifolds for exact representation of open quantum systems

## TL;DR

This paper introduces methods to efficiently approximate open quantum systems by identifying low-dimensional manifolds of quasi-classical states, optimizing transformations to minimize quantum relative entropy, and enabling simpler numerical simulations.

## Contribution

It develops a family of analytical and computational techniques for deriving optimal unitary transformations based on Lie group representations to simplify open quantum system descriptions.

## Key findings

- Transforms minimize quantum relative entropy to quasi-classical states
- Coupled equations enable efficient numerical simulation
- Quantifies non-classicality and compares system complexities

## Abstract

Weakly nonlinear degrees of freedom in dissipative quantum systems tend to localize near manifolds of quasi-classical states. We present a family of analytical and computational methods for deriving optimal unitary model transformations based on representations of finite dimensional Lie groups. The transformations are optimal in that they minimize the quantum relative entropy distance between a given state and the quasi-classical manifold. This naturally splits the description of quantum states into quasi-classical coordinates that specify the nearest quasi-classical state and a transformed quantum state that can be represented in fewer basis levels. We derive coupled equations of motion for the coordinates and the transformed state and demonstrate how this can be exploited for efficient numerical simulation. Our optimization objective naturally quantifies the non-classicality of states occurring in some given open system dynamics. This allows us to compare the intrinsic complexity of different open quantum systems.