# Symmetries and physically realizable ensembles for open quantum systems

## TL;DR

This paper introduces symmetry-based methods to identify physically realizable ensembles in open quantum systems, simplifying the complex task of finding pure state trajectories in higher-dimensional systems.

## Contribution

The paper develops symmetry-based techniques, focusing on invariant subspaces and Wigner symmetries, to facilitate the discovery of physically realizable ensembles in complex quantum systems.

## Key findings

- Symmetry techniques can reduce the complexity of finding PREs.
- Analysis of known PREs reveals new insights into system dynamics.
- Foundation laid for studying higher-dimensional open quantum systems.

## Abstract

A $D$-dimensional Markovian open quantum system will undergo stochastic evolution which preserves pure states, if one monitors without loss of information the bath to which it is coupled. If a finite ensemble of pure states satisfies a particular set of constraint equations then it is possible to perform the monitoring in such a way that the (discontinuous) trajectory of the conditioned system state is, at all long times, restricted to those pure states. Finding these physically realizable ensembles (PREs) is typically very difficult, even numerically, when the system dimension is larger than 2. In this paper, we develop symmetry-based techniques that potentially greatly reduce the difficulty of finding a subset of all possible PREs. The two dynamical symmetries considered are an invariant subspace and a Wigner symmetry. An analysis of previously known PREs using the developed techniques provides us with new insights and lays the foundation for future studies of higher dimensional systems.