Determining stationary-state quantum properties directly from system-environment interactions

TL;DR

This paper establishes a direct link between the properties and symmetries of open quantum systems and their dynamical parameters, enabling the prediction and engineering of steady-state quantum features without full state reconstruction.

Contribution

It introduces a method connecting Lyapunov equations to steady-state properties and symmetries, facilitating targeted steady-state quantum property engineering.

Findings

Conditions on dynamical parameters for entanglement, classicality, and steerability in steady states.

A symmetry-based approach to characterize steady states.

Application of the method to various examples for steady-state engineering.

Abstract

Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona-fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady-state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering process.