# Learning the dynamics of open quantum systems from their steady states

## TL;DR

This paper demonstrates that the steady states of open quantum systems governed by local Markovian dynamics contain enough information for full reconstruction of their dynamics using only local measurements, even in the presence of dissipation.

## Contribution

It introduces a method for reconstructing the Lindbladian of open quantum systems from local steady-state measurements, extending previous work to include dissipative dynamics.

## Key findings

- Reconstruction is feasible for generic local Markovian dynamics.
- The method accurately recovers the Lindbladian with fewer measurements for systems with finite-range interactions.
- External environment couplings can aid in reconstructing Hamiltonians with commuting terms.

## Abstract

Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to coupling to an external environment. This raises the question whether the steady states of such open quantum systems contain sufficient information allowing for full and efficient reconstruction of the system's dynamics. We find that such a reconstruction is possible for generic local Markovian dynamics. We propose a recovery method that uses only local measurements; for systems with finite-range interactions, the method recovers the Lindbladian acting on each spatial domain using only observables within that domain. We numerically study the accuracy of the reconstruction as a function of the number of measurements, type of open-system dynamics and system size. Interestingly, we show that couplings to external environments can in fact facilitate the reconstruction of Hamiltonians composed of commuting terms.