# Monitoring the dynamics of an open quantum system via a single qubit

## TL;DR

This paper demonstrates how a single qubit probe can effectively monitor the dissipative dynamics of an open quantum harmonic oscillator, providing detailed information about system parameters through coherence measurements.

## Contribution

It introduces a method to extract system dynamics and parameters of an open quantum system using a single qubit probe coupled via dephasing, with analytical results for a dissipative harmonic oscillator.

## Key findings

- Qubit coherence reveals detailed dissipative dynamics.
- Two initial states allow determination of all coupling constants and temperature.
- Analytical relation between qubit coherence and quantum fidelity.

## Abstract

We investigate the possibility to monitor the dynamics of an open quantum system with the help of a small probe system, coupled via dephasing coupling to the open system of interest. As an example, we consider a dissipative harmonic oscillator and a single qubit as probe system. Qubit plus oscillator are described by a finite temperature quantum master equation, where the dynamics of the whole system can be obtained analytically. We find that the short time behavior of the reduced qubit state (its coherence) provides exhaustive information on the dissipative dynamics of the oscillator. Observing this coherence for two initial states with different out-of-equilibrium temperatures, one can determine all coupling constants and the equilibrium temperature fixed by the external heat bath. In addition, the dephasing coupling to the qubit probe, may be considered as a perturbation of the dissipative oscillator. The corresponding quantum fidelity can be calculated analytically, also. Hence, we find the precise relation between the behavior of the reduced qubit state (its coherence) and that fidelity.