# A Direct Coupling Coherent Quantum Observer for a Qubit, including Observer Measurements

## TL;DR

This paper introduces a novel direct coupling coherent quantum observer for a two-level quantum system, integrating homodyne detection, ensuring non-intrusive measurement, and demonstrating convergence of the observer to the plant variable.

## Contribution

It presents a new design for a coherent quantum observer that includes measurement capabilities and guarantees non-disturbance of the quantum plant's variable.

## Key findings

- Observer design ensures convergence to the plant variable.
- Inclusion of homodyne detection allows measurement without disturbance.
- Linear quantum stochastic differential equations describe the system.

## Abstract

This paper proposes a direct coupling coherent quantum observer for a quantum plant which consists of a two level quantum system. The quantum observer, which is a quantum harmonic oscillator, includes homodyne detection measurements. It is shown that the observer can be designed so that it does not affect the quantum variable of interest in the quantum plant and that measured output converges in a given sense to the plant variable of interest. Also, the plant variable of interest-observer system can be described by a set of linear quantum stochastic differential equations. A minimum variance unbiased estimator form of the Kalman filter is derived for linear quantum systems and applied to the direct coupled coherent quantum observer.