Flag-based Control of Orbit Dynamics in Quantum Lindblad Systems

TL;DR

This paper introduces a flag-based control approach for quantum Lindblad systems, enabling the separation of orbit dynamics and analysis of controllability using a finite set of flags, with implications for low-purity states.

Contribution

It presents a novel control framework that separates orbit dynamics in quantum Lindblad systems using flag variables and analyzes controllability with finite flag sets.

Findings

Dynamics can be separated into inter- and intra-orbit components.

Controllability can be analyzed with a finite set of flags.

Effective flag sets are identified for low-purity orbits.

Abstract

In this paper, we demonstrate that the dynamics of an $n$-dimensional Lindblad control system can be separated into its inter- and intra-orbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density operator spectra, where the flag representing the eigenspaces is viewed as a control variable. The local controllability properties of this control system can be analyzed when the control-set of flags is limited to a finite subset. In particular, there is a natural finite subset of $n!$ flags that are effective for low-purity orbits.