# Reachability in Infinite Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators

## TL;DR

This paper extends the understanding of reachability in infinite dimensional open quantum systems, demonstrating approximate controllability under certain conditions with switchable noise and bounded control Hamiltonians.

## Contribution

It generalizes finite-dimensional majorization results to infinite dimensions for quantum control systems with switchable noise and bounded Hamiltonians.

## Key findings

- Systems can approximately reach any state majorized by the initial state.
- The results apply to systems with switchable noise and bounded control Hamiltonians.
- Majorization-based controllability extends to infinite-dimensional quantum systems.

## Abstract

In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems following a unital Kossakowski-Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term $H_0$, finitely many bounded control Hamiltonians $H_j$ allowing for (at least) piecewise constant control amplitudes $u_j(t)\in{\mathbb R}$ plus a bang-bang (i.e. on-off) switchable noise term $\mathbf{\Gamma}_V$ in Kossakowski-Lindblad form. Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one, as up to now only has been known in finite dimensional analogues.---The proof of the result is currently limited to the control Hamiltonians $ H_j$ being bounded and noise terms $\mathbf{\Gamma}_V$ with compact normal $V$.