On structure-preserving transformations of the Ito generator matrix for model reduction of quantum feedback networks

TL;DR

This paper presents a unified framework for two common quantum feedback network model reduction techniques, showing they can be viewed as structure-preserving transformations of Ito generator matrices, and that their order of application does not matter.

Contribution

It introduces a novel perspective by casting model reduction operations as structure-preserving transformations of Ito generator matrices, demonstrating their commutativity.

Findings

Elimination of internal connections and adiabatic elimination are shown as structure-preserving transformations.

The order of applying these model reduction techniques is proven to be inconsequential.

The approach unifies different model reduction methods under a common mathematical framework.

Abstract

Two standard operations of model reduction for quantum feedback networks, elimination of internal connections under the instantaneous feedback limit and adiabatic elimination of fast degrees of freedom, are cast as structure-preserving transformations of It\=o generator matrices. It is shown that the order in which they are applied is inconsequential.