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

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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