  Inevitably, assessing the overall performance of a quantum computer must rely
on characterizing some of its elementary constituents and, from this
information, formulate a broader statement concerning more complex
constructions thereof. However, given the vastitude of possible quantum errors
as well as their coherent nature, accurately inferring the quality of composite
operations is generally difficult. To navigate through this jumble, we
introduce a non-physical simplification of quantum maps that we refer to as the
leading Kraus (LK) approximation. The uncluttered parameterization of LK
approximated maps naturally suggests the introduction of a unitary-decoherent
polar factorization for quantum channels in any dimension. We then leverage
this structural dichotomy to bound the evolution -- as circuits grow in depth
-- of two of the most experimentally relevant figures of merit, namely the
average process fidelity and the unitarity. We demonstrate that the leeway in
the behavior of the process fidelity is essentially taken into account by
physical unitary operations.
