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 almost entirely taken into account by physical unitary operations. This result allows to separate coherent and decoherent signatures in signals and extract the level of coherence in noisy quantum devices of large dimensions.