  An average gate fidelity is a standard performance metric to quantify
deviation between an ideal unitary gate transformation and its realistic
experimental implementation. The average is taken with respect to states
uniformly distributed over the full Hilbert space. We analytically
(single-qubit) and numerically (two-qubit) show how this average changes if the
uniform distribution condition is relaxed, replaced by parametrized
distributions - polar cap and von Mises-Fisher distributions - and how the
resulting fidelities can differentiate certain noise models. In particular, we
demonstrate that Pauli channels with different noise rates along the three axes
can be faithfully distinguished using these augmented fidelities.
