  We provide new results for computing and comparing the quantum gate fidelity
of quantum channels via their Choi matrices. We extend recent work that showed
there exist non-dual pairs of quantum channels with equal gate fidelity by
providing an explicit characterization of all such channels. We use our
characterization to show that when the dimension is 2 (or 3, under slightly
stronger hypotheses), the gate fidelity of two channels is equal if and only if
their difference equals the difference of some unital map and its dual -- a
fact that has been shown to be false when the dimension is 4 or larger. We also
present a formula for the minimum gate fidelity of a channel in terms of a
well-studied norm on a compression of its Choi matrix. As a consequence,
several new ways of bounding and approximating the minimum gate fidelity
follow, including a simple semidefinite program to compute it for qubit
channels.
