  The paper analyzes the behavior of quantum channels, particularly in large
dimensions, by proving various properties of the quantum gate fidelity. Many of
these properties are of independent interest in the theory of distance measures
on quantum operations. A non-uniqueness result for the gate fidelity is proven,
a consequence of which is the existence of non-depolarizing channels that
produce a constant gate fidelity on pure states. Asymptotically, the gate
fidelity associated with any quantum channel is shown to converge to that of a
depolarizing channel. Methods for estimating the minimum of the gate fidelity
are also presented.
