Typical behavior of the quantum gate fidelity

The quantum gate fidelity provides methods for measuring the distance between unitary and general quantum operations. The goal of this paper is to discuss and prove various properties of the gate fidelity, some of which help characterize quantum processes. 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 for an arbitrary quantum channel is shown to become indistinguishable from that of a depolarizing channel. Methods for estimating the minimum of the gate fidelity are also presented.