  Noise mechanisms in quantum systems can be broadly characterized as either
coherent (i.e., unitary) or incoherent. For a given fixed average error rate,
coherent noise mechanisms will generally lead to a larger worst-case error than
incoherent noise. We show that the coherence of a noise source can be
quantified by the unitarity, which we relate to the average change in purity
averaged over input pure states. We then show that the unitarity can be
efficiently estimated using a protocol based on randomized benchmarking that is
efficient and robust to state-preparation and measurement errors. We also show
that the unitarity provides a lower bound on the optimal achievable gate
infidelity under a given noisy process.
