When applied to different input states, an imperfect quantum operation yields output states with varying fidelities, defined as the absolute square of their overlap with the desired states. We present an expression for the distribution of fidelities for a class of operations applied to a general qubit state, and we present general expressions for the variance and input-space averaged fidelities of arbitrary linear maps on finite dimensional Hilbert spaces.
@article{arxiv.0807.4843,
title = {The distribution of quantum fidelities},
author = {Line Hjortshoj Pedersen and Niels Martin Moller and Klaus Molmer},
journal= {arXiv preprint arXiv:0807.4843},
year = {2009}
}