Abstract

Majorana fermions offer a possible way to realize the universal quantum computation. It was shown if the noisy ancillae are convex mixtures of Gaussian fermionic states and the computation involves only non-interacting fermions operations, one can classically simulate such quantum computation. Hence rises the interest in developing a complete criterion that determines whether a state is convex-Gaussian. I will review a criterion by de Melo et al. that aims at characterizing the set of convex-Gaussian state from the outside and introduce a new one that characterizes the set from the inside. If a state fails the first program, it is not convex-Gaussian, and if it is passes the new one, it is convex-Gaussian. Both criteria are complete, i.e. the set of convex-Gaussian states can be approximated with an arbitrary precision by states that pass these criteria.