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We extend to "Euclidean" fields on a wide class of Riemannian manifolds two results which have proven to be crucial in the construction of interacting quantum fields in the flat case, namely local regularity properties of the free covariance in two dimensions and Osterwalder-Schrader positivity.

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The transmission of an excitation along a spin chain can be hindered by the presence of small fixed imperfections that create trapping regions where the excitation may get caught (Anderson localization). A certain degree of noise, ensuing from the interaction with a thermal bath, allows to overcome localization (noise-assisted transport). In this paper we investigate the relation between noise-assisted transport and (quantum) computation. In particular we prove that noise does assist classical computation on a quantum computing device but hinders the possibility of creating entanglement.