  We compute the entanglement entropy and mutual information for two disjoint
intervals in two-dimensional conformal field theories as a function of time
after a local quench, using the replica trick and boundary conformal field
theory. We obtain explicit formulae for the universal contributions, which are
leading in the regimes of, for example, close or well-separated intervals of
fixed length. The results are largely consistent with the quasiparticle
picture, in which entanglement above that present in the ground state is
carried by pairs of entangled, freely propagating excitations. We also
calculate the mutual information for two disjoint intervals in a proposed
holographic local quench, whose holographic energy-momentum tensor matches the
conformal field theory one. We find that the holographic mutual information
shows qualitative differences from the conformal field theory results and we
discuss possible interpretations of this.
