  The study of the dynamics of entanglement measures after a quench has become
a very active area of research in the last two decades, motivated by the
development of experimental techniques. However, exact results in this context
are available in only very few cases. In this work, we present the proof of the
quasiparticle picture for the dynamics of entanglement entropies for two
disjoint blocks in the XY chain after a quantum quench. As a byproduct, we also
prove the quasiparticle conjecture for the mutual information in that model.
Our calculations generalize those presented in [M. Fagotti, P. Calabrese, Phys.
Rev. A 78, 010306 (2008)] to the case where the correlation matrix is a
block-Toeplitz matrix, and rely on the multidimensional stationary phase
approximation in the scaling limit. We also test the quasiparticle predictions
against exact numerical calculations, and find excellent agreement. In the case
of three blocks, we show that the tripartite information vanishes when at least
two blocks are adjacent.
