The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasi-particle picture, which states that local entanglement spreads as if it was carried by quasi-particles which separate at a fixed speed. We extend the quasi-particle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.

7 pages, 7 figures, close to the published version