  We theoretically investigate the entanglement dynamics in photonic Mott
insulators in the presence of particle losses and dephasing. We explore two
configurations where entanglement is generated following the injection or
extraction of a photon in the central site of a chain of cavity resonators. We
study the entanglement negativity of two-site reduced density matrices as a
function of time and inter-site distance. Our findings show that in spite of
particle losses the quantum entanglement propagation exhibits a ballistic
character with propagation speeds related to the differerent quasiparticles
that are involved in the dynamics, namely photonic doublons and holons
respectively. Our analysis reveals that photon dissipation has a strikingly
asymmetric behavior in the two configurations with a much more dramatic role on
the holon entanglement propagation than for the doublon case.
