The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles1. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system’s interactions2. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions3,4. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts5,6,7,8,9,10,11. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply7,12. Our results will enable experimental studies of a range of quantum phenomena, including transport13,14, thermalization15, localization16 and entanglement growth17, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.