Wireless communication derives its power from the simultaneous emission of signals in multiple directions. However, in the context of quantum communication, this phenomenon must be reconciled carefully with the no-cloning principle. In this context, we here study how wireless communication of quantum information can be realized via relativistic fields. To this end, we extend existing frameworks to allow for a non-perturbative description of, e.g. quantum state transfer. We consider, in particular, the case of 1+1 spacetime dimensions, which already allows for a number of interesting scenarios, pointing to, for example, new methods for tasks similar to quantum secret sharing.