That would mean that quantum communication is not possible — yet it has been demonstrated.

What quantum says is that you cannot create entanglement among two particles when they are separated by a distance that is greater than the individual wave function of each particle (i.e., their wave functions must overlap to be able to entangle them); but once particles are entangled, the entanglement can span any distance, and that entanglement can be used to communicate information, because the two particles behave as one wave function, and so if one observes the wave function in one place, that observation must be consistent with any observation in any other place — i.e., where the second entangled particle is.

** Except** for the case when the state of the first and second particle are never compared. That is, the observer of the first particle must be considered to be part of the wave function that is observed by a second observer.