In this case, you have to "measure" the particle in a particular way to retrieve the energy, and that way depends on what happened to the particle on the other side while the energy is being "pumped in" (so you cannot know in advance).
So you take a trillions and trillions and trillions of particles, and start measuring them randomly at once... Eventually you get lucky, and one of them gives you a return on energy. Poof, instant information transfer, but without having the data that you "needed" to do it. No waiting in line!