This bugs me, and I don't know if I would be able to understand reasoning in answers on this thought experiment. Let say observer is on the earth in this example. Let him use quantum entangled pair of particles for sending information. Let information move from Earth to Proxima Centauri and back in one second... and that one second is the time where it is by Proxima Centauri. It means it will arrive to Proxima ~4 years before light manages to get there and then it will travel back instantaneously so it will be back after 1 second of being not on Earth. Where is time travel? Is it traveling in time only because light is slower? What happens in present time around Proxima Centauri could be observed after 4 years here. In my opinion what we will observe 4 years in future will be information from 4 years in past(from this present) and not from that present (4 years in future when the light will arrive) It would be time travel if in that first jump we travel 4 years into past and with second jump it would be second jump 4 years into past... Therefore the ship or information would appear 8??? years before starting the experiment on Earth.
edit: There was suggested answer to this example but I don't feel it was specific. Or I'm too stupid to understand it :) There was one example of sending signal by normal means and then it was prevented to send it before he sent it and thus breaking causality. Why should and how could anyone send signal in this example and then be prevented to send it by instantaneous signal from Proxima Centauri before he sends it? I mean,time is everywhere the same, there isn't time shift between relatively stationary objects, or is it?