The time of the change is controllable only by the first person to do it. The other person has no way to tell when the first person did it. You cannot see whether a photon has collapsed until you measure it. When you look at your photon and observe it collapse to a particular state you don't know if the other guy did it first or if you were the first one to do it. Thus timing information cannot be exchanged.
You cannot remove the random choice for input. When you look at a photon, its state collapses randomly, you have no way to influence its final state. You must take what you get.
You cannot remove the random choice for input. When you look at a photon, its state collapses randomly, you have no way to influence its final state. You must take what you get.