There's a result called the no-signaling theorem; the choice of measurement on side A has no effect on the reduced quantum state on side B, therefore does not i

There's a result called the no-signaling theorem; the choice of measurement on side A has no effect on the reduced quantum state on side B, therefore does not influence the outcome statistics of any measurement on side B: https://en.m.wikipedia.org/wiki/No-communication_theorem https://en.m.wikipedia.org/wiki/No-communication_theorem A might know exactly what B is going to measure, after he's done his part, but that doesn't mean any information can be transmitted.