In every entanglement experiment I've seen, it's not actually possible to use the entanglement to communicate faster than light or backward in time (which are effectively equivalent), even though it can be made clear from the results that entangled particles must exhibit supeluminal influence on each other. That influence always ends up disguised by quantum randomness. I don't expect that this experiment would be any different.

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Conserve energy. Commute with the Hamiltonian.