I don't understand. If they can measure and compare the states of two entangled photons to determine that the states are identical, then couldn't they encode information in the intervals between state changes by measuring the photons at a previously agreed upon rate? Or is it simply impossible to impute a state transition on one of the entangled photons?
Comparison of the states of each entangled particle, to find the signal, requires communication (light-speed); so while there was information sent, you can't figure out what it is until you receive a signal from the source of the transmission, thus no causal violations.
This is also why it's interesting cryptographically, unless you have information on the movements of both particles you can't pull a signal from the movements.
Why would you need to compare the states of the particles if you know a priori that they are entangled? Doesn't the theory say that the states will always match? I still don't understand why one side couldn't just measure the interval between state changes and use that channel to read information.
Correct. But in theory a small classical signal could be sent to essentially say "measure/extract data from the entangled particles in this way", and then the bandwidth from this communication would be based on the amount of data extractable from the entangled particles, while the latency will still be capped at however long it takes to send the classical signal
