Maybe in general, but this is in the context of "time loop logic". Ordinarily, you can have entangled states where measuring both parts will produce the same (random) outcome. Unfortunately the outcome cannot be influenced by either party, so it's useless for communication, as you say.

Now suppose that the first party resolves to go back in time and kill his grandfather unless the bits he measures are precisely the message he wishes to send. The universe can't tolerate the paradox, so it is corralled into the only non-paradoxical outcome: both parties read the desired message. Something like that, anyway.

Ah I guess I misunderstood what was being claimed. I thought the claim was "you can use entanglement to instantly send messages", but it's actually "you can use entanglement and this model of how time travel might work to send messages instantly".

Obviously these are rather different. In fact I feel like the entanglement doesn't even help in the time-travel protocol. If you want to send messages instantly and you can send messages back in time, you can "just" send yourself the message distance/c seconds in the past and send it then. Some messing around let's you arrange for it to arrive at exactly the time you want to send it in the future.

Assuming what I wrote above is correct (I don't actually know anything about closed time-like curves), it's actually weirder than just going back in time and mailing a letter early so it arrives when you want. Specifically, once you set up the entangled state, no other communication between the parties is necessary.

Yeah I understand the proposed protocol using entanglement. I'm just saying that if you're assuming we have access to the ability to send messages back in time there are much simpler protocols to achieve instant communication /without/ having to do anything involving entanglement.

IMO this is like those discussions where someone says FTL communication is possible by using a very long solid rod, jiggling one and and monitoring the other... except on closer inspection it'll only work if the rod is infinitely rigid, which is already a violation of many of the same underlying physical laws.

So it's a kind of circular logic, or at best an observation that having one kind of supernatural magic power would let you cause another kind of supernatural magic outcome.

In this case, if only I had a time machine I could break the speed of light. (Or possibly vice-versa.)