> I don't think that it can be used to transmit information at all

What if the "no-cloning theorem"[0] wasn't actually right? That would enable doing a bunch of copies of the same particle state, making it possible to predict the probability distribution of each particle. That way it would be possible to send information doing measurements[1] rather than forcing a particle state.

[0] https://en.wikipedia.org/wiki/No-cloning_theorem

[1] https://www.forbes.com/sites/chadorzel/2016/05/04/the-real-r...