That is also my understanding, you can of course not make absolutely arbitrary choices or you could trivially turn two distinct physical states into each other

That is also my understanding, you can of course not make absolutely arbitrary choices or you could trivially turn two distinct physical states into each other but as far as I know you still have huge freedoms. I read the paper some time ago but I don't remember it as especially enlightening. Maybe I will take the opportunity to read it again over the weekend, maybe I can get something new out of it now that I missed the first time.