Doesn't this depend on the universe being not entirely discrete? If the universe is entirely discrete, then it should be possible to represent the exact state o

Doesn't this depend on the universe being not entirely discrete? If the universe is entirely discrete, then it should be possible to represent the exact state of it? In any case, I don't think it follows that an infinite amount of information is necessary to describe e.g. a dog to the extent to which it could be transferred and there being no functional difference to the copy, even though the exact state is not represented.