Why can't the commitment schemes have both information theoretic hiding and binding properties? The commitment schemes like Pedersen's or Hash based, either have information theoretic hiding and computational binding or computational hiding and information theoretic binding. So can we ever get both information theoretic hiding and binding? Is it ever possible to do, or it is proven to be impossible?
It's impossible. In order to be perfectly hiding, it must be the case that two different messages can produce the same commitment string. But then that commitment can be opened in two ways (by an unbounded committer), so the scheme is not perfectly binding.