Anyway, I think I understand better now. It is best to think of it in terms of a single particle in a single dimension.
If I have the quantum state of a single particle in one dimension and the expectation value for position then I could evolve it forward and get the quantum state at a future date with the expectation value of where the particle would be then.
Then I could start with the future quantum state and evolve it backwards and get my original quantum state with the same expectation value.
So Laplace's Demon doesn't need information about a particular momentum and position, rather he needs the quantum state - the probability distribution.
Similarly, in order to get back to the encyclopedia Laplace's Demon would not need a particular state of ashes and light, but rather a probability distribution of all the ways that the ashes and light could be as a result of the encyclopedia burning.