In quantum mechanics, all behavior is reduced to a mathematical representation, i.e. information and a set of rules. This should not be construed to mean that the universe is made of waves of probability or anysuch, but merely that these are the rules that precisely (albeit stochastically) describe all interactions, and that any interactions between local fields are interlinked, and interactions between distant (non-local) fields can be either connected via some kind of remote link (entanglement) or obey a set of rules that are not available to the observer embedded in that universe (non-local hidden variables). The idea that information cannot travel faster than light is an assumption in special and general relativity, but does not hold in most interpretations of quantum mechanics, or at least, not without a lot of additional gyrations to explain transactional mechanics (the apparent non-causal interactions) in a way that doesn’t violate local causality or local reality.
In QM terms, Laplace’s Daemon, containing all the information of the universe, would in essence be the universe itself. That is to say, in order to embed all the information to describe the universe it would have to have at least the same information volume and complexity as the universe, and therefore functionally indistinguishable from it. There is no possibility of representing the universe in toto as a synecdoche of itself, any more than you could have an exact copy of the Empire State Building down to the last fastener, brick, and window that would take any less information to replicate than building the Empire State Building itself, even if it physically occupied less room.