"So, you might think, as you possibly did, that QM has lost information vis-a-vis classical mechanics, but it is the other way round. The classical limit has higher, not lower, entropy than the original QM description. (You know that: think of the ℏ-dependent info suppressed in the classical limit. Think of quantum computing.) In a sense, the momentum information of the classical trajectory is embedded in the x-spread of the Wigner function of its quantum progenitor, which the formalism correlates to its p-profile in an eerie way, thus ensuring the uncertainty principle prevails."