[Q_is_4_Quantum]

It is possible to make quantitative statements that I think capture many of the intuitions you assert. Here was one attempt:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.10...

That particular proposal was mathematically wrong for reasons I still find physically perplexing (it turns out that for some events quantum theory allows for stronger memory records - defined via classial mutual information - of entropy decreasing events!). A simple example is in here: https://arxiv.org/abs/0909.1726 (I am second author).

[lisper]

Very interesting! Thanks for the pointers! I'll need to take some time to digest these.