Say I start with an amplitude distribution- essentially an n (potentially infinite) dimensional configuration space with a complex numbered value at each point.

This is essentially an infinite set of (n+2)tuplets. If I knew the dimensionality of the configuration space, I could also determine the cardinality of the set of n+2-tuplets for a particular distribution, as well as that of the set of all possible such sets of n+2-tuplets. (Unless, of course, one of these collections turns out to be pathologically large, hence not a set, but I don't know why that should be).

Then it would seem that I can represent a quantum amplitude distribution as a single point moving around in a configuration space- albeit a much, much larger one.