So can someone who understands quantum theory higher level than a simple idiot like myself confirm if this actually holds to real quantum physics, or is it just words?
As an expert scientician with a degree in science, I can tell you in my educated opinion that Santa's Quantum Superposition Theory is the best explanation for how I got a Zartan action figure in 1985 without ever telling my mom and dad I wanted one.
It also explains how everyone gets exactly what they asked Santa for. Before the present is opened it contains all possible presents and once you open it, it collapses to what you expected.
To a degree, yes. As was mentioned elsewhere there is a thing called Wave Function Collapse, which occurs when a measurement is taken of a quantum system and forces the system from superposition (multiple states at once) into a single state. A measurement could be seeing it, scanning it, bumping into it, etc (not human conscious observation, that's an old and weird interpretation and not relevant nowadays).
Before (and after as well) you actually collapse the wave function you can perform meaningful math using the quantum particles. The one way I'm familiar with is for computer calculations, which is what quantum computers are aiming for. This is basically done by canceling out certain possibilities to only allow the wave function to collapse into ways that give meaningful mathematic results.
As such, this is barely relatable to a quantum Santa which uses this nature to perform meaningful present sharing actions simultaneously using quantum superposition of a quantum system that is spread out over a very large area. Of course, basic quantum mechanics becomes statistically the same as normal physics (i.e. 10 quadrillion particles average out to one normal human), so Santa would need to be a reality bender to allow for such small chances to occur to allow a human sized being to affect a huge area... but whatever.
A quantum Santa could deliver presents to every house simultaneously if nothing observed his passage. On the other hand, at some point the wave function will collapse, like say when people check what presents are under the tree. When the wave function collapses, the probabilities all go away and there's a single answer, so he could deliver presents to one and only one house.