TITLE: Toy Models of Quantum Mechanics
QUESTION [33 upvotes]: Do toy models of quantum mechanics help us better understand "regular" quantum mechanics? For example, if we look at quantum mechanics over a finite field $F$ (e.g. $\mathbb{Z}_2$), can this lead to new insights for "regular" quantum mechanics? Or do these toy models just help clarify our understanding of "regular" quantum mechanics without actually providing any new insight? In other words, what is the utility of having toy models of quantum mechanics?

REPLY [2 votes]: The theory of nonlocal boxes is quite illuminating to the beginner (or expert) trying to get a handle on entanglement.  (Google "nonlocal box" or "box world".)