@vzn The reason why I was looking for toy models was to ease my own understanding of QM, not to accurately reproduce QM in every respect. But a significant learning experience come especially from understanding how exactly a certain toy model fails to accurately reproduce QM. The advanced areas come up, because I have heard them a long time ago without understanding them, and can understand them now.

ok so yet another zen question for you TK...

what is the simplest classical system with a born-like measurement rule? dont actually know the answer to that my self, but one answer may surprise you...

was heavily googling yesterday & actually, see that this ref is similar to the Qiaochu Yuan post you cited "Finite noncommutative probability, the Born rule, and wave function collapse"...

> The previous post on noncommutative probability was too long to leave much room for examples of random algebras. In this post we will describe all finite-dimensional random algebras with faithful states and all states on them. This will lead, in particular, to a derivation of the Born rule from statistical mechanics. We will then give a mathematical description of wave function collapse as taking a conditional expectation.

this is helpful but again at a very advanced & abstract level. how about something a little more applied?

this ref predates the Yuan blog by over a year...

Born's rule from measurements of classical signals by threshold detectors which are properly calibrated / Khrennikov

an admirable goal indeed going back to einsteinian gedanken.

... & have other physicists/ scientists succeeded?

plz star this over in physics chat room, might be able to draw in some new recruit(s)