Question

What are some experimental verifications of Born's rule in quantum mechanics?

Answer 1

Born's rule in quantum mechanicsstates that when measuring a system using a measuring device that can detect (=project onto) an orthogonal basis of states, the probability of obtaining a certain outcome equals tothe square of the modulus of theprojection of the (normalized) system's state onto the corresponding 

Answer 2

Born's rule (square of the modulus) has been verified experimentally numerous times. However, only the overall averages have been verified. For example if the prediction is 60% probability, then over large number of trials, the average outcome will approach the predicted value of 60%. This has been verified by measuring particle spin at angle A relative to the angle of its previously known spin angle. The prediction is square of cos(A/2). These predictions have also been verified with entangled pairs (Bell's state) where the same spin prediction is square of sin(A/2).

What has not been verified is whether the outcomes are due to independent probability, or they are guided by some balancing mechanism.

Hope it helps you.