Gleason's theorem

Gleason's theorem is a fundamental result in quantum physics that explains how probabilities of measurement outcomes are determined. It states that, in the mathematical framework of quantum mechanics, the likelihood of observing a particular result can be derived from the structure of the underlying mathematical objects called "states" and "measurements." Essentially, it shows that the way we assign probabilities in quantum systems must follow a specific rule, which aligns with the standard probability rules used in quantum theory. This theorem underpins the consistency and foundation of how quantum probabilities are mathematically justified.