Theorem of Gleason

Gleason’s theorem addresses how quantum measurements relate to the mathematical framework of quantum mechanics. It states that, for a broad class of quantum systems, the probability of observing a particular measurement outcome can be described by a specific mathematical object called a density operator. Essentially, Gleason's theorem shows that the rules for calculating probabilities in quantum mechanics naturally follow from the structure of the theory itself, without needing additional assumptions. This theorem provides a foundational justification for why quantum states are represented mathematically by density operators, ensuring consistency in the probabilistic predictions of quantum physics.