Gleason's Theorem shows that the Born rule, the rule used to calculate probabilities in quantum physics, can be derived from the ordinary mathematical representation of quantum measurements together with the assumption of non-contextuality, meaning a measurement's outcome probability does not depend on which other compatible measurements are performed alongside it. Andrew Gleason first proved the theorem in 1957, answering a question posed by George Mackey, and the result proved historically significant for showing that broad classes of hidden-variable theories are inconsistent with quantum physics; it remains especially important to the field of quantum logic and its search for a minimal set of axioms for quantum theory.
Facts
StatementEvery assignment of probabilities to unit vectors of a Hilbert space of dimension 3 or greater that sums to 1 over each orthonormal basis takes the form of applying the Born rule to some density operator. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Sources
1. Gleason's theorem (Wikipedia)
Statement of the theorem, Conceptual background, final paragraph
take the form of applying the Born rule to some density operator
Introduction, sentence 2
Andrew M. Gleason first proved the theorem in 1957
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