 As Fuchs argues, the theorem "is an extremely powerful result", because "it indicates the extent to which the Born probability rule and even the state-space structure of density operators are "dependent" upon the theory's other postulates".In consequence, quantum theory is "a tighter package than one might have first thought".Various approaches to rederiving the quantum formalism from alternative axioms have, accordingly, employed Gleason's theorem as a key step, bridging the gap between the structure of Hilbert space and the Born rule.