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The Correct Formulation of Gleason’s Theorem in Quaternionic Hilbert Spaces

Moretti, Valter ; Oppio, Marco



Abstract

Quantum Theories can be formulated in real, complex or quaternionic Hilbert spaces as established in Soler's theorem. Quantum states are here pictured in terms of sigma-additive probability measures over the non-Boolean lattice of orthogonal projectors of the considered Hilbert space. Gleason's theorem proves that, if the Hilbert space is either real or complex and some technical hypotheses are ...

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