We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

Jan 10, 201928 citations

A Gleason-type theorem for qubits based on mixtures of projective measurements

Victoria J Wright, Stefan Weigert

Abstract We derive Born’s rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason’s theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

arXiv:1808.08091Journal of Physics A Mathematical and TheoreticalDec 18, 201818 citations