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.
|Number of pages||19|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Early online date||18 Dec 2018|
|Publication status||Published - 10 Jan 2019|
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- Gleason's theorem
- postulates of quantum theory
- quantum measurement
- projective-simulable measurements
- frame functions
- quantum probability rule