GleasonType Theorems from Cauchy's Functional Equation
Abstract
Gleasontype theorems derive the density operator and the Born rule formalism of quantum theory from the measurement postulate, by considering additive functions which assign probabilities to measurement outcomes. Additivity is also the defining property of solutions to Cauchy's functional equation. This observation suggests an alternative proof of the strongest known Gleasontype theorem, based on techniques used to solve functional equations.
 Publication:

Foundations of Physics
 Pub Date:
 June 2019
 DOI:
 10.1007/s1070101900275x
 arXiv:
 arXiv:1905.12751
 Bibcode:
 2019FoPh...49..594W
 Keywords:

 Gleason's theorem;
 Born rule;
 POVMs;
 Functional equations;
 Density operators;
 Axioms of quantum theory;
 Quantum Physics
 EPrint:
 A corrected proof of Theorem 1 is given which closes a gap in its previous (and published) version