English

Gleason-type Theorems from Cauchy's Functional Equation

Quantum Physics 2019-12-10 v2

Abstract

Gleason-type 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 Gleason-type theorem, based on techniques used to solve functional equations.

Cite

@article{arxiv.1905.12751,
  title  = {Gleason-type Theorems from Cauchy's Functional Equation},
  author = {Victoria J Wright and Stefan Weigert},
  journal= {arXiv preprint arXiv:1905.12751},
  year   = {2019}
}

Comments

A corrected proof of Theorem 1 is given which closes a gap in its previous (and published) version

R2 v1 2026-06-23T09:32:24.786Z