Gleason-Type Theorems from Cauchy’s Functional Equation

Victoria J Wright, Stefan Weigert

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)594-606
Number of pages13
JournalFoundations of Physics
Issue number6
Early online date4 Jun 2019
Publication statusPublished - 15 Jun 2019

Bibliographical note

Funding Information:
VJW gratefully acknowledges funding from the York Centre for Quantum Technologies and the WW Smith fund.

Publisher Copyright:
© 2019, The Author(s).


  • Axioms of quantum theory
  • Born rule
  • Density operators
  • Functional equations
  • Gleason’s theorem
  • POVMs

Cite this