Gleason-Type Theorems from Cauchy's Functional Equation
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.
- Publication:
-
Foundations of Physics
- Pub Date:
- June 2019
- DOI:
- 10.1007/s10701-019-00275-x
- 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
- E-Print:
- A corrected proof of Theorem 1 is given which closes a gap in its previous (and published) version