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.
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 language | English |
|---|---|
| Pages (from-to) | 594-606 |
| Number of pages | 13 |
| Journal | Foundations of Physics |
| Volume | 49 |
| Issue number | 6 |
| Early online date | 4 Jun 2019 |
| DOIs | |
| Publication status | Published - 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).
Keywords
- Axioms of quantum theory
- Born rule
- Density operators
- Functional equations
- Gleason’s theorem
- POVMs