Quantum Observables and Effect Algebras

TL;DR

This paper investigates the conditions under which spectral resolutions lead to observables in monotone sigma-complete effect algebras, exploring the structure of sharp elements and compatibility in orthoalgebras.

Contribution

It establishes criteria linking spectral resolutions to observables and analyzes the structure of sharp elements and compatibility in effect algebras.

Findings

Spectral resolution implies observable existence under certain conditions.

Sharp elements form a monotone sigma-complete subalgebra.

Compatibility in orthoalgebras is characterized and studied.

Abstract

We study observables on monotone $\sigma$-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp elements of a monotone $\sigma$-complete homogeneous effect algebra is a monotone $\sigma$-complete subalgebra. In addition, we study compatibility in orthoalgebras.