Foundations of Physics

, Volume 38, Issue 9, pp 783–795

A Representation of Quantum Measurement in Order-Unit Spaces

Authors

Article

DOI: 10.1007/s10701-008-9236-y

Cite this article as:
Niestegge, G. Found Phys (2008) 38: 783. doi:10.1007/s10701-008-9236-y

Abstract

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.

Keywords

Operator algebras Jordan algebras Convex sets Quantum measurement Quantum logic

Copyright information

© Springer Science+Business Media, LLC 2008