Foundations of Physics

, Volume 38, Issue 9, pp 783-795

First online:

A Representation of Quantum Measurement in Order-Unit Spaces

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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.


Operator algebras Jordan algebras Convex sets Quantum measurement Quantum logic