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A Representation of Quantum Measurement in Order-Unit Spaces

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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.

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  1. Zillertalstrasse 39, 81373, Muenchen, Germany

    Gerd Niestegge

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  1. Gerd Niestegge
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Niestegge, G. A Representation of Quantum Measurement in Order-Unit Spaces. Found Phys 38, 783–795 (2008). https://doi.org/10.1007/s10701-008-9236-y

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