Quantum measures and the coevent interpretation

Abstract

This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)${}^2$ integrals. The rest of the paper only considers finite spaces. Anhomomorphic logics are discussed and the classical domain of a coevent is studied. Pure quantum measures and coevents are considered and it is shown that pure quantum measures are strictly contained in the extremal elements for the set of quantum measures bounded above by one. Moreover, we prove that any quantum measure on a finite event space $\ascript$ can be transferred to an ordinary measure on an anhomomorphic logic $\ascript ^*$. In this way, the quantum dynamics on $\ascript$ can be described by a classical dynamics on the larger space $\ascript ^*$.